Geometry GT/Honors 3 rd 9 weeks Homework Answers

Transcription

1 School holiday winter break. Geometry GT/Honors rd 9 weeks Homework Answers Monday Tuesday Wednesday Thursday Friday School holiday winter break. Finish notes/classwork on Inequalities in Triangles. Ex: Ex: G, Y, R Ex: ST, SU, TU a) N b) T c) T a) CE b) BE c) BE d) CD Inequality Review. x. x -1/. (all real numbers) n < -16 c > (all real numbers) 7. - < x < 8. (no solution) 9. t x x - 10 < b < 14 - < d 1 y -4 or y 6 1 < n < < k < c x k 1/ 0. < v 10 < x < 5 Vocabulary cards for IIT unit. WS Inequalities in One Triangle. 1 < x < 15; {4, 7, 9., 14}.. 0 < x < 10; {1/, 1, 4, 7, 9.}.. 7 < x < 9; (no solution). < x < 9; {4, 7}. 0 < x < 0; {1/, 1, 4, 7, 9., 14, 19}. 6. < x < /; {4, 7, 9.} < x < 9.5; {1, 4, 7, 9.} < x < 6.; {4}. 9. < x < 8; {4, 7} < x < 16; {7, 9., 14}. 1 6 < x < 10. < x < < x < < x < 16. not possible 17. possible 18. not possible 19. not possible 0. possible possible. not possible. not possible not possible AB. 6. R. 7. AC. 8. The side opposite the right angle (hypotenuse) RT. DB is longest, CA is shortest. m B = 44.. GH is longest, GI and HI are shortest.. DF is longest, EF is shortest. SW is longest, TW is shortest. x > 6. x > 16/5 7. Anchorhead to Mos Eisley 8. Towers L and K. 9. More than 5 light years and less than 77 light years. 40. W, D, C 4 A Ex: 5 < x < 19 Ex: 1 < x < 45 Page 9 #1-8, ) check in class 4) M, L, K 5) D, C, E 6) G, H, I 7) A, B, C 8) E, F, D 9) Z, X, Y 10) MN, ON, MO 11) FH, GF, GH 1) TU, UV, TV 1) AC, AB, CB 14) EF, DE, DF 15) ZY, XZ, XY 16) no 17) yes 18) no 19) yes 0) yes 1) no ) 4<s<0 ) 11<s<1 4) 0<s<1 5) 5<s<41 6) <s<11 7) 15<s<55 8) check in class 1)The path that he is taking is shorter than the sum of the other two distances. ) AB is the longest side WS Inequalities in Triangles. sometimes. sometimes. always always always 6. never 7. AB 8. AB 9. BD 10. BD m > m 1 > m. 16. DC > AB > BC > DA. 17. RB 18. WT 19. AD 0. a) WY; b) WZ and WY. CE DE; EA BA.. BE. DE BE AD 6. AC 7. RT 8. -/ < x < 17. Pythagorean Theorem-More or Less. obtuse. obtuse. right right acute 6. not a triangle 7. obtuse 8. acute 9. acute 10. not a triangle 1 obtuse right acute 1 acute 1 obtuse 16. right 17. acute 18. acute 19. right 0. Either 16 feet or feet, depending on if the 8x8 wall or 8x15 wall is the front wall. WS Pythagorean Converse. yes, acute. not possible. yes, obtuse not possible yes, right 6. yes, obtuse 7. yes, obtuse 8. yes, acute 9. obtuse isosceles 10. right isosceles 1 acute isosceles not a triangle (slopes are parallel) obtuse scalene

2 Page 94 #5-7. 5) RS 6) CD 7) XY WS 8. A. x = 6, y = 6. x =, y = 6. x = 4, y = 4 x = 1, y = 1 x = 10, y = x = ( )/, y = 1/ 7. x = 10, y = 5 8. x = 7, y = 7 9. x = 9, y = x = 6, y = 6 1 x =, y = x = 10, y = 5 x = 6, y = 1 x = 6, y = 1 1 x = 10, y = x = 8, y = x = 17/, y = (17 )/ 18. x = 1, y = ( )/ 19. x = 10, y = 5 0. x = 1, y = 1 x =, y = 6. x = 4 5, y = 15. x = 7.5, y =.5 if the hypotenuse is 5. (x = 5 6, y = 5 if hypotenuse is 10.) x = 14 6, y = 1 Review: Pythagorean Theorem and more x = 9, y = cm. 6. Using the Pythagorean Theorem, BD = and BC = 6. AC = AB + BC since 1 = 6 + (6 ), so ABC is right since Pyth Thm works cm. 1 7 in. 1 8 in mi cm units. 19. B units XZ = 1; WXZ YXZ; HL; CPCTC.. Pg 48 #15-, ) 50 ft 16) ft 17) a=7, b=14, c=7, d= 7 18) a=6, b= 6, c=, d=6 19) a=10, b= 5, c=15, d=5 0) a=4, b=4 1) a=, b=7 ) a=14, b= 6 ) check in class 5) a. 16 8, b. 0.8 min 6) a m b. 6.1 m WS 8. - Special Right Triangles (GT/Honors) #1- x=7; y= 7. x=10; y=5. x= 4 ; y=8 x= 4 ; y= 8 x= 6 ; y=1 6. x= 4 6 ; y= 8 7. x= 10 ; y= 0 8. x= 5 ; y=5 9. x=1; y= x=; y=4 1 x=8; y= 4 x= 7 4 ; y= 7 8 x=45 ; y= 7 1 x=10; y= 5 1 x=6; y= ft.. 18 units 5 ft. Worksheet on Right Triangles.. x=1; y= 6 ; k= 6 ; m=6 6. MP= ; PR= PQ= 7. AC=8; AB=16; CD= Finish WS 8. - Special Right Triangles (GT/Honors) # in. 9. (7, ) 5 0., 4 m.. a = 7, b = 4, c = 11, d = 0.. w = 1, x = 1, y = 0, z = 0 1, s = 1, v = 6 in by in. Yolanda is ft behind the screen; Kim is 4904 ft behind the screen. Vocabulary cards for RTA unit. WS Trig Ratios in Right Triangles (#1-1). x=7; y=6.5. x=60; y=0. x=6.0; y=7.8 x=9; y=11 x=18.4; y=76 6. x=7.7; y=.6 7. x=19.; y=5; m B=74 8. x=6.8; y=1; m A=5 9. w=9; x=1; y=7.6; z= h=9.4; x=15; y= ft 49.0 ft WS Trig Word Problems ft ft 6. 8 ft mile m ft..75 cm. p. 47 (5-58) p. 447 #9-18,, 8, m meters. B 560 ft m ft p. 44 #10,, yd. 48 m. D School holiday Martin Luther King Jr. Day. 5 cm. WS 8.5 (Angles of Elevation & Depression) ft 41 ft 18.6 ft ft ft ft 10.0 ft ft ft below; 15 ft away. p. 441 #10, 17,, 4, 1, ft Right Triangle Practice ft x= 5 ; y= 8 ; z= 10. No (check in class). 1 AB= 1 ; BC= 1 Trig Application Word Problems m , 10, and m m. Two angles in the rhombus measure 16 and the other two angles measure Yes, since the angle is The building is not built to code since the angle is 45. WS-7.4 Right Triangles with an Altitude And finish the Radical Review WS. Check in class. Estimate Radicals WS. Check in class.

3 ft 7.85 in. w=; x = 41 w=68.; x=156 check in class. check in class x= ; y= 5 ; z= yes. 8 ft. 6. Bonus: ft. Ch. 8 Extra Practice (with answers). Answers on worksheet Read pages and work the following problems: p. 08 (1-1, 19-6, 45-48) 1-1 check in class 19. x=11; y=9 0. x=4; y=8 x=; y=6. x=1. x=; y=5 x=5; y=4 a=15; c=40 6. x=58; r=5; b= check in class Quad unit vocab. Inclement Weather Day Pythagorean Theorem in Three Dimensions ( 70)/7, (6 70)/7, (10 70)/7, (1 70)/ , 4, 6, , 5 15, 10, , 4, 4 10, , 6, 109, , 418, 18, 7. Quadrilaterals: Classifying on the Coordinate Plane and Linear Equations Note: Only partial answers are shown below. Ask your teacher to check your WTP & Work. Rhombus y 1 = 4(x ) or y 5 = 4(x ) 1 Kite y = 1, and x = 0 1 Trapezoid Segments JK and ML y+1 = 1(x ) or y = 1(x 6) 16. Rectangle y + 5 = 1/8 (x 1) 17. Quadrilateral (, 7) NT: y + 4 = 1(x + 6) TQ: y = (x 0) 18. Isosceles Trapezoid x = 9 Parallelogram y + 6 = 1/5 (x ) Can You Create. Create Square: C(7, -) and D(1, -4), or C(, 10) and D(-, 8).. Create Rhombus: D(, -1).. Create Rectangle: B(7/5, 11/5) and D(-7/5, -1/5). Quadrilaterals from Slopes and Equations of Lines. Notes Quadrilaterals from Slopes & Equations of Lines. Quadrilateral Proof #1-. Quadrilaterals in a Coordinate Plane (use diagonal properties only!) Quadrilateral Properties- Always, Sometimes, Never. always. sometimes (when it is also a rectangle). never sometimes (when it is a square) sometimes (it could also be an isosceles trapezoid) 6. sometimes (only when it is a rhombus) 7. always 8. sometimes (only when it is a square) 9. sometimes (only when it is a square) 10. sometimes (only when it is a rhombus) 1 sometimes (only when it is an isosceles trapezoid) always always 1 always 1 sometimes (only when it is a rectangle) 16. always 17-. WS Properties of Parallelograms WS 6. Parallelograms not a parallelogram #9-: Only the partial answers are shown below. Remember to show work (all sides slopes and/or lengths). 9. Pa- yes, opp sides. Re- yes, consecutive sides. Rh- no, all sides not. Sq- no, not a rhombus. 0. Pa- yes, opp sides. Re- no, cons sides not. Rh- yes, all sides. Sq- no, not a rectangle. Pa- yes, opp sides. Re- yes, cons sides. Rh- yes, all sides. Sq- yes, both a rect. and rhom.. Pa- yes, opp sides. Re- no, cons sides not. Rh- no, all sides not. Sq- no, not a rect. or a rhom. WS Rectangles, Squares & Rhombi. WS- Trapezoids (6.5) 1- check in class WS Trapezoids and Kites.

4 y = 10. y = 15. x = 10 y = 15 z = 6 6. y =.5 7. y = 6; z = y = -40; z = x = 1; y = x = 15; y = 6 1 x = 6; y = x = 5; y = 1 p. 16 (1-16, 1-, 41) 1; m Q=m S=6; m P=m R=144 6; m H=m J=0; m I=m K=150 1 x = 6; y = 8 1 x = 5; y = x = 7; y = 10 BC=AD = 15; AB=CD = 9.5. AB=CD = 1 BC=AD =. A 4 18 and 16 Quadrilateral Proof #. diag. bisect each other. both pairs opp sides = not a parallelogram one pair opp sides = & 6. both pairs opp sides 7. both pairs opp sides 8. not a parallelogram 9. one pair opp sides = & 10. both pairs opp angles = (or both pairs opp sides ) 1 both pairs opp sides = diag. bisect each other both pairs opp angles = 1 both pairs opp sides (or both pairs opp angles =) 1 one pair opp sides = & 16. one pair opp sides = & 17. diag bisect each other 18. both pairs opp sides 19. not a parallelogram 0. one pair opp sides = & both pairs opp sides. both pairs opp sides =. both pairs opp sides not a parallelogram one pair opp sides = & 6. both pairs opp sides 7. one pair opp sides = & 8. not a parallelogram 9. both pairs opp angles = 0. both pairs opp sides WS Rectangles, Squares & Rhombi (6.4) x=5; y=4. x=. m QZR=140 m RTS=17.5 m TCQ=90 6. x=, x=6 7. x=; y=; rhombus AC=0 x=9; x= x=; y=- check in class. x=11; AC=BD=16. c=; diag= x=; y=4 8. x=5; SR=QR=15 Quadrilateral Proof #6-8. V(1, ); W(7, ) P(1, 4); O(1, 4) 6. QR=9 6 n 7. XY 8. TS + QR = 9. m R = 50 a b 10. XY 1 m R = or 5 Notes Special Rights and Trig in Quadrilaterals. Quadrilateral Proof # WS Kites & Coord Work with Quadrilaterals check in class KF = ; KJ = 6 x = 5; y = 0 6. UI = 6; IT = 15; UT = , 1, 1, 1 8. rhombus 9. kite 10. trapezoid 1 rectangle quadrilateral isos. Trap. 1 square 1 D 16. (4, 0) 17. (6, 6) 18. (-, 4) 19. G(-4, 1), H(1, ) Page 5 (14-19, 6) 1 x=15; y=5 1 x=; y= a=4; c=8 17. k = 9, m = D /6 Quadrilateral Proof #1 Page 44 (-7, -5). W(0, h); Z(b, 0). W(a, a); Z(a, 0) W(-b, b); Z(-b, -b) W(0, b); Z(a, 0) 6. W(-r, 0); Z(0, -t) 7. W(-b, c); Z(0, c). A. P(c-a, b) P(a, 0) P(-b, 0) Practice 6-6 Midpoint Length (a/, b) a. (a/, b) a 4b. (a/, 0) a (a/, b) a 4b Slope zero / b / a 10. -b / a 1 b / a -b / a E(a, b); I(4a, 0) 1 E(-a, -b); M(a, -b); O(a, b) 1 D(4a, b); I(a, 0) 16. A(a, 4b); L(a, b); T(0, b) 17. R(-4a, b) 18. C(-b, 0) Practice 6-7. a) (-a, 0). b) (-a, b). Quadrilateral Proof # WS 6.7 Proofs Using Coordinate Geometry Check in class WS Connecting Midpoints b = 5. rhombus; 5. m 1=40; m 5=160 m =0; m 6=0 m =10; m 7=10 m 4=60; DE =.5 m 1=80; m 9=70 m =50; m 10=55 m =90; m 11=90 m 4=40; m 1=5 m 5=105; m 1=105 m 6=5; m 14=40 m 7=90; m 15=90 m 8=55; m 16=50 SE = 14; RA = 7 m 1=110; m 9=70 m =5; m 10=5 m =10; m 11=10 m 4=5; m 1=5 m 5=110; m 1=70 m 6=45; m 14=85 m 7=50; m 15=50 m 8=85; m 16=45 Quadrilaterals from Midpoints yes. EF is parallel to and half the length of AC.. HG is parallel to and half the length of AC. WS Chapter 6 Review x=1; y= and 6 9. x=, y= & Diagonals bisect each other parallelogram. none, only one pair of opp. sides. one pair opp sides & parallelogram 4-6 check in class 7. (, -); (-7, 1); (5,5) 8. m 8 = 50 m ADC = 105 BD = m 1=10 m =90 m =0 m 4=40 m 1=75 m =70 m =5; RA=6; AP=6 Page 59 #0-4 Check in class WS Quadrilateral Relationships Quadrilaterals. Trapezoids. Parallelograms Kites Isos. Trapezoids 6 & 7 Rectangles & Rhombuses 8. Squares 9. A 10. S 1 S A A 1 S 1 S 16. S 17. A 18. True 19. F 0. T F. T. F F F 6. F 7. F 8. T 9. T 0. F F. F. F F T 6. T 7. F 8. T 9. T 40. T WS Quadrilateral Word Problems. Page 09 (9-41, 50-5, 56-59) 9-5 check in class 6. true; a square is both a rectangle & a rhombus 7. False; a trap. Only has one pair of sides. Worksheet Algebra & Areas. 7x 0x 1.. 9x x 9 1x 7 x 16x 0x 104 4x x 6. 5x 10.5x or or ft or in m or cm ft or 8 yd 10.8 in 4 in by 0 in 1 4 ft 1 1: % in by 5 in Area and Perimeter Applications.

5 c) (-a/, b/). d) b/a.. a) (-4a, 0). b) (-a, a). c) /. d) (a, -a). e) 1/. HP = 4a 4b. C is (a, 0) and D is (0, b), so DC = 4a 4b. So DC = HP. Slope = d b or b d c a a c. Midpoint is a c, b d. Dist. = d b c a 6. Vertical, undefined Horizontal, zero Horizontal, zero Oblique, negative Vertical, undefined Oblique, positive or negative parallelogram One pair of opposite sides is both parallel and congruent. 6. parallelogram 7. One pair of opposite sides is both parallel and congruent. 8. right 9. rectangle 10. congruent 1 rhombus 1 square parallelogram rhombus 1 rectangle 1 parallelogram 16. rectangle 17. rhombus 18. regular polygon 8. False; a kite does not have = opp. sides 9. true; all squares are parallelograms 40. false; kites are not parallelograms 4 false; only rhombuses with right angles are squares 50. rectangle, parallelogram, kite 5 rhombus, parallelogram square, rhombus, parallelogram rhombus, parallelogram, kite 56. parallelogram, rectangle, trapezoid 57. parallelogram, kite, rhombus, trapezoid, isos trap. 58. kite, parallelogram, rhombus, trap., isos. Trap. 59. parallelogram, rectangle, square, rhombus, kite, trap. APC unit vocab. Example from Page 4: see textbook. Page 45 #9-15, the diagonals are 10. parallelogram AFHC 1 rhombus rectangle AEFB, AEHD, CGHD square AEBC, BFHD 1 trapezoid AEGD 1 isos. Trap. AFGD, BEHC 6-7. check in class Detailed quadrilaterals venn diagram. The Quadrilateral Family: Definitions, Properties Chart, Family Tree, and Venn Diagram. Unit Conversion Worksheet (1-D and -D). Tiling Tubs. Page 565 # ;.1 in.;.6 in. 67 ; 75 ; 18.8 ft. (also 11 ; 9 ; 9.6 ft.) ; 5 ; yd.; 7 ; 16. Composite Area I Worksheet. 16( ) mm 7. 4 cm cm 1 85 m Worksheet - Composite Area II units cm in 66( ) units 17. 5/4 or 8.75 units bricks units 0. 1 units ft p. 56 (1-9; 1-14; 19-7; -9) 40 cm in. 0. m / m 8. 5 y d 9. ft B 14 cm 1 18 in, 1in units 0. 1 units 7 units. units. 1 units a) b) 5 units Worksheet units. 50 in. $ in. & in 4 u m 7. 1 unit 8. 4 cm 9. 5 cm u 1 10 u 85 u 4 ft 1 40 u 1 44 u u p. 54 (4, 8-18, -, 5) 110,6 mi 8. 0 ft 9. 7 m ft 1 80 in 18 m 4 ft ft 1 96 in m in p. 548 (1-, 10-18, 4-5, 9) m 1 10, m 60 m 0. m 4 90, m 5 45 = m 6. m 7 m 9 60 m ft in 9.5 m 10 in 1 7 cm 1 84 in m m in D 9.1 in, 6 in,.7 in m p. 561 (1, 4, 7, 8) 17.8 cm yd in cm Finish the Shaded Area matching game. 68 u. 57 u. 60 u 0 u Multiple choice packet (answers are at the end of the packet).

6 a) b) 18 units 6. a) b) 16 units 18. b. 48 m c 10m. 1 cm ft 8 m 18 units 6 15 units units 8. C 9. trapezoid, 4 units cm m. 18 b=1 cm, 4 cm, h=18cm 90 u u u 8. 4 u 9. 7 u u u 48 u 96 u 1 66 u 1 19 u u Quadrilaterals with algebra, right triangles, area and perimeter. Geoboard WS 1) 5 ) 8 ) 8.5 4) 9.5 5) 7 6) 6 7) 10 8) 7. a) b) 6 units Multiple choice packet (answers are at the end of the packet).. 0 units. 88 units 5 ft 55 cm 6. 1,800 m 7. 4 in m 9. a)54 in b) 54 in p. 561 (, 5, 11-17). 8 in 6 m, 8.8 m m 18 ft 7554 m 1 1 km mm ft yd Pg 58 # in m 9. a)54 in b) 54 in WS Heron s Formula & Circle Areas. h 4 6in... A 0 7in A (0 14 )u 15 h in C 14 u and A 49 u 6. C 10 u and A 5 u in 8. 60,000π 816,811 in revolutions 10. (160 70) 7ft p. 571 (57-59) 57. B 58. : ft p. 578 (,5-8,0,,5,40). (4п+16) ft (4-п) ft 6. (65-16п) ft 7. ( п) in. 1 in (49п-7.5 ) m b. Find the area of ¾ of a circle of radius 10 and add ¼ of a circle of radius c. 9 ft Worksheet Arc Length, Sector Area, Segment Area. Area = 6π u and arc length = 6π u. Area = 147π u and arc length = 14π u. Area = 8π/ u and arc length = 4π/ u 8 4 u (5π 50) u 6. (48π - 6 ) u 7. 1 Word Problem Practice (Glencoe 11-1, 11-, 11-, 11-4) ( )/16 u Shaded Areas ft. 191 ft a. a u 7 5 u 16( ) 8 / u 6. ab/ u p. 555 (,, 5-10, 1-16, 19-, 8-, 5-7, 41-44). 4:, 16:9. :, 4:9 4 in m ft m 9. $ $47.0 7:, 7: 1 :4, :4 1 4:1, 4: :10, 1: :, 4:5. C 8. x = 4 cm, y = 6 cm 9. x = 8 cm y = 4 cm 0. x= 4 cm y = 6 cm x= 8 cm y = 1 cm. ¼in by 1in 5/, 5/4 6. 8/, 64/9 7. /1, 4/1 4 Always Sometimes Never 4Sometimes

7 p. 584 (1-6, 15-0, -6, - 5, 47) ½. 1/10. /5 / /10 1 ¼ or 5% 16. 5% 17. /4 or 40% 18. / or 67% 19. or 61 % 0. 4 or 1% or 16% 00. /5. /10 9/ /49 or about 49%; the probability is the same ft A (7 18 )u P 1 A 1 P (6 1 )u ( )u 14 u WS - Chapter 10 Review. (1) 75 u ; () 4 6 cm ; () (4) (5) u ; 144 u ; (96 4 )u ; (4 + 1 )u; (6) 70 u ; (7) 890. cm ; (8) u ; (9) (10) (11) (1) 6 55 u ; 15 u ; 5 u ; 5/18 (6 9 ) u ; (6 + ) u;.0; 100 u ; (1) 156 cm ; (14) 99.8 cm ; (15) 4 u ; (16) 45 u ; (17) ( )u, Area with Parallel and Perpendicular Lines. 64 u. 5 u 4 u. 15 u Chapter 10 Extra Practice. 560 in.. 4 ft.. 14 revolutions cm..1 units in in ft ft ft ft. Shaped Areas: Farmer's sheep: 148 ft. Johnny's dog Spot: 450 ft. Read "Sphereland" - Einstein Happened; Preface; etc. through page 6. Finish reading "Sphereland" by the end of Spring Break. (18) ( ) u; 46 ft WS- Distance; and Areas of Regular Polygons and Area Review. (Review quizzes) Practice: Finding Area using Exponents and Variables (front) x = 4. n = 1. t = 9 y = 15 11x x + x x 6x (x + 4)(x + 4) x(x) ft, or (1x + 16) ft. 10 ft. (x + )(x + 5) x(x+) ft, or (4x + 10) ft ft. (back) C. G. F Spring Break! Review all tests and quizzes from rd 9 weeks to study for cumulative retest. Practice: Perimeter using Exponents and Variables. 4x + 0. x + x x + 6x + 4 x + x x 6. 10x +.8 C. C. A C B 6. D 7. H 8. A 9. H 10. A 1 C D Complete all the study sheets, including the Character List, for "Sphereland".

8 H G 6. C 7. J cm. 9. Omit (missing diagram). 10. B 1 B