Slide, Flip, Turn: The Latest Dance Craze?


 Francis Robertson
 1 years ago
 Views:
Transcription
1 LESSON.1 Skills Practice Name Date Slide, Flip, Turn: The Latest Dance Craze? Translating, Rotating, and Reflecting Geometric Figures Problem Set Transform each given geometric figure on the coordinate plane as described. 1. Translate trapezoid BCD 11 units to the right. B 9 B9 C D D9 0 C9. Translate triangle EFG units up. 0 E F G Chapter Skills Practice 55
2 LESSON.1 Skills Practice page 3. Rotate rectangle HJKL 90 counterclockwise about the origin. H J L K 0. Rotate triangle MNP 10 counterclockwise about the origin. 0 N M P 55 Chapter Skills Practice
3 LESSON.1 Skills Practice page 3 Name Date 5. Rotate trapezoid QRST 90 counterclockwise about the origin. 0 R S Q T. Rotate parallelogram WXYZ 10 counterclockwise about the origin. X Y W 0 Z Chapter Skills Practice 559
4 LESSON.1 Skills Practice page. Reflect triangle BC over the ais. B C 0. Reflect parallelogram DEFG over the ais. 0 E F D G 50 Chapter Skills Practice
5 LESSON.1 Skills Practice page 5 Name Date 9. Reflect trapezoid HJKL over the ais. J K H L Reflect quadrilateral MNPQ over the ais. 0 N M Q P Chapter Skills Practice 51
6 LESSON.1 Skills Practice page Determine the coordinates of each translated image without graphing. 11. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Translate the triangle units to the left to form triangle B C. The vertices of triangle B C are (1, 3), B (, ), and C (10, 5). 1. The vertices of rectangle DEFG are D (, 1), E (, ), F (1, ), and G (1, 1). Translate the rectangle 10 units down to form rectangle D E F G. 13. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (, 1), and L (, ). Translate the parallelogram units up to form parallelogram H J K L. 1. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Translate the trapezoid units to the right to form trapezoid M N P Q. 15. The vertices of triangle RST are R (0, 3), S (, ), and T (3, 1). Translate the triangle 5 units to the left and 3 units up to form triangle R S T. 1. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, ). Translate the quadrilateral 5 units to the right and units down to form quadrilateral W X Y Z. Determine the coordinates of each rotated image without graphing. 1. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Rotate the triangle about the origin 90 counterclockwise to form triangle B C. The vertices of triangle B C are (3, 5), B (, ), and C (5, ). 1. The vertices of rectangle DEFG are D (, 1), E (, ), F (1, ), and G (1, 1). Rotate the rectangle about the origin 10 counterclockwise to form rectangle D E F G. 5 Chapter Skills Practice
7 LESSON.1 Skills Practice page Name Date 19. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (, 1), and L (, ). Rotate the parallelogram about the origin 90 counterclockwise to form parallelogram H J K L. 0. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Rotate the trapezoid about the origin 10 counterclockwise to form trapezoid M N P Q. 1. The vertices of triangle RST are R (0, 3), S (, ), and T (3, 1). Rotate the triangle about the origin 90 counterclockwise to form triangle R S T.. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, ). Rotate the quadrilateral about the origin 10 counterclockwise to form quadrilateral W X Y Z. Determine the coordinates of each reflected image without graphing. 3. The vertices of triangle BC are (5, 3), B (, ), and C (, 5). Reflect the triangle over the ais to form triangle B C. The vertices of triangle B C are (5, 3), B (, ), and C (, 5).. The vertices of rectangle DEFG are D (, 1), E (, ), F (1, ), and G (1, 1). Reflect the rectangle over the ais to form rectangle D E F G. 5. The vertices of parallelogram HJKL are H (, ), J (3, 1), K (, 1), and L (, ). Reflect the parallelogram over the ais to form parallelogram H J K L.. The vertices of trapezoid MNPQ are M (, 5), N (0, 5), P (1, ), and Q (, ). Reflect the trapezoid over the ais to form trapezoid M N P Q. Chapter Skills Practice 53
8 LESSON.1 Skills Practice page. The vertices of triangle RST are R (0, 3), S (, ), and T (3, 1). Reflect the triangle over the ais to form triangle R S T.. The vertices of quadrilateral WXYZ are W (10, ), X (, 1), Y (0, 0), and Z (3, ). Reflect the quadrilateral over the ais to form quadrilateral W X Y Z. 5 Chapter Skills Practice
9 LESSON. Skills Practice Name Date ll the Same to You Congruent Triangles Problem Set Identif the transformation used to create nxyz on each coordinate plane. Identif the congruent angles and the congruent sides. Then, write a triangle congruence statement. 1. Triangle BC was reflected over the ais to create triangle XYZ. BC > XY, C > YZ, and B > XZ ; /B > /X, /C > /Y, and / > /Z. B 0 X C Y nbc > nxyz Z. X Z Y 0 D E F Chapter Skills Practice 55
10 LESSON. Skills Practice page 3. P M T 0 Z X Y. B D X Z N 0 Y 5 Chapter Skills Practice
11 LESSON. Skills Practice page 3 Name Date 5. Y X Z 0 F W. Z X 0 Y Q M R Chapter Skills Practice 5
12 LESSON. Skills Practice page. Y Z N G X 0 R. Y X Z 0 W H F 5 Chapter Skills Practice
13 LESSON. Skills Practice page 5 Name Date 9. T Y Z V X M B 0 Y X Z G Chapter Skills Practice 59
14 LESSON. Skills Practice page List the corresponding sides and angles, using congruence smbols, for each pair of triangles represented b the given congruence statement. 11. njpm > ntrw JP > TR, PM > RW, and JM > TW ; /J > /T, /P > /R, and /M > /W. 1. neu > nbcd 13. nluv > nmth 1. nrwb > nvcq 15. ntom > nben 1. njkl > nrst 1. nct > nsup 1. ntop > ngun 50 Chapter Skills Practice
15 LESSON.3 Skills Practice Name Date SideSideSide SideSideSide Congruence Theorem Vocabular Define the term in our own words. 1. SideSideSide (SSS) Congruence Theorem Problem Set Determine whether each pair of given triangles are congruent b SSS. Use the Distance Formula and a protractor when necessar. 1. B 5 DE 5 3 C 5 DF 5 B d 5 ( 1 ) 1 ( 1 ) C BC 5 ( 9 ) 1 ( ) BC 5 1 (3) 0 BC F D BC 5 5 <. d 5 ( 1 ) 1 ( 1 ) E EF 5 ( 1 ) 1 ( 3 () ) EF 5 ( ) 1 3 EF EF 5 5 <. BC 5 EF The triangles are congruent b the SSS Congruence Theorem. Chapter Skills Practice 51
16 LESSON.3 Skills Practice page. J G H 0 L K M 5 Chapter Skills Practice
17 LESSON.3 Skills Practice page 3 Name Date 3. B R G 0 D M Chapter Skills Practice 53
18 LESSON.3 Skills Practice page. P M N 0 Y X Z 5 Chapter Skills Practice
19 LESSON.3 Skills Practice page 5 Name Date 5. C M W 0 Q P S Chapter Skills Practice 55
20 LESSON.3 Skills Practice page. N P Q 0 T S R 5 Chapter Skills Practice
21 LESSON.3 Skills Practice page Name Date Perform the transformation described on each given triangle. Then, verif that the triangles are congruent b SSS. Use the Distance Formula and a protractor when necessar.. Reflect nbc over the ais to form nxyz. Verif that nbc > nxyz b SSS. B 5 XY B C Z X Y BC 5 YZ 5 5 d 5 ( 1 ) 1 ( 1 ) C 5 ( (9) ) 1 ( ) C ( 1 ) C C d 5 ( 1 ) 1 ( 1 ) XZ 5 ( 9 ) 1 ( ) XZ 5 ( 5 ) 1 ( 1 ) XZ XZ C 5 XZ The triangles are congruent b the SSS Congruence Theorem. Chapter Skills Practice 5
22 LESSON.3 Skills Practice page. Rotate ndef 10 clockwise about the origin to form nqrs. Verif that ndef > nqrs b SSS. D E F 0 5 Chapter Skills Practice
23 LESSON.3 Skills Practice page 9 Name Date 9. Reflect njkl over the ais to form nmnp. Verif that njkl > nmnp b SSS. 0 J K L Chapter Skills Practice 59
24 LESSON.3 Skills Practice page Translate nhmz 10 units to the left and 1 unit down to form nbny. Verif that nhmz > nbny b SSS. H M 0 Z 50 Chapter Skills Practice
25 LESSON.3 Skills Practice page 11 Name Date 11. Rotate nfp 90 counterclockwise about the origin to form ndhw. Verif that nfp > ndhw b SSS. F 0 P Chapter Skills Practice 51
26 LESSON.3 Skills Practice page 1 1. Translate nce 3 units to the right and 9 units up to form njkq. Verif that nce > njkq b SSS. 0 C E 5 Chapter Skills Practice
27 LESSON. Skills Practice Name Date SidengleSide SidengleSide Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the SidengleSide Congruence Theorem in our answer. 1. C B 0 X Z Y Chapter Skills Practice 53
28 LESSON. Skills Practice page Problem Set Determine whether each pair of given triangles are congruent b SS. Use the Distance Formula and a protractor when necessar. 1. Determine whether nbc is congruent to ndef b SS. B 5 DE 5 5 BC 5 EF 5 m/b 5 m/e 5 90 The triangles are congruent b the SS Congruence Theorem. B C 0 F E D. Determine whether ncky is congruent to ndlz b SS. C L Z 0 Y K D 5 Chapter Skills Practice
29 LESSON. Skills Practice page 3 Name Date 3. Determine whether nfmr is congruent to njqw b SS. M F W 0 R Q J. Determine whether nqrs is congruent to nxyz b SS. Q R S 0 Y Z X Chapter Skills Practice 55
30 LESSON. Skills Practice page 5. Determine whether njkl is congruent to nmnp b SS. J K L 0 P N M 5 Chapter Skills Practice
31 LESSON. Skills Practice page 5 Name Date. Determine whether ntv is congruent to ndnp b SS. T 0 V N D P Chapter Skills Practice 5
32 LESSON. Skills Practice page Perform the transformation described on each given triangle. Then, verif that the triangles are congruent b SS. Use the Distance Formula and a protractor when necessar.. Reflect nbc over the ais to form nxyz. Verif that nbc > nxyz b SS. B 5 XY 5 5 B Y X C 5 XZ 5 5 m/ 5 m/x 5 90 The triangles are congruent b the SS Congruence Theorem. C Z 0. Translate ndef 11 units to the left and 10 units down to form nqrs. Verif that ndef > nqrs b SS. D F E 0 5 Chapter Skills Practice
33 LESSON. Skills Practice page Name Date 9. Rotate njkl 10 counterclockwise about the origin to form nmnp. Verif that njkl > nmnp b SS. 0 L J K 10. Reflect nfp over the ais to form ndhw. Verif that nfp > ndhw b SS. F 0 P Chapter Skills Practice 59
34 LESSON. Skills Practice page 11. Translate nce units to the right and units down to form njkq. Verif that nce > njkq b SS. E C Chapter Skills Practice
35 LESSON. Skills Practice page 9 Name Date 1. Rotate nbmz 90 counterclockwise about the origin to form ndrt. Verif that nbmz > ndrt b SS. B M Z 0 Chapter Skills Practice 591
36 LESSON. Skills Practice page 10 Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b SS. 13. In nrt, R 5 1, RT 5, and m/r 5 0. In nbsw, BS 5 1, and m/s 5 0. SW 5 1. In ncde, CD 5, and DE In nfgh, FG 5, GH 5 11, and m/g In njkl, JK 5, KL 5 3, and m/k 5 0. In nmnp, NP 5 3, and m/n In nqrs, QS 5, RS 5, and m/s 5 0. In ntuv, TV 5, and UV T Z 11 in. D 15 in. 15 in. B 5 11 in. W R 1. K ft T M X 0 ft L ft N 59 Chapter Skills Practice
37 LESSON. Skills Practice page 11 Name Date 19. C m O m 50 G m m T D 0. V E 35 1 ft R P 1 ft 1 ft W 35 M Chapter Skills Practice 593
38 LESSON. Skills Practice page 1 Determine whether there is enough information to prove that each pair of triangles are congruent b SSS or SS. Write the congruence statements to justif our reasoning. 1. nmnp >? npqm. nwxy >? nzyx 1 in. N 10 in. W 30 X M P ft ft 10 in. 1 in. Y 30 Z Q QM The triangles are congruent b SSS. MN > PQ NP > MP > PM 3. nbce >? ndf. nhjm >? nmkh B J K cm E F cm C H M D 59 Chapter Skills Practice
39 LESSON. Skills Practice page 13 Name Date 5. npqr >? nstw. nmt >? nmht Q S T R M T P W H. nbdw >? nbrn. nbc >? nedc 5 m D 3 m N B B C 5 m R 3 m W E D Chapter Skills Practice 595
40 59 Chapter Skills Practice
41 LESSON.5 Skills Practice Name Date You Shouldn t Make ssumptions nglesidengle Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the nglesidengle Congruence Theorem in our answer. 1. P N M 0 C B Chapter Skills Practice 59
42 LESSON.5 Skills Practice page Problem Set Determine whether each pair of given triangles are congruent b S. Use the Distance Formula and a protractor when necessar. 1. Determine whether nbc is congruent to ndef b S. B C m/b 5 m/e 5 90 m/c 5 m/f 5 5 BC 5 EF 5 5 The triangles are congruent b the S Congruence Theorem. 0 E D F. Determine whether nnpq is congruent to nrst b S. N Q P 0 S R T 59 Chapter Skills Practice
43 LESSON.5 Skills Practice page 3 Name Date 3. Determine whether ngp is congruent to nbhq b S. P G 0 Q H B. Determine whether ncky is congruent to ndlz b S. Z C K 0 Y D L Chapter Skills Practice 599
44 LESSON.5 Skills Practice page 5. Determine whether nfmr is congruent to njqw b S. M F 0 J W R Q. Determine whether nghj is congruent to nklm b S. G H L 0 J M K 00 Chapter Skills Practice
45 LESSON.5 Skills Practice page 5 Name Date Perform the transformation described on each given triangle. Then, verif that the triangles are congruent b S. Use the Distance Formula and a protractor when necessar.. Reflect nbc over the ais to form nxyz. Verif that nbc > nxyz b SS. m/c 5 m/z 5 90 m/ 5 m/x 5 3 C 5 XZ 5 3 The triangles are congruent b the S Congruence Theorem. 0 X Y Z C B. Rotate ndef 90 clockwise about the origin to form nqrs. Verif that ndef > nqrs b SS. D E F 0 Chapter Skills Practice 01
46 LESSON.5 Skills Practice page 9. Translate nhmz units to the right and 10 units up to form nbny. Verif that nhmz > nbny b S. 0 H M Z 10. Reflect nfp over the ais to form ndhw. Verif that nfp > ndhw b S. F 0 P 0 Chapter Skills Practice
47 LESSON.5 Skills Practice page Name Date 11. Rotate nce 10 counterclockwise about the origin to form njkq. Verif that nce > njkq b SS. C 0 E 1. Reflect njkl over the ais to form nmnp. Verif that njkl > nmnp b S. J K L 0 Chapter Skills Practice 03
48 LESSON.5 Skills Practice page Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b S. 13. In ndz, m/ 5 0, D 5 9, and m/d 5 0. In nben, BE 5 9, and m/e 5 0. m/b In ncup, m/u 5 5, and m/p In nht, T 5 1, m/ 5 5, and m/t In nhow, m/h 5 10, HW 5 3, and m/w 5 0. In nfr, FR 5 3, and m/f In ndry, m/d 5 100, DR 5 5, and m/r In nwet, m/w 5 100, and m/e B D W 0 ft T R ft Z 1. K M 30 in. 0 T L 30 0 X N 0 Chapter Skills Practice
49 LESSON.5 Skills Practice page 9 Name Date 19. R G F 0 1 m 1 m 0 W 0 Z S 0. 0 P T 5 in X D M Chapter Skills Practice 05
50 0 Chapter Skills Practice
51 LESSON. Skills Practice Name Date hhhhh... We re Sorr We Didn t Include You! nglengleside Congruence Theorem Vocabular Describe how to prove the given triangles are congruent. Use the nglengleside Congruence Theorem in our answer. 1. B C 0 X Z Y Chapter Skills Practice 0
52 LESSON. Skills Practice page Problem Set Determine whether each set of given triangles are congruent b S. Use the Distance Formula and a protractor when necessar. 1. Determine whether nbc is congruent to ndef b S. C B 0 D F m/ 5 m/d 5 5 m/b 5 m/e 5 5 BC 5 EF 5 The triangles are congruent b the S Congruence Theorem. E. Determine whether nghj is congruent to nklm b S. G J H 0 L M K 0 Chapter Skills Practice
53 LESSON. Skills Practice page 3 Name Date 3. Determine whether ngp is congruent to nbhq b S. G Q B 0 P H. Determine whether ncky is congruent to ndlz b S. C Y K 0 L Z D Chapter Skills Practice 09
54 LESSON. Skills Practice page 5. Determine whether nfmr is congruent to njqw b S. F M 0 W R Q J. Determine whether nnpq is congruent to nrst b S. P T N 0 R Q S 10 Chapter Skills Practice
55 LESSON. Skills Practice page 5 Name Date Perform the transformation described on each given triangle. Then, verif that the triangles are congruent b S. Use the Distance Formula and a protractor when necessar.. Reflect nbc over the ais to form nxyz. Verif that nbc > nxyz b S. m/b 5 m/y 5 X m/c 5 m/z 5 90 C 5 XZ 5 1 The triangles are congruent b the S Congruence Theorem. 0 Y Z C B. Translate ndef 11 units to the left and 11 units down to form nqrs. Verif that ndef > nqrs b S. D F 0 E Chapter Skills Practice 11
56 LESSON. Skills Practice page 9. Rotate njkl 10 counterclockwise about the origin to form nmnp. Verif that njkl > nmnp b S. 0 K L J 10. Translate ncup 9 units to the left and units up to form njr. Verif that ncup > njr b S. 0 U C P 1 Chapter Skills Practice
57 LESSON. Skills Practice page Name Date 11. Reflect nfp over the ais to form ndhw. Verif that nfp > ndhw b S. 0 F P Chapter Skills Practice 13
58 LESSON. Skills Practice page 1. Rotate nce 0 counterclockwise about the origin to form njkq. Verif that nce > njkq b S. C 0 E Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent b S. 13. In nnt, m/ 5 30, m/n 5 0, and NT 5 5. In nbug, m/u 5 0, and UG 5 5. m/b In nbcd, m/b 5 5, and m/d In nrst, RS 5 1, m/r 5 5, and m/t In nemz, m/e 5 0, EZ 5, and m/m 5 0. In ndgp, DP 5, and m/d In nbmx, m/m 5 90, BM 5 1, and m/x In ncny, m/n 5 90, and m/y Chapter Skills Practice
59 LESSON. Skills Practice page 9 Name Date 1. B D 1 in. 1 in. 0 T R 0 0 W Z 1. K 0 X 30 N T 3 ft 30 M 0 L 19. F S Z 0 50 R 50 5 m G 0 W Chapter Skills Practice 15
60 LESSON. Skills Practice page D 0 in P M 30 0 in. X T Determine whether there is enough information to prove that each pair of triangles are congruent b S or S. Write the congruence statements to justif our reasoning.? 1. nbd > ncbd?. nefg > nhjk B F J D The triangles are congruent b S. /BD > /BCD C E K G H /DB > /CDB BD > BD? 3. nmnq > npqn?. nrst > nwzt N P W M Q S R T Z 1 Chapter Skills Practice
61 LESSON. Skills Practice page 11 Name Date? 5. nbdm > nmdh?. nfgh > njhg D F J B 0 H 0 M G H?. ndfg > njmt?. nrst > nwxy D M 5 T 50 S W R ft F 5 G ft J 0 T 3 cm X 50 3 cm 0 Y Chapter Skills Practice 1
62 1 Chapter Skills Practice
63 LESSON. Skills Practice Name Date Congruent Triangles in ction Using Congruent Triangles Problem Set Construct a perpendicular bisector to each line segment. Connect points on the bisector on either side of the line segment to form the new line segment indicated. 1. MN bisected b PR at point Q P M Q N R. HJ bisected b KM at point L H J Chapter Skills Practice 19
64 LESSON. Skills Practice page 3. B bisected b CE at point D. PQ bisected b RT at point S P B Q 5. FG bisected b HK at point J. ST bisected b UW at point V F T G S 0 Chapter Skills Practice
65 LESSON. Skills Practice page 3 Name Date Use a triangle congruence theorem to complete each proof. Some of the statements and reasons are provided for ou.. Given: HK is a perpendicular bisector of FJ at point J Prove: Point H is equidistant to points F and G H F J G K 1. FG ' HK, HK bisects FG 1. Definition of perpendicular bisector. /FJH and /GJH are right angles.. Definition of perpendicular lines 3. /FJH > /GJH 3. ll right angles are congruent.. FJ > GJ 5. HJ > HJ. Definition of bisect 5. Refleive Propert. nfjh > ngjh. SS Congruence Theorem. FH > GH. Point H is equidistant to points F and G. Corresponding sides of congruent triangles are congruent. Definition of equidistant Chapter Skills Practice 1
66 LESSON. Skills Practice page. Given: PM is a perpendicular bisector of ST at point N Prove: Point M is equidistant to points S and T P S N T M Definition of perpendicular bisector.. Definition of perpendicular lines ll right angles are congruent Point M is equidistant to points S and T. Definition of equidistant Chapter Skills Practice
67 LESSON. Skills Practice page 5 Name Date 9. Given: C is a perpendicular bisector of UW at point B Prove: Point C is equidistant to points U and W U C B W 1. UW ' C, C bisects UW 1. Definition of perpendicular bisector ll right angles are congruent... Definition of bisect Corresponding sides of congruent triangles are congruent.. Chapter Skills Practice 3
68 LESSON. Skills Practice page 10. Given: TK is a perpendicular bisector of LM at point R Prove: Point T is equidistant to points L and M L T R K M Definition of perpendicular lines ll right angles are congruent TR > TR 5. Refleive Propert Definition of equidistant Chapter Skills Practice
69 LESSON. Skills Practice page Name Date 11. Given: HT is a perpendicular bisector of UV at point P Prove: Point H is equidistant to points U and V H V P T U /UPH and /VPH are right angles.. Definition of perpendicular lines Definition of bisect Chapter Skills Practice 5
70 LESSON. Skills Practice page 1. Given: UW is a perpendicular bisector of CD at point V Prove: Point U is equidistant to points C and D C U V W D Definition of perpendicular bisector.. 3. /CVU > /DVU 3. ll right angles are congruent Corresponding sides of congruent triangles are congruent.. Chapter Skills Practice
71 LESSON. Skills Practice page 9 Name Date Complete each diagram to provide a countereample that proves the indicated theorem does not work for congruent triangles. Eplain our reasoning. hint is provided in each case. 13. nglenglengle (Hint: Use vertical angles.) D C Etend C and BC, and connect points D and E so that B is parallel to DE. Since vertical angles are congruent, all three corresponding angles of the two triangles are congruent. The side lengths, however, are different, so nbc is not congruent to ndec. B E 1. SideSidengle (Hint: Draw a triangle that shares /P with the given triangle.) Q P R 15. nglenglengle (Hint: Draw a triangle that shares /T with the given triangle.) T S U Chapter Skills Practice
72 LESSON. Skills Practice page SideSidengle (Hint: Draw a triangle that shares /L with the given triangle.) L K M 1. nglenglengle (Hint: Draw a triangle that has an angle with the same measure as /E.) E D F 1. SideSidengle (Hint: Draw a triangle that shares /U with the given triangle.) T U V Chapter Skills Practice
73 LESSON. Skills Practice page 11 Name Date State the congruence theorem that proves the triangles in each diagram are congruent. If not enough information is given, name an eample of information that could be given that ou could use to prove congruenc. Eplain our reasoning. 19. Given: V W > XW W Prove: nvyw > nxyw Not enough information is given. If /VWY > /XWY is given, then nvyw > nxyw b the SS Triangle Congruence Theorem. V Y X 0. Given: CE is a perpendicular bisector of FD Prove: nfec > ndec C D E F 1. Given: /WST > /VUT, ST > UT S U Prove: nwst > nvut T W V Chapter Skills Practice 9
74 LESSON. Skills Practice page 1. Given: nbd is isosceles with B > D Prove: nbc > ndc B C D 3. Given: GH > JK, HJ > KG Prove: nghk > njkh H G J K. Given: PT > SR, /PQT > /RQS Prove: ntpq > nsrq P R T Q S 30 Chapter Skills Practice
Standardized Test A For use after Chapter 5
Standardized Test A For use after Chapter Multiple Choice. Ever triangle has? midsegments. A at least B eactl C at least D eactl. If BD, DF, and FB are midsegments of TACE, what is AF? A 0 B C 0 D 0. If
More informationSkills Practice Skills Practice for Lesson 9.1
Skills Practice Skills Practice for Lesson.1 Name Date Meeting Friends The Distance Formula Vocabular Define the term in our own words. 1. Distance Formula Problem Set Archaeologists map the location of
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'
More information12 Measuring and Constructing Segments
12 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
EOCT Practice Items 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B'
More informationName: Date: Period: 1. In the diagram below,. [G.CO.6] 2. The diagram below shows a pair of congruent triangles, with and. [G.CO.
Name: Date: Period: Directions: Read each question carefully and choose the best answer for each question. You must show LL of your work to receive credit. 1. In the diagram below,. [G.CO.6] Which statement
More informationName: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?
GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and
More informationChapter 2 Segment Measurement and Coordinate Graphing
Geometry Concepts Chapter 2 Segment Measurement and Coordinate Graphing 2.2 Find length segments (1.3) 2.3 Compare lengths of segments (1.3) 2.3 Find midpoints of segments (1.7) 2.5 Calculate coordinates
More informationThe Coordinate Plane. Circles and Polygons on the Coordinate Plane. LESSON 13.1 Skills Practice. Problem Set
LESSON.1 Skills Practice Name Date The Coordinate Plane Circles and Polgons on the Coordinate Plane Problem Set Use the given information to show that each statement is true. Justif our answers b using
More information12 Measuring and Constructing Segments
12 Measuring and Constructing Segments Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance
More information0116ge. Geometry Regents Exam RT and SU intersect at O.
Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram
More informationDEPARTMENT OF MATHEMATICS
Wynberg Boys High School DEPARTMENT OF MATHEMATICS Name: Teacher: Class: PAPER 2 GRADE 9 MATHEMATICS JUNE 2017 MARKS: 75 TIME: 1 1 2 hours EXAMINER: Mr Biggs This examination booklet consists of 12 pages.
More information9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.
3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem
More informationGeometry. Midterm Review
Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water
More information); 5 units 5. x = 3 6. r = 5 7. n = 2 8. t =
. Sample answer: dilation with center at the origin and a scale factor of 1 followed b a translation units right and 1 unit down 5. Sample answer: reflection in the axis followed b a dilation with center
More information51 Perpendicular and Angle Bisectors
51 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and
More informationGeometry Midterm REVIEW
Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw
More informationName Geometry Common Core Regents Review Packet  3. Topic 1 : Equation of a circle
Name Geometry Common Core Regents Review Packet  3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter
More informationb The ratio of a to b can also be written as a : b. Ratios are usually expressed in simplified form (lowest terms).
Chapter 8  Similarity 8.1  Ratio and Proportion  1 a 1. If a and b are two quantities measured in the same units, then the ratio of a to b is  with b + 0. b The ratio of a to b can also be written
More information9.3. Practice C For use with pages Tell whether the triangle is a right triangle.
LESSON 9.3 NAME DATE For use with pages 543 549 Tell whether the triangle is a right triangle. 1. 21 2. 3. 75 6 2 2 17 72 63 66 16 2 4. 110 5. 4.3 6. 96 2 4.4 10 3 3 4.5 Decide whether the numbers can
More informationSkills Practice Skills Practice for Lesson 11.1
Skills Practice Skills Practice for Lesson.1 Name ate Riding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. circle X T 2. center of the circle H I
More informationGeometry M1: Unit 3 Practice Exam
Class: Date: Geometry M1: Unit 3 Practice Exam Short Answer 1. What is the value of x? 2. What is the value of x? 3. What is the value of x? 1 4. Find the value of x. The diagram is not to scale. Given:
More informationALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r R e v i e w
ALLEN PARK HIGH SCHOOL i r s t S e m e s t e r R e v i e w G EOMERY APHS/MAH Winter 2010 DIRECIONS his section of test is 68 items, which you will work in this booklet. Mark the correct answer as directed
More informationExercise. and 13x. We know that, sum of angles of a quadrilateral = x = 360 x = (Common in both triangles) and AC = BD
9 Exercise 9.1 Question 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. Solution Given, the ratio of the angles of quadrilateral are 3 : 5 : 9
More informationHigher Geometry Problems
Higher Geometry Problems (1) Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More information10.3 Coordinate Proof Using Distance with Segments and Triangles
Name Class Date 10.3 Coordinate Proof Using Distance with Segments and Triangles Essential Question: How do ou write a coordinate proof? Resource Locker Eplore G..B...use the distance, slope,... formulas
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More information2. A diagonal of a parallelogram divides it into two congruent triangles. 5. Diagonals of a rectangle bisect each other and are equal and viceversa.
QURILTERLS 1. Sum of the angles of a quadrilateral is 360. 2. diagonal of a parallelogram divides it into two congruent triangles. 3. In a parallelogram, (i) opposite sides are equal (ii) opposite angles
More informationChapter 1 Line and Angle Relationships
Chapter 1 Line and Angle Relationships SECTION 1.1: Sets, Statements, and Reasoning 1. a. Not a statement. b. Statement; true c. Statement; true d. Statement; false 5. Conditional 9. Simple 13. H: The
More informationCHAPTER 5 : THE STRAIGHT LINE
EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P 4 2 4 3 2 1 0 1 2 2 2. Find (a) the intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More information2. P lies on the perpendicular bisector of RS ; Because. 168 ft. 3. P lies on the angle bisector of DEF;
9. = 9 x 9. = x 95. a. ft b. ft b ft c. 9. a. 0 ft b. ft c. hapter. Start Thinking ft ft The roof lines become steeper; The two top chords will get longer as the king post gets longer, but the two top
More informationChapter 6. WorkedOut Solutions. Chapter 6 Maintaining Mathematical Proficiency (p. 299)
hapter 6 hapter 6 Maintaining Mathematical Proficiency (p. 99) 1. Slope perpendicular to y = 1 x 5 is. y = x + b 1 = + b 1 = 9 + b 10 = b n equation of the line is y = x + 10.. Slope perpendicular to y
More information3.5. Did you ever think about street names? How does a city or town decide what to. composite figures
.5 Composite Figures on the Coordinate Plane Area and Perimeter of Composite Figures on the Coordinate Plane LEARNING GOALS In this lesson, ou will: Determine the perimeters and the areas of composite
More information1 = 1, b d and c d. Chapter 7. WorkedOut Solutions Chapter 7 Maintaining Mathematical Proficiency (p. 357) Slope of line b:
hapter 7 aintaining athematical Proficienc (p. 357) 1. (7 x) = 16 (7 x) = 16 7 x = 7 = 7 x = 3 x 1 = 3 1 x = 3. 7(1 x) + = 19 = 7(1 x) = 1 7(1 x) 7 = 1 7 1 x = 3 1 = 1 x = x 1 = 1 x = 3. 3(x 5) + 8(x 5)
More informationMultiple Choice. 3. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
Accelerated Coordinate Algebra/Analtic Geometr answers the question. Page 1 of 5 Multiple Choice 1. The dashed triangle is an image of the solid triangle. What is the scale factor of the image?. The polgons
More informationCommon Core Readiness Assessment 4
ommon ore Readiness ssessment 4 1. Use the diagram and the information given to complete the missing element of the twocolumn proof. 2. Use the diagram and the information given to complete the missing
More informationLESSON 2 5 CHAPTER 2 OBJECTIVES
LESSON 2 5 CHAPTER 2 OBJECTIVES POSTULATE a statement that describes a fundamental relationship between the basic terms of geometry. THEOREM a statement that can be proved true. PROOF a logical argument
More informationCumulative Test. 101 Holt Geometry. Name Date Class
Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst
More informationGeometry S1 (#2211) Foundations in Geometry S1 (#7771)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: Geometry S1 (#2211) Foundations
More informationGeometry: A Complete Course
Geometry: omplete ourse (with Trigonometry) Module  Student WorkText Written by: Thomas E. lark Larry E. ollins Geometry: omplete ourse (with Trigonometry) Module Student Worktext opyright 2014 by VideotextInteractive
More informationProperties of Isosceles and Equilateral Triangles
Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg
More informationGH Chapter 2 Test Reviewincludes Constructions
Name: Class: Date: Show All Work. Test will include 2 proofs from the proof practice worksheet assigned week of 9/8. GH Chapter 2 Test Reviewincludes Constructions ID: A 1. What is the value of x? State
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More information0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
More informationPreTest. Name Date. List the side lengths from shortest to longest. 3. Explain how to construct a triangle given two line segments.
PreTest Name Date List the side lengths from shortest to longest. 1. 70 a 48 b c 62 2. 122 d 30 f 28 e 3. Explain how to construct a triangle given two line segments. 4. Explain why triangles constructed
More information+2 u, 2s ) [D] ( r+ t + u, 2s )
1. Isosceles trapezoid JKLM has legs JK and LM, and base KL. If JK = 3x + 6, KL = 9x 3, and LM = 7x 9. Find the value of x. [A] 15 4 [] 3 4 [] 3 [] 3 4. Which best describes the relationship between the
More informationProperties of Triangles and FourSided Figures Lesson 13.1 Classifying Triangles
HPTR13 Properties of Triangles and oursided igures Lesson 13.1 lassifying Triangles 1. lassify the following triangles by sides as a scalene triangle, an isosceles triangle, or an equilateral triangle.
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationGeometry Arcs and Chords. Geometry Mr. Austin
10.2 Arcs and Chords Mr. Austin Objectives/Assignment Use properties of arcs of circles, as applied. Use properties of chords of circles. Assignment: pp. 607608 #347 Reminder Quiz after 10.3 and 10.5
More informationGeometry 21  More Midterm Practice
Class: Date: Geometry 21  More Midterm Practice 1. What are the names of three planes that contain point A? 6. If T is the midpoint of SU, what are ST, TU, and SU? A. ST = 7, TU = 63, and SU = 126 B.
More informationCHAPTER 4. Chapter Opener PQ (3, 3) Lesson 4.1
CHAPTER 4 Chapter Opener Chapter Readiness Quiz (p. 17) 1. D. H; PQ **** is horizontal, so subtract the xcoordinates. PQ 7 5 5. B; M 0 6, 4 (, ) Lesson 4.1 4.1 Checkpoint (pp. 17 174) 1. Because this
More information95 Holt McDougal Geometry
1. It is given that KN is the perpendicular bisector of J and N is the perpendicular bisector of K. B the Perpendicular Bisector Theorem, JK = K and K =. Thus JK = b the Trans. Prop. of =. B the definition
More informationGEO 9 CH CH ASSIGNMENT SHEET GEOMETRY Points, Lines, Planes p all,15,16,17,21,25
GEO 9 CH12.2 1 CH 12.2 ASSIGNMENT SHEET GEOMETRY 9 DAY SECTION NAME PAGE ASSIGNMENT 1 Algebra Review/Assignment #1 Handout 2 Algebra Review/Assignment #2 Handout 3 1.2 Points, Lines, Planes p. 78 110
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More information4) Find the value of the variable and YZ if Y is between X and Z. XY = 2c +1, YZ = 6c, XZ = 9c 1 6(2) 12 YZ YZ
PreAP Geometry 1 st Semester Exam Study Guide 1) Name the intersection of plane DAG and plane ABD. (left side and back) AD ) Name the intersection of HI and FJ E 3) Describe the relationship between the
More informationGEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?
GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)
More information55 The Triangle Inequality
Is it possible to form a triangle with the given side lengths? If not, explain why not. 1. 5 cm, 7 cm, 10 cm Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5 3. 6 m, 14 m, 10 m Yes; 6 + 14 > 10, 6 + 10 > 14,
More informationQuads. 4. In the accompanying figure, ABCD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x.
Name: Date: 1. In the accompanying diagram of rhombus ACD, the lengths of the sides A and C are represented by 3x 4 and 2x + 1, respectively. Find the value of x. 4. In the accompanying figure, ACD is
More information103 Arcs and Chords. ALGEBRA Find the value of x.
ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.
More informationTest Review: Geometry I Period 3,5,7. ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know:
Test Review: Geometry I Period 3,5,7 ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know: 1) How to create proportions from a. a word problem b. a pair of similar triangles
More informationProperties of Triangles and FourSided Figures Lesson 13.1 Classifying Triangles
HPT13 Properties of Triangles and oursided igures Lesson 13.1 lassifying Triangles 1. lassify the following triangles by sides as a scalene triangle, an isosceles triangle, or an equilateral triangle.
More informationEOC Review MC Questions
Geometry EOC Review MC Questions Name Date Block You must show all work to receive full credit.  For every 5 answers that are correct, you may receive 5 extra points in the quiz category for a total of
More informationJEFFERSON MATH PROJECT REGENTS AT RANDOM
JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008August 2009 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished
More informationGeometry CP Semester 1 Review Packet. answers_december_2012.pdf
Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet
More informationReteaching , or 37.5% 360. Geometric Probability. Name Date Class
Name ate lass Reteaching Geometric Probability INV 6 You have calculated probabilities of events that occur when coins are tossed and number cubes are rolled. Now you will learn about geometric probability.
More informationChapter 2. WorkedOut Solutions Quiz (p. 90)
2.1 2.3 Quiz (p. 90) 1. Ifthen form: If an angle measures 167, then the angle is an obtuse angle. (True) Converse: If an angle is obtuse, then the angle measures 167. (False) Inverse: If an angle does
More informationChallenge: Skills and Applications For use with pages P( 1, 4) R( 3, 1)
LESSON 8.4 NME TE hallenge: Skills and pplications For use with pages 480 487 1. Refer to the diagram, where VW YZ. a. Write a similarit statement. b. Write a paragraph proof for our result. V X Y W Z.
More informationAnswers. Chapter10 A Start Thinking. and 4 2. Sample answer: no; It does not pass through the center.
hapter10 10.1 Start Thinking 6. no; is not a right triangle because the side lengths do not satisf the Pthagorean Theorem (Thm. 9.1). 1. (3, ) 7. es; is a right triangle because the side lengths satisf
More informationChapter (Circle) * Circle  circle is locus of such points which are at equidistant from a fixed point in
Chapter  10 (Circle) Key Concept * Circle  circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle  Circle having same centre called concentric circle.
More informationTest Corrections for Unit 1 Test
MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are
More informationTransforming to a New Level!
LESSON.1 Skills Practice Name Date Transforming to a New Level! Using Transformations to Determine Area Problem Set Translate each given rectangle or square such that one verte of the image is located
More informationiii (a, c), (a, e), (c, e), (b, d), (b, f), (d, f), (l, h), (l, j), (h, j), (g, i), (g, k), (i, k)
Cambridge Essentials Mathematics Core 8 GM1.1 Answers GM1.1 Answers 1 a There is more than one valid reason for each statement; those given are the simplest. i Corresponding angles ii Vertically opposite
More informationSample Copyright. Academic Group. 15 Geometric Proofs using Vectors. Calculator Assumed. 1. [6 marks: 2, 2, 2,]
alculator ssumed 1. [6 marks: 2, 2, 2,] Given that a and b are nonparallel vectors. Find α and β if: (a) 2a + (β 2) b = (1 α) a (b) α (3a 4b) = 6a + βb (c) αa + 5b is parallel to 3a + βb 2. [4 marks:
More informationPreTest. Use the following figure to answer Questions 1 through 6. B C. 1. What is the center of the circle? The center of the circle is point G.
PreTest Name Date Use the following figure to answer Questions 1 through 6. A B C F G E D 1. What is the center of the circle? The center of the circle is point G. 2. Name a radius of the circle. A radius
More information6.2: Isosceles Triangles
6.2: Isosceles Triangles Dec 5 4:34 PM 1 Define an Isosceles Triangle. A triangle that has (at least) two sides of equal length. Dec 5 4:34 PM 2 Draw an Isosceles Triangle. Label all parts and mark the
More informationGeometry Advanced Fall Semester Exam Review Packet  CHAPTER 1
Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet  CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)
More information13.3 Special Right Triangles
Name lass ate. Special Right Triangles Essential Question: What do you know about the side lengths and the trigonometric ratios in special right triangles? Eplore Investigating an Isosceles Right Triangle
More informationGEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity
GEOMETRY Teacher: Mrs. Flynn Topic: Similarity Name: Date: Teacher: Mrs. Flynn Topic: Similarity 1. A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find
More informationEC and AB because AIA are congruent Substituting into the first equation above
4.1 Triangles Sum onjectures uxillary line: an extra line or segment that helps you with your proof. Page 202 Paragraph proof explaining why the Triangle Sum onjecture is true. onjecture: The sum of the
More informationRiding a Ferris Wheel
Lesson.1 Skills Practice Name ate iding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. center of the circle 6. central angle T H I 2. chord 7. inscribed
More informationA Little Dash of Logic
Lesson. Skills Practice Name Date A Little Dash of Logic Foundations for Proof Vocabulary Define each term in your own words.. induction. deduction. counterexample 4. conditional statement 5. propositional
More informationMaharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40
Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note: () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.
More information) = (3.5, 3) 53. check it out!
44. Let be the irumenter of the. Given: = m; so by the properties of 69,. So = + = _ 5 = _ () = 4 m. medians and altitudes of Triangles hek it out! 1a. KZ + ZW = KW _ KW + ZW = KW ZW KW 7 KW 1 = KW
More informationEssential Question How can you prove a mathematical statement?
.5 TEXS ESSENTIL KNOWLEDGE ND SKILLS Preparing for G.6. G.6. G.6.D G.6.E RESONING To be proficient in math, you need to know and be able to use algebraic properties. Proving Statements about Segments and
More informationVerifying Properties of Quadrilaterals
Verifing roperties of uadrilaterals We can use the tools we have developed to find, classif, or verif properties of various shapes made b plotting coordinates on a Cartesian plane. Depending on the problem,
More informationNAME DATE PERIOD. Study Guide and Intervention
71 tudy Guide and Intervention atios and Proportions Write and Use atios ratio is a comparison of two quantities by divisions. The ratio a to b, where b is not zero, can be written as a b or a:b. ample
More information(Chapter 10) (Practical Geometry) (Class VII) Question 1: Exercise 10.1 Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only. Answer 1: To
More informationCONGRUENCE OF TRIANGLES
Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationGM1.1 Answers. Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.
Cambridge Essentials Mathematics Extension 8 GM1.1 Answers GM1.1 Answers Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.
More informationGeometry Arcs and Chords. Geometry Mr. Peebles Spring 2013
10.2 Arcs and Chords Geometry Mr. Peebles Spring 2013 Bell Ringer: Solve For r. B 16 ft. A r r 8 ft. C Bell Ringer B 16 ft. Answer A r r 8 ft. C c 2 = a 2 + b 2 Pythagorean Thm. (r + 8) 2 = r 2 + 16 2
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C'
More informationTheorems on Area. Introduction Axioms of Area. Congruence area axiom. Addition area axiom
3 Theorems on rea Introduction We know that Geometry originated from the need of measuring land or recasting/refixing its boundaries in the process of distribution of certain land or field among different
More informationGeometry  Review for Final Chapters 5 and 6
Class: Date: Geometry  Review for Final Chapters 5 and 6 1. Classify PQR by its sides. Then determine whether it is a right triangle. a. scalene ; right c. scalene ; not right b. isoceles ; not right
More informationChapter 5: Properties and Attributes of Triangles Review Packet
Geometry B Name: Date: Block: Chapter 5: Properties and Attributes of Triangles Review Packet All work must be shown to receive full credit. Define the following terms: 1. altitude of a triangle 2. centroid
More informationTriangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.
Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?
More informationLESSON 7.1 FACTORING POLYNOMIALS I
LESSON 7.1 FACTORING POLYNOMIALS I LESSON 7.1 FACTORING POLYNOMIALS I 293 OVERVIEW Here s what you ll learn in this lesson: Greatest Common Factor a. Finding the greatest common factor (GCF) of a set of
More information