CHAPTER 7. Chapter Opener. m 10. Lesson x x 24 3x 24 x 8 EF 2x ; FG x ft

Transcription

1 HAPTER 7 hapter Opener hapter Readiness Quiz (p. 35).. G; B; Lesson heckpoint (pp ). EF FG EG EF 8 ; FG 8. l 4, w 3 l w P (4) (3) l feet; w feet m (m ) m m 50 m 5 in.. in. in mi mi 8 0 mi mi The distance between The distance between El Paso and Amarillo Houston and Austin is is about 30 miles. about 4 miles. 7. Guided Practice (p. 3). Sample answer: The teacher-pupil ratio at the elementar school is to 9.. The means are b and 3; the etremes are a and m 0 m pencils pencils ears 5. months 8 months 8 months 4 months 8 months d. 3 ft ft ft ft ft FG GH FH FG ; GH l, w l w 7 () () l 4.5 9; w t t t 5 t Geometr, oncepts and Skills 0

2 ( ) Practice and Applications (pp. 3 33) wins 3. 8 l osses 8 4 wins numbe r of meets l oss wi es ns losses. numb er of meets l l b b in in mi 3 5 mi das das das 0. 4 weeks 4 7 das 8 das ft. 3 in. in. in. 3 in. 3 3 in. d. 3 0 ft 0 ft ft 8 ft ft cm 0 cm 0 cm m 00 cm 00 cm m 400 m m km m 500 m l eng wid th th 0 mm mm 4 4. l eng wid th th 7 cm cm l ength ft in. 4 in 4 width in. in. in. AB 8. D 3 9. B D 7 F 7 BF F 7 A D 9 AB 3. FG GH FH 33. JK KL JL FG 3; JK ; GH KL 34. MN NP MP MN ; NP l w 0 (4) () l inches; w inches 3. 5 l w 84 (5) () l ft; w ft l w 3 (8) (3) l meters; w meters 0 Geometr, oncepts and Skills

3 a 5 5 a 30 a 5 a z 4. b z 4 3 b z 44 5b 80 z b 5 4. r s (r 7) (s ) 5r s 5r 35 s 8 r 9 s t (t 8) (5 3) 90 3t t t , ft in. 440 in. ft 35 in. 35 in ft 9 ft 0 ft 3.5 ft ` The diameter of Babe The diameter of the Ruth s bat near the handle of Babe Ruth s base is about. inches. bat is about.0 inches. in. 50. in. in in. 0 mi mi 0 mi mi The distance between The distance between harlotte and Durham Shelb and Elizabeth is about 0 miles. it is about 300 miles. in in. in in. 0 mi mi 0 mi mi The distance between The distance between Elizabeth it and Asheville and Shelb is Asheville is about 30 about 0 miles. miles. 7. Standardized Test Practice (p. 33) 54. B; l, w 5 l w 88 () (5) l 4 4 w H; ( 7) Mied Review (p. 33) 5. aq ab 57. a ap 58. **** AB **& RQ 59. Yes; the polgon has five sides, so it is a pentagon. 0. No; the sides are not segments.. Yes; the polgon has eight sides, so it is an octagon. 7. Algebra Skills (p. 33) Lesson Activit (p. 34) Measurement Photo Photo Ratio AB cm 5 cm. AF 4 cm 3.3 cm. D.5 cm. cm. ma ma Geometr, oncepts and Skills 03

4 . When a figure is enlarged, corresponding lengths have the same ratio.. When a figure is enlarged, corresponding angles have the same measure cm 7. heckpoint (pp. 3 38). Yes; from the diagram, ax ad, ay ae, and az af. Also, E D YX , E F YZ 8 8 3, and F D ZX B definition, T EDF T YXZ. The scale factor of Figure B to Figure A is 3. TU. No; P Q U V RQ The corresponding side lengths are not proportional 5 3. PR PQ 3. S U ST ST TU US ST 7 4. P Q QR RP P Q Guided Practice (p. 38). Yes; congruent triangles have congruent corresponding angles and corresponding side lengths have the ratio :.. No; two similar triangles are congruent onl if their scale factor is :. 3. aa al, ab am, a an AB B 4. M A L M N NL 5. L M AB B. A M N LN SR 7 7. No; J H 5 QR 4 G H The corresponding side lengths are not proportional Practice and Applications (pp ) 8. ap ad, aq ae, ar af; P Q Q R RP DE EF F D 9. aa aq, ab ar, a as, ad at, ae au; AB B D DE EA Q R RS ST TU U Q 0. F J K G af aj, ag ak, ah al; F G GH H F JK KL LJ. Yes; from the diagram, ag ad, aj af, and ah ae. Also, ED H G , D F 9 GJ 9 3 3, and 3 4 F E 8 JH B definition, T DEF T GHJ. The scale factor of Figure B to Figure A is Yes; from the diagram, ap ak, am al, and an aj. Also, KJ P N, JL N M , and LK 0 P M B definition, T KJL T PNM. The scale factor of Figure B to Figure A is. H L 04 Geometr, oncepts and Skills

5 3. Yes; from the diagram, all the angles are right angles, so the are all congruent. Also, H G 5 ML 4 and F G 5 KL 4. B definition, JKLM EFGH. The scale factor of Figure B to Figure A is No; from the diagram, av az, as aw, at ax, and au ay. However, W X 7 and ST 0 XY U T 8 3. The corresponding side lengths are not 4 proportional No; from the diagram, all the angles are right angles, so the are all congruent. However, H G 3 and UV 4 FG 4 W V. The corresponding side lengths are not 3 proportional Yes; from the diagram, ar ay, at ax, and as az. Also, RS Y Z , ST Z X , and T R 8 XY B the definition, T RTS T YXZ. The scale factor of Figure B to Figure A is 3. JK 7. P R LK HJ 8. H G QR E D EF ; 4 ; JL P Q LK GJ HG QR F D EF JK 9. M L LM 0. N P RQ G H P N KJ ; ; JK JM LM LP N P N R G H G K in in. in in.; ft 9 in. ft ft 4 in. in. 3 ft 73.5 in. in. 8 ft ft in.. man maj maf mak F G JH KL N M 5. FJ JH KN N M KL LM MN NK. N M 8 HJ 8 3 FG GH HJ JF perimeter T XYZ 7. p erimeter T QRS 7 8. p erimeter T STU ST perimeter T JKL J K The perimeter of T JKL is 4 feet. standard definition length 4 9. No; and high definition length 4 standard definition width high definition width The corresponding lengths and widths are not proportional 4 3. Geometr, oncepts and Skills 05

6 30. Two isosceles triangles are sometimes similar. 3. Two rhombuses are sometimes similar. 3. Two equilateral triangles are alwas similar. 33. A right and an isosceles triangle are sometimes similar. 7. Standardized Test Practice (p. 37) 34. B; ap af and ad am. 7. Mied Review (p. 37) 35. es; ASA ongruence Postulate 3. No; the congruent angles are not included b the congruent sides. 37. Yes; HL ongruence Theorem or AAS ongruence Theorem. 7. Algebra Skills (p. 37) 38. Sample answer: , Sample answer: , Sample answer: , Sample answer: , Lesson Geo-Activit (p. 37) Step 3. es Step 4. Answers will var. Step 5. Yes; the corresponding angles are congruent, and the corresponding sides are proportional. 7.3 heckpoint (pp ). Yes; ar am and mas maN, so as an. T RST T MNL b the AA Similarit Postulate.. Yes; aghl agjk and ag ag (Refleive Propert of ongruence), so T GHL T GJK b the AA Similarit Postulate. 3. aa ad and ab ae, so T AB T DEF b the AA Similarit Postulate; AB B D E E F Geometr, oncepts and Skills 4. ad a and aabd aeb (Vertical angles are congruent.), so T ABD T EB b the AA Similarit Postulate; A B A D EB E z z z 3 z Guided Practice (p. 375). If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.. No; onl one pair of angles is congruent. 3. Yes; ad ag and af ah, so T DEF T GJH b the AA Similarit Postulate. 4. Yes; al ap and almk apmn (Vertical Angles Theorem), so T LMK T PMN b the AA Similarit Postulate. 5. Yes; arqt asqu (Refleive Propert of ongruence) and aqrt aqsu (All right angles are congruent.), so T QRT T QSU b the AA Similarit Postulate.. ah ak and ahjg aklj, so T HJG T KLJ b the AA Similarit Postulate; HJ G J K L JL Practice and Applications (pp ) 7. No; onl one pair of angles is congruent. 8. No; onl one pair of angles is congruent. 9. Yes; ab ae and a af (ma maF), so T AB T DEF. 0. Yes; ah am (All right angles are congruent.) and aj al (mal 90358maJ), so T GJH T KLM.. Yes; ax ag and ay af (maf maY), so T XYZ T GFH.. Yes; al am and amjn aljk (Vertical Angles Theorem), so T MJN T LJK. 3. Yes; as awvu and avuw asut (Refleive Propert of ongruence), so T VUW T SUT b the AA Similarit Postulate.

7 4. No; onl one pair of angles is congruent. 5. Yes; Sample answer: Because DE **** **** BA, corresponding angles are congruent, so ade aba and aed aab. So, T DE T BA b the AA Similarit Postulate.. T PQR T LMN 7. L M PQ M N 8. 5 QR M N 5 QR The scale factor of T LMN to T PQR is p z p z 8p z 4 p 3 z a a a 4 4 a p p 40 p 0 p 7. True; the right angles are congruent to each other and so are the acute angles. So, b the AA Similarit Postulate, the triangles are similar. 8. False; all equilateral triangles have three 0 angles. So, b the AA Similarit Postulate, the are all similar. 9. True; all isosceles triangles with a verte angle of 40 have two base angles with measures of ft ft 3. T ABE T DE 00 ft ft AB AE BE D E D E Meredith is right; maab , so aab aade; aa aa b the Refleive Propert of ongruence, so T AB T AED b the AA Similarit Postulate. 7.3 Standardized Test Practice (p. 377) 38. a.julia and the flagpole are both perpendicular to the ground, and the overlapping triangles share a common angle. Therefore, the overlapping triangles are similar b the AA Similarit Postulate. b c feet 7.3 Mied Review (p. 378) 39. maf mar mat GH **& ST **** 4. T TSR T HGF Geometr, oncepts and Skills 07

8 7.3 Algebra Skills (p. 378) G Quiz (p. 378) z (z 3) 8 5 z z 0 30 z z 0 z 5 8 0z 00 z 0 7. Yes; maa maf, so aa af and ab ag. So, T AB T FGH b the AA Similarit Postulate. 8. Yes; maj mar, so aj ar and ak ap. So, T JKL T RPQ b the AA Similarit Postulate. 9. Yes; vertical angles are congruent, so asut awuv; also at av, so T STU T WVU b the AA Similarit Postulate. Lesson 7.4 A K B D 7.4 heckpoint (pp ) AB. shortest sides: 3 D F 8 A longest sides: 8 D E 3 remaining sides: B E 5 FE 0 3 Because the ratios are equal, T AB T DFE. F J. shortest sides: K L 5 ST 9 JL longest sides: 3 R T 5 remaining sides: J K RS Because the ratios are not equal, T JKL and T RST are not similar. 3. No; ah and am both measure 90, so ah am. However, the lengths of the sides that include ah and a M are not proportional. shorter sides: G H 8 LM 4 3 H longer sides: J M N Yes; b the Refleive Propert of ongruence, ap ap; the lengths of the sides that include ap are proportional. shorter sides: P Q 3 PS longer sides: P R 5 PT 0 So, T PQR T PST b the SAS Similarit Theorem. 7.4 Guided Practice (p. 38). No; to conclude that the triangles are similar, ou must also know that the included angles are congruent. A 8. shortest sides: F G 4 AB longest sides: F H 8 A 8 remaining sides: F G 4 Because the ratios are equal, T AB T FHG b the SSS Similarit Theorem. 3. No; ad and ar both measure 84, so ad ar. However, the lengths of the sides that include ad and a R are not proportional. shorter sides: D E 8 RS 4 3 longer sides: D F 0 5 RT 8 4 AB 4. shortest sides: L M 4 3, A B XY B longest sides: 3 M N 8, B YZ 3 4 remaining sides: A 9 LN 7, A 9 XZ 3 4 T LMN is not similar to T AB because the ratios of corresponding sides are not equal. T AB T XYZ b the SSS Similarit Theorem because the ratios of corresponding sides are all equal to Geometr, oncepts and Skills

9 7.4 Practice and Applications (pp ) GF 5. shortest sides: D 9 3 longest sides: F H 0 E 5 3 remaining sides: G H DE 8 3 Because the ratios are equal, T GFH T DE; the scale factor of Triangle B to Triangle A is 3.. shortest sides: P Q JK longest sides: P R 0 JL remaining sides: Q R KL Because the ratios are equal, T PQR T JKL; the scale factor of Triangle B to Triangle A is shortest sides: W V 5 PQ 4 VX longest sides: Q R 5 remaining sides: W X 5 PR 4 T PQR is not similar to T WVX because the ratios of corresponding sides are not equal. TS 8. shortest sides: 5 M P 8 5 RT longest sides: 3 0 N M 3 5 R remaining sides: S N P Because the ratios are equal, T RTS T NMP; the scale factor of Triangle B to Triangle A is shortest sides: G H 3 VW 8 GJ longest sides: V U 4 3 HJ remaining sides: 8 W U 3 Because the ratios are equal, T GHJ T VWU; the scale factor of Triangle B to Triangle A is 3. HJ 0. shortest sides: 8 Z X 4 3 JK longest sides: 4 X Y remaining sides: K H 4 YZ 9 3 T HJK is not similar to T ZXY because the ratios of corresponding sides are not equal.. shortest sides: A B RS 4, A B YX 3 longest sides: A RT 8, A XZ 5 remaining sides: B ST 8 3 4, B YZ 4 3 T RST is not similar to T AB because the ratios of corresponding sides are not equal. T AB T XYZ b the SSS Similarit Theorem because the ratios of corresponding sides are all equal to 3.. shortest sides: B ST 4 3, B YZ longest sides: A 0 RT 5, A 0 XZ 5 5 remaining sides: A B 8 RS 0 4 5, A B XY 80 5 T RST is not similar to T AB because the ratios of corresponding sides are not equal. T AB T XYZ b the SSS Similarit Theorem because the ratios of corresponding sides are all equal to shortest sides: A B 8 RS 9, A B 8 XY longest sides: A 3 3 RT 40, A 3 3 XZ remaining sides: B ST , B YZ T RST is not similar to T AB because the ratios of corresponding sides are not equal. T AB T XYZ b the SSS Similarit Theorem because the ratios of corresponding sides are all equal to Yes; the peak angles both measure 0, so the are congruent; both sides 3 0 ft 5 ; the lengths of the 34 ft 7 sides that include the peak angles are proportional, so the triangles are similar b the SAS Similarit Theorem. 5. Yes; aa and ad both measure 50, so aa ad; also, the lengths of the sides that include aa and ad are proportional. A shorter sides: D E 9 3 AB 8 longer sides: D F 3 So, T AB T DFE b the SAS Similarit Theorem.. Yes; ah ax; also the lengths of the sides that include ah and ax are proportional. shorter sides: H G XZ HJ longer sides: X Y 3 So, T HGJ T XZY b the SAS Similarit Theorem. Geometr, oncepts and Skills 09

10 7. No; a aj, however, the lengths of the sides that include a and aj are not proportional. shorter sides: A JK longer sides: B JL So, T AB is not similar to T KJL. 8. Yes; vertical angles are congruent, so amdn afde; also, the lengths of the sides that include amdn and a FDE are proportional. shorter sides: N D 5 ED 8 5 longer sides: M D 5 FD 30 5 So, T MDN T FDE b the SAS Similarit Theorem. 9. aa aa; also, the lengths of the sides that include aa are proportional. AE shorter sides: A longer sides: A D 9 AB So, T AED T AB b the SAS Similarit Theorem. 0. aj aj; also, the lengths of the sides that include aj are proportional. shorter sides: J M JK longer sides: J N JL So, T JMN T JKL b the SAS Similarit Theorem. JK. shortest sides: 8 7 X Y 8 JL longest sides: 3 5 X Z 0 7 remaining sides: L K ZY Because the ratios are equal, T JLK T XZY b the SSS Similarit Theorem.. mag maL, so ag al and aj am. T GHJ T LKM b the AA Similarit Postulate. 3. at ap; however, the lengths of the sides that include at and ap are not proportional. ST shorter sides: 3 N P 4 RT longer sides: 5 Q P So, T STR is not similar to T NPQ. AB 4. shortest sides: 8 U V longest sides: B 3 VT remaining sides: A 0 UT Because the ratios are not equal, T AB and T UVT are not similar. 5. ap ad; also, the lengths of the sides that include ap and ad are proportional. shorter sides: P Q 4 DE 0 5 PR longer sides: 3 0 D F 5 5 So, T PQR T DEF b the SAS Similarit Theorem.. aw aw b the Refleive Propert of ongruence and axpw ayzw b the orresponding Angles Postulate, so T XWP T YWZ b the AA Similarit Postulate. AE 7. You need to know that A A D A D E. B B 8. You need to know that the angles included b the proportional sides are congruent. So, aade aab. 9. When, S U SR and S V ST 7 9. When 5, S U SR and S V ST 5. Jon is right because the lengths of the sides that include as are proportional when, so T SUV T SRT b the SAS Similarit Theorem. 30. maab SAS Similarit Theorem 7.4 Standardized Test Practice (p. 385) G; N M SR P N TS Mied Review (p. 385) 34. ST **** UT *& 35. avtu avts 3. mastu mastv mavtu Yes; Sample answer: TV&*( bisects astu, so astv autv; atsv atuv and TV **** TV ****, so T STV T UTV b the AAS ongruence Theorem; corresponding parts of congruent triangles are congruent, so atvs atvu. 0 Geometr, oncepts and Skills

11 38. b b b 0 4 b c a c 5 a c 5a 0 35 c a Algebra Skills (p. 385) Lesson Geo-Activit (p. 38) Step 3. Measures will var, but B D BE. DA E Step 4. When a line parallel to one side of a triangle cuts the other two sides, the ratios of the segment lengths of the divided sides are equal. 7.5 heckpoint (pp ) (4 ) No; P R 5 RT 5 7 and P Q 7 QS , so QR **& is not parallel to ST 3 ****. 4. Yes; P Q 4 QS 8 and P R RT. QR **& **** ST b the onverse of the Triangle Proportionalit Theorem. 5. p () 8. 4 q 8 q 7. AB 3 3, A 4 4 8, and B 5 0; AB A B Guided Practice (p. 390). The onverse of the Triangle Proportionalit Theorem states that if a line divides two sides of a triangle proportionall, then it is parallel to the third side.. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. 3. A D AE 4. B D E DB E DA E A 5. A D AE. B D E AB A BA A z 8 z 7.5 Practice and Applications (pp ) 0. 3 m m 7 3m 4 m. t t t t r r r 9 3 r p 7 5 p p p Geometr, oncepts and Skills

12 5 q c c q 0 c (4 c) 0 5q 0c 88 c 8 q 3c 88 c 9 z z 3 z 3 (55 z) 3z 0 z 44z 0 z 5 0. Yes; R Q 4 QP 4 and R S 8 ST 4. QS **** **** PT b the onverse of the Proportionalit Theorem.. Yes; R S.5 5 ST 5 and R Q 0 5 QP 4. QS **** **** PT b the onverse of the Proportionalit Theorem.. No; R S 5 ST 34 and R Q QP 35. 5, so QS **** is not parallel to **** PT Yes; R Q 4 QP 9 3 and R S 0 ST QS **** **** PT b the onverse of the Proportionalit Theorem. 4. (4) 5. a. b (8) 9 a 7. 5 c 8. () 0 c 9. z (7) The length of each midsegment is () 8. The perimeter of the dark blue triangle is 3(8) The length of each midsegment of the small dark blue triangles is (8) 4. The perimeter of each small triangle is 3(4). There are 3 small and large dark blue triangles in stage so the total perimeter is 3() (4) The length of each midsegment of the smallest triangles is (4). The perimeter of each of the smallest triangles is 3(). There are 9 of these triangles, so the total perimeter of the smallest triangles is 9() 54. Add our answer from Eercise 3 to this to find the total perimeter of all the dark blue triangles in stage 3. So, the total perimeter is **& LM B **** 34. AB **** **& MN 35. If A 5, then LN (5) If MN 7.4, then AB (7.4) If N 9.5, then LM B ( ) (9) The ratios remain equal. 39. If a ra bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. 7.5 Standardized Test Practice (p. 39) A; Mied Review (p. 39) 4. es; 4. no 43. es; 7.5 Algebra Skills (p. 39) 44. slope 45. slope slope 47. slope (5) slope undefined 0 4 (4) slope Geometr, oncepts and Skills

13 50. slope 5. slope 3 5 (4) slope ( 3) 7 9 Lesson Geo-Activit (p. 393) Step 5. P R PR, R Q RQ, and Q P Q P ; b the SSS Similarit Theorem, T PQR T PQR. Step. The scale factor of T PQR to T PQR is, which is the same as the ratio P. P 7. heckpoint (p. 395). The dilation is an enlargement because the image is larger than the original figure; scale factor P P The dilation is a reduction because the image is smaller than the original figure; scale factor P 8 P The dilation is a reduction because the image is smaller than the original figure; scale factor P 3 P m 5. 3 n 4 8 m n 8m 40 n m 5 n 7. Guided Practice (p. 39). In a dilation, ever image is similar to the original figure. P. Katie found P 4 instead of P P The dilation is an enlargement because the red image is larger than the blue original figure. 4. The dilation is a reduction because the image (PQRS) is smaller than the original figure (PQRS). 5. The dilation is an enlargement because the image (T XYZ) is larger than the original figure (T XYZ). 7. Practice and Applications (pp ). The dilation is a reduction because the image is smaller than the original figure; scale factor P P The dilation is an enlargement because the image is larger than the original figure; scale factor P P The dilation is a reduction because the image is smaller than the original figure; scale factor P P The dilation is an enlargement because the image is larger than the original figure; scale factor P P Sample answer: H H. The dilation is an enlargement because the red figure (image) is larger than the blue figure; The dilation is an enlargement because the red figure (image) is larger than the blue figure; 4 8 n 4 8 n 8 8n n 3. The dilation is a reduction because the red figure (image) is smaller than the blue figure; E E G G F 4. The dilation is a reduction because the red figure (image) is smaller than the blue figure; 4 7 m m 7 7m m F Geometr, oncepts and Skills 3

14 0 cm 5. scale factor 4. 5 cm. h h.5 0.5h 8 cm h 7. Standardized Test Practice (p. 397) 7. ; M L ML % 7. Mied Review (p. 398) 8. ma ma 4980 ma 3 9. ma ma 3380 ma ma d 7 8 d 8 7 8d 84 d t 3 35( ) (t 3) t t 5 t 7. Algebra Skills (p. 398) 4. 8 (3) (3) ( )( 5) (3 )(3 5) ()(8) (5) (3) 3 (7) (3) 3(3) 4(9) Quiz (p. 398). Yes; aa af; also, the lengths of the sides that include aa and af are proportional. shorter sides: longer sides: So, T AB T FGH b the SAS Similarit Theorem. 4. shortest sides: 3 longest sides: remaining sides: 4 3 Because the ratios are equal, T JKL T PQR b the SSS Similarit Theorem JK HG 5. ST PQ (3) 8 (z) 44 z. The dilation is an enlargement because the image is larger than the original figure; scale factor P P The dilation is a reduction because the image is smaller than the original figure; scale factor H H Technolog Activit (p. 399). The image of each point (, ) is the point (0.5, 0.5).. For a dilation with center at (0, 0) and scale factor k, the image of point P(, ) is the point P(k, k). 3. The coordinates of the vertices of the image are X(3, 9), Y(, ), and Z(0, 3). hapter 7 Summar and Review (pp ) f h. In the proportion, g and h are the means, g j and f and j are the etremes.. An equation that states that two ratios are equal is a proportion. 3. The ratio of the lengths of two corresponding sides of two similar polgons is called the scale factor. 4. Two polgons are similar if corresponding angles are congruent and corresponding sides are proportional. 4 Geometr, oncepts and Skills

15 5. A segment that connects the midpoints of two sides of a triangle is called the midsegment.. A dilation is a transformation that maps a figure onto a similar figure. 7. If the image of a dilation is larger than the original figure, then the dilation is an enlargement s s s 8 s z (z ) ( 4)(5) z z 5 00 z 0 A AB. F 3. M L KL F H G SR Q R 0 5 z 35 0 z z z Q R QS AB A Yes; astp aqrp and ap ap (Refleive Propert of ongruence), so T SPT T QPR b the AA Similarit Postulate.. The triangles are not similar because onl one pair of angles is congruent. 7. Yes; ab af (All right angles are congruent.) and maa mad so aa ad. T AB T DFE b the AA Similarit Postulate. 8. Yes; au ax; also, the lengths of the sides that include au and ax are proportional. UT shorter sides: X W 4 3 longer sides: S U VX So, T SUT T VXW b the SAS Similarit Theorem. 9. Yes; b the Vertical Angles Theorem, arsq atsu; also, the lengths of the sides that include arsq and a TSU are proportional. shorter sides: R S 3 0 TS longer sides: S Q SU So, T RSQ T TSU b the SAS Similarit Theorem. 0. shortest sides: M L 4 JG 3 longest sides: M N 7 JF LN remaining sides: G F 39 3 Because the ratios are not equal, T MLN is not similar to T JGF.. 9 a a a 3 a. 4 b 8 7 b 4(8 b) 7b 5 4b 7b 5 b b 3. c (0) 0 4. The dilation is reduction because the image is smaller than the original figure; scale factor P P The dilation is an enlargement because the image is larger than the original figure; scale factor P P The dilation is a reduction because the image is smaller than the original figure; scale factor P 5 5. P 5 hapter 7 Test (p. 404) 3. 0 h h 0 0h h; The height of the wall is feet Geometr, oncepts and Skills 5

16 ( 3)(7) No; from the diagram, all the angles are right angles, so the are all congruent. However, B HJ 4 and D G H 4 7. The corresponding side lengths are not proportional Yes; as ay and mar 90358maZ, so ar az; T RST T ZYX b the AA Similarit Postulate. AB 8. shortest sides: D E 0 5 A longest sides: 4 D F 35 5 remaining sides: B 0 EF 5 5 Because the ratios are equal, T AB T DEF b the SSS Similarit Theorem. 7. No; amnl aqnp, however, the lengths of the sides that include amnl and aqnp are not proportional. shorter sides: M N 0 QN LN longer sides: P N 3 4 So, T MNL is not similar to T QNP. 8. 3:7 RT PS 9. T Q S Q 3 T Q 3 TQ 3 TQ 8 TQ 0. 9 a a a a 35. The midsegment (ST **** ) of T PRQ should be half as long as the side to which it is parallel (RQ **&). So, ST should be 0, or RQ should be. 3. The dilation is an enlargement because the image is larger than the original figure; scale factor P P The dilation is a reduction because the image is smaller than the original figure; scale factor P 3 P hapter 7 Standardized Test (p. 405). B; ft ft ft 4 4 d 4 3 ft ft 3. G; mae mab 59, so 59; EF FD B A D 4. H; (48) 4 5. B; 4 8 inches. F; 3 4 inches ( 4) B; The dilation is an enlargement because the image is larger than the original figure; scale factor P 4 P a. astr aprq and apqr asrt, so T PQR T SRT b the AA Similarit Postulate. b. scale factor Q R 7 80 RT.5 0 RT SR c. Q R P Q h.5 h h 30 h 480 feet hapter 7 Algebra Review Geometr, oncepts and Skills

17 A bh A h b 0. V 3 Bh 3V Bh 3 hv B. S B Ph S B Ph S B P h. A (b b )h A (b b )h A b b h ha b b Geometr, oncepts and Skills 7