1. ~, rectangle, rhombus, square 2. parallelogram 3. trapezoid 4. ~, rhombus 5. kite 6. trapezoid, isosc. trapezoid 7. rhombus 8.

Transcription

1 Answers for Lesson 6-1, pp Exercises 1. ~, rectangle, rhomus, square. parallelogram 3. trapezoid 4. ~, rhomus 5. kite 6. trapezoid, isosc. trapezoid 7. rhomus 8. parallelogram 9. rhomus 10. rectangle 11. kite 1. isosc. trapezoid 13. rhomus 14. kite 5 y y A B X W Yx D C O 4 6 x Z 15. trapezoid 16. rectangle y K y J L 4 O O 6 x V R M T x S Geometry Chapter 6 15

2 Answers for Lesson 6-1, pp Exercises (cont.) 17. quadrilateral 18. isos. trapezoid R y y E H 4 x 8 O 8 F G Q 4 P 6 O x 4 N 19. x 11, y 9; 13, 13, 3, 3 0. x 4, y 4.8; 4.5, 4.5, 6.8, x, y 6;, 7, 7,. x 1; 4,, 4, 7 3. x 3, y 5; 15, 15, 15, x 5, y 4; 3, 3, 3, , 40, 140, 140; 11, 11, 15, , 58, 1, 1; 6, 6, 6, 6 7. rectangle, square, trapezoid 8. D Answers may vary. Samples are given. 9. y x O y 4 x O Impossile; a trapezoid with one rt. must have another, since two sides are. Geometry Chapter 6 16

3 Answers for Lesson 6-1, pp Exercises (cont.) 3. y y O 4 x O x y O 4 6 Rhomuses Kites Quadrilaterals Parallelograms Squares 36. True; a square is oth a rectangle and a rhomus. 37. False; a trapezoid only has one pair of sides. 38. False; a kite does not have opp. sides. 39. True; all squares are?. 40 False; kites are not?. 41. False; only rhomuses with rt. are squares. 4. Rhomus; all 4 sides are ecause they come from the same cut. 43. Check students work. x Rectangles Trapezoids Geometry Chapter 6 17

4 Answers for Lesson 6-1, pp Exercises (cont.) 44. A rhomus has 4 sides, while a kite has pairs of adj. sides, ut no opp. sides are. Opp. sides of a rhomus are, while opp. sides of a kite are not Check students sketches. 45. some isos. trapezoids, some trapezoids 46. ~, rhomus, rectangle, square 47. rectangle, square 48. rhomus, square, kite, some trapezoids 49. A trapezoid has only one pair of sides Check students sketches. 50. rectangle, ~, kite 51. rhomus, ~ 5. square, rhomus, ~ 53. rhomus, ~, kite Check students work Explanations may vary. Samples are given. 56. ~, rectangle, trapezoid 57. ~, kite, rhomus, trapezoid, isos. trapezoid 58. kite, ~, rhomus, trapezoid, isos. trapezoid 59. ~, rectangle, square, rhomus, kite, trapezoid Geometry Chapter 6 18

5 Answers for Lesson 6-, pp Exercises ; 10, 0, 0 8. ; 18.5, 3.6, ; m Q m S 36, m P m R ; m H m J 30, m I m K x 6, y x 5, y x 7, y x 6, y x 3, y ; 4 0. Pick 4 equally spaced lines on the paper. Place the paper so that the first utton is on the first line and the last utton is on the fourth line. Draw a line etween the first and last uttons. The remaining uttons should e placed where the drawn line crosses the lines on the paper BC AD 14.5 in.; AB CD 9.5 in. 3. BC AD 33 cm; AB CD 13 cm 33. A 34. The opp. are, so they have measures. Consecutive are suppl., so their sum is 180. Geometry Chapter 6 19

6 Answers for Lesson 6-, pp Exercises (cont.) 35. a.. DC AD c. d. Reflexive e. ASA f. CPCTC 36. MNPQ is a. Given M and N are suppl. M P , 3, , 8, , 37, The lines going across may not e since they are not marked as , 16 N and P are suppl. Consec. in a 4. Answers may vary. Sample: P and Q are suppl. are suppl. N Q Two suppl. to the same are. 1. LENS and NGTH are ~s. (Given). ELS ENS and GTH GNH (Opp. of a ~ are.) 3. ENS GNH (Vertical are.) 4. ELS GTH (Trans. Prop. of ) Geometry Chapter 6 130

7 Answers for Lesson 6-, pp Exercises (cont.) 43. Answers may vary. Sample: In? LENS and NGTH, GT EH and EH LS y the def. of a ~. Therefore LS GT ecause if lines are to the same line then they are to each other. 44. Answers may vary. Sample: 1. LENS and NGTH are?. (Given). GTH GNH (Opp. of a ~ are.) 3. ENS GNH (Vertical are.) 4. LEN is supp. to ENS (Consec. in a ~ are suppl.) 5. ENS GTH (Trans. Prop. of ) 6. E is suppl. to T. (Suppl. of are suppl.) 45. x 1, y x 0, y x 9, y Answers may vary. Sample: In ~ RSTW and ~ XYTZ, R T and X T ecause opp. of a ~ are. Then R X y the Trans. Prop. of. 49. In ~ RSTW and ~ XYTZ, XY TW and RS TW y the def. of a ~. Then XY RS ecause if lines are to the same line, then they are to each other. 50. AB DC and AD BC y def. of ~. 3 and 1 4 y alt. int.. 1 y def. of isect., so 3 4 y Trans. Prop. of. 51. a. Answers may vary. Check students work.. No; the corr. sides can e ut the may not e. Geometry Chapter 6 131

8 Answers for Lesson 6-, pp Exercises (cont.) * AB ) * CD ) * EF ) 5. a. and AC CE (Given). ABGC and CDHE are parallelograms. (Def. of a ~) c. BG AC and DH CE (Opp. sides of a ~ are.) d. BG DH (Trans. Prop. of ) e. BG DH (If lines are to the same line, then they are to each other.) f. 1, 1 4, 4 5, and 3 6 (If lines are, then the corr. ' are.) g. 5 (Trans. Prop. of ) h. BGD DHF (AAS) i. BD DF (CPCTC) 53. a. Given: sides and the included of ~ABCD are to the corr. parts of ~WXYZ. Let A W, AB WX and AD WZ. Since opp. of a ~ are, A C and W Y. Thus C Y y the Trans. Prop. of. Similarly, opp. sides of a ~ are, thus AB CD and WX ZY. Using the Trans. Prop. of, CD ZY.The same can e done to prove BC XY. Since consec. of a ~ are suppl., A is suppl. to D, and W is suppl. to Z. Suppls. of are, thus D Z. The same can e done to prove B X. Therefore, since all corr. and sides are, ~ABCD ~WXYZ.. No; opp. and sides are not necessarily in a trapezoid. Geometry Chapter 6 13

9 Answers for Lesson 6-3, pp Exercises x 3, y 4 3. x 1.6, y Yes; oth pairs of opp. sides are. 8. No; the quad. could e a kite. 9. Yes; oth pairs of opp. are. 10. It remains a ~ ecause the shelves and connecting pieces remain. 11. A quad. is a ~ if and only if opp. sides are (6-1 and 6-5); opp. ' are (6- and 6-6); diags. is. each other (6-3 and 6-7). 1. a. Distr. Prop.. Div. Prop. of Eq. c. AD BC, AB DC d. If same-side int. are suppl., the lines are. e. Def. of ~ 13. Draw diagonals TX and WY intersecting at R. a. TW YX (Given). TWR XYR (Alt. Int. ) c. WTR YXR (Alt. Int. ) d. TWR YXR (ASA) e. WR YR (CPCTC) f. TR XR (CPCTC) g. The diagonals isect each other. (def. of is.) h. TWXY is a ~ (Thm. 6-7). Geometry Chapter 6 133

10 Answers for Lesson 6-3, pp Exercises (cont.) 14. x 15, y x 3, y c 8, a k 9, m D 19. Answers may vary. Sample: F A B E 0. JKN LMN (given), LKN JMN (given), and MK MK, so JKM LMK y ASA. JK ML and MJ LK (CPCTC), so JKLM is a ~ ecause opp. sides are (Thm. 6-5). 1. TRS RTW (given), so ST RW and SR TW. RSTW is a ~ ecause opp. sides are (Thm. 6-5).. (4, 0) 3. (6, 6) 4. (, 4) 5. You can show a quad. is a ~ if oth pairs of opp. sides are or, if oth pairs of opp. ' are, if diagonals isect each other, if all consecutive ' are suppl., or if one pair of opp. sides is oth and. 6. D 1 6 C H G Geometry Chapter 6 134

11 Answers for Lesson 6-3, pp Exercises (cont.) 7. Answers may vary. Sample: 1. AB CD, AC BD (Given). ACDB is a ~. (If opp. sides of a quad. are, then it is a ~.) 3. M is the midpoint of BC. (The diag. of a ~ isect each other.) 4. AM is a median. (Def. of a median) 8. G( 4, 1), H(1, 3) Geometry Chapter 6 135

12 Answers for Lesson 6-4, pp Exercises 1. 38, 38, 38, 38. 6, 18, , 31, , 33.5, 113, , 90, 58, , 60, 60, , 35, 55, , 90, , 55, ; LN MP ; LN MP ; LN MP ; LN MP ; LN MP ; LN MP rhomus; one diag. is. ' of the ~ (Thm. 6-1). 17. rhomus; the diags. are # neither; the figure could e a ~ that is neither a rhomus nor a rect. 19. The pairs of opp. sides of the frame remain, so the frame remains a ~. 0. After measuring the sides, she can measure the diagonals. If the diags. are, then the figure is a rectangle y Thm Square; a square is oth a rectangle and a rhomus, so its diag. have the properties of oth Geometry Chapter 6 136

13 Answers for Lesson 6-4, pp Exercises (cont.). a. Def. of a rhomus. Diagonals of a ~ isect each other. d. Reflexive Prop. of e. ABE ADE f. CPCTC g. Add. Post. h. AEB and AED are rt.. i. suppl. are rt. Thm. j. Def. of # 3. Answers may vary. Sample: The diagonals of a ~ isect each other so AE CE. Both AED and CED are right ecause AC # BD, and since DE DE y the Reflexive Prop., AED CED y SAS. By CPCTC AD CD, and since opp. sides of a ~ are, AB BC CD AD.So ABCD is a rhomus ecause it has 4 sides. 4. A c. AE AE Symols may vary. Samples are given: parallelogram: ~ rhomus: ~ R rectangle: ` square: h S 5. ~ R, h S 6. ~, ~ R,`, h S 7. ~, ~,`, 8. ~, ~ R R,`, h S 9. `, h S 30. ~,,`, h S 31. ~, ~ R,`, h S 3. `, h S ~ R h S Geometry Chapter 6 137

14 Answers for Lesson 6-4, pp Exercises (cont.) ~ R 33., 34., h S ~ R h S Diag. are, diag. are #. Diag. are # and. Diag. are, diag. are #. 38. a. Opp. sides are and ; diag. is. each other; opp. are ; consec. are suppl.. All sides are ; diag. are. c. All are rt. ; diag. are # is. of each other; each diag. is. two ABCD is a parallelogram. (Given) AC isects BAD and BCD. (Given). 1, 3 4 (Def. of isect) 3. AC AC (Refl. Prop. of ) 4. ABC ADC (ASA) 5. AB AD (CPCTC) 6. AB DC, AD BC (Opp. sides of a ~ are.) 7. AB BC CD AD (Trans. Prop. of ) 8. ABCD is a rhomus. (Def. of rhom.) Geometry Chapter 6 138

15 Answers for Lesson 6-4, pp Exercises (cont.) 40. ABCD Given AC BD Given AD AD Ref. Prop. AB CD Opp. sides of a are. ABD DCA SSS 41. Yes; since all right are, the opp. are and it is a ~. Since it has all right, it is a rectangle. 4. Yes; 4 sides are, so the opp. sides are making it a ~. Since it has 4 sides it is also a rhomus. 43. Yes; a quad. with 4 sides is a ~ and a ~ with 4 sides and 4 right is a square m A m D 180 Consecutive of a are suppl. m D 90; m A 90 Div. Prop. of Eq. CPCTC m D m D 180; m A m A 180 Sustitution D B; A C Opp. of a are. ABCD is a rectangle Def. of a rectangle A D Geometry Chapter 6 139

16 Answers for Lesson 6-4, pp Exercises (cont.) 45. x 5, y 3, z x 7.5, y Drawings may vary. Samples are given. 47. Square, rectangle, isosceles trapezoid, kite a 48. Rhomus, ~, trapezoid, kite a 49. For a : trapezoid, isosc. a trapezoid Qa. 1 R, ~, rhomus, kite For a : trapezoid, isosc. trapezoid, ~, rhomus (a ), kite, rectangle, square Qif a "R , , 5. 1, , Answers may vary. Samples are given. 54. Draw diag. 1, and construct its midpt. Draw a line through the mdpt. Construct segments of length diag. in opp. directions from mdpt. Then, isect these segments. Connect these mdpts. with the endpts. of diag. 1. a Geometry Chapter 6 140

17 Answers for Lesson 6-4, pp Exercises (cont.) 55. Construct a rt., and draw diag. 1 from its vertex. Construct the # from the opp. end of diag. 1 to a side of the rt.. Repeat to other side. 56. Same as 54, ut construct a # line at the midpt. of diag Same as 56, except make the diag Draw diag. 1. Construct a # at a pt. different than the mdpt. Construct segments on the # line of length diag. in opp. directions from the pt. Then, isect these segments. Connect these midpts. to the endpts. of diag Draw an acute. Use the compass to mark the length of diag. 1 on one side of the angle. The other side will e a ase for the trap. Construct a line to the ase through the nonvertex endpt. of diag. 1. Set the compass to the length of diag. and place the point on the non-vertex endpt. of the ase. Draw an arc that intersects the line to the ase. Draw diag. through these two points. Finish y drawing the non- sides of the trap. 60. Impossile; if the diag. of a ~ are, then it would have to e a rectangle and have right. 61. Yes; diag. in a ~ mean it can e a rectangle with opp. sides cm long. 6. Impossile; in a ~, consecutive must e supp., so all must e right. This would make it a rectangle. 63. Given ~ABCD with diag. AC. Let AC isect BAD. Because ABC DAC, AB DA y CPCTC. But since opp. sides of a ~ are, AB CD and BC DA. So AB BC CD DA, and ~ABCD is a rhomus. The new statement is true. Geometry Chapter 6 141

18 Answers for Lesson 6-5, pp Exercises 1. 77, 103, , 69, , 131, , 75, , 115, , 10, a. isosc. trapezoids. 69, 69, 111, , , 45, , , 6, , 40, , 55, 90, 55, , 5, 38, 37, , 90, 90, 90, 46, 34, 56, 44, 56, , Answers may vary. Sample: 18. 1, 1, 1, Explanations may vary. Sample: If oth ' are isected, then this comined with KM KM y the Reflexive Prop. means KLM KNM y SAS. By CPCTC, L N. L and N are opp. ', ut if KLMN is isos., oth pairs of ase ' are also. By the Trans. Prop., all 4 angles are,so KLMN must e a rect. or a square. This contradicts what is given, so KM cannot isect LMN and LKN Geometry Chapter 6 14

19 Answers for Lesson 6-5, pp Exercises (cont.) x 35, y x 18, y Isosc. trapezoid; all the large rt. > appear to e , 68, Yes, the can e otuse. 3. Yes, the can e otuse, as well as one other. 33. Yes; if are rt., they are suppl. The other are also suppl. 34. No; if two consecutive are suppl., then another pair must e also ecause one pair of opp. is. Therefore, the opp. would e, which means the figure would e a ~ and not a kite. 35. Yes; the may e 45 each. 36. No; if two consecutive were compl., then the kite would e concave. 37. Rhomuses and squares would e kites since opp. sides can e also. Geometry Chapter 6 143

20 Answers for Lesson 6-5, pp Exercises (cont.) ABCD is an isos. trapezoid, AB DC. (Given). Draw AE DC. (Two points determine a line.) 3. AD EC (Def. of a trapezoid) 4. AECD is a ~. (Def. of a ~) 5. C 1 (Corr. are.) 6. DC AE (Opp. sides of a ~ are.) 7. AB AE (Trans. Prop. of ) 8. AEB is an isosc.. (Def. of an isosc. ) 9. B 1 (Base of an isosc. are.) 10. B C (Trans. Prop. of ) 11. B and BAD are suppl., C and CDA are suppl. (Same side int. are suppl.) 1. BAD CDA (Suppl. of are.) 39. Answers may vary. Sample: Draw TA and RP. 1. isosc. trapezoid TRAP (Given). TA PR (Diag. of an isosc. trap. are.) 3. TR PA (Given) 4. RA RA (Refl. Prop. of ) 5. TRA PAR (SSS) 6. RTA APR (CPCTC) Geometry Chapter 6 144

21 Answers for Lesson 6-5, pp Exercises (cont.) 40. Draw BI as descried, then draw BT and BP. 1. TR PA (Given). R A (Base of isosc. trap. are.) 3. RB AB (Def. of isector) 4. TRB PAB (SAS) 5. BT BP (CPCTC) 6. RBT ABP (CPCTC) 7. TBI PBI (Compl. of are.) 8. BI BI (Refl. Prop. of ) 9. TBI PBI (SAS) 10. BIT BIP (CPCTC) 11. BIT and BIP are rt..( suppl. are rt..) 1. TI PI (CPCTC) 13. BI is # is. of TP. (Def. of # is.) Check students justifications. Samples are given. 41. It is one half the sum of the lengths of the ases; draw a diag. of the trap. to form >. The ases B and of the trap. are each a ase of a. Then the segment joining the midpts. of the non- sides is the sum of the midsegments of the >. 1 1 This sum is B (B ). 1 Geometry Chapter 6 145

22 Answers for Lesson 6-5, pp Exercises (cont.) 4. It is one half the difference of the lengths of the ases. By the Midsegment Thm. and the Post., midpoints L, M, N, and P are collinear. MN 5 LN LM 5 1 B 1 ( Midsegment Thm.) 5 1 (B ). L M N P 43. D is any point on such that ND BN and D is elow N AB CB, AD CD (Given). BD BD (Refl. Prop. of ) 3. ABD CBD (SSS) 4. A C (CPCTC) A B D B C * BN ) Geometry Chapter 6 146

23 Answers for Lesson 6-6, pp Exercises 1. a. (a,0). (0, ) c. (a, ) d. e. f. " 1 a " 1 a " 1 a g. MA MB MC. W(0, h); Z(, 0) 3. W(a, a); Z(a, 0) 4. W(, ); Z(, ) 5. W(0, ); Z(a,0) 6. W( r, 0); Z(0, t) 7. W(, c); Z(0, c) 8. Answers may vary. Sample: r 3, t ; slopes are and ; all lengths are "13; the opp. sides have the same slope, so they are. The 4 sides are. 9. a. Diag. of a rhomus are #.. Diag. of a ~ that is not a rhomus are not # Answers may vary. Samples are given. 10. A, C, H, F 11. B, D, H, F 1. A, B, F, E 13. A, C, G, E 14. A, C, F, E 15. A, D, G, F 16. W(0, h); Z(, 0) 17. W(a, a); Z(a, 0) 18. W(,); Z(, ) 19. W(0, ); Z(a, 0) 0. W( r, 0); Z(0, t) 1. W(,c); Z(0, c). A 3 3 Geometry Chapter 6 147

24 Answers for Lesson 6-6, pp Exercises (cont.) 3. (c a, ) 4. (a,0) 35. (,0) 6. a. (0, ) y x (, 0) O (, 0) (0, ). (, 0), (0, ), (, 0), (0, ) 7 a. c. " d. 1, 1 e. Yes, ecause the product of the slopes is 1.. c. d. y (, c) x O (, 0) (0, c) y O x (, 0) (, 0) " 1 4c " 1 4c e. The lengths are. y 8. (0, ) x (, 0) O (, 0) (0, ) Geometry Chapter 6 148

25 Answers for Lesson 6-6, pp Exercises (cont.) 9. Step 1: (0, 0) Step : (a,0) Step 3: Since m 1 m , 1 and must e compl. 3 and are the acute of a rt.. Step 4: (, 0) Step 5: (, a) Step 6: Using the formula for slope, the slope for / 1 the slope for /. Mult. the slopes, a a a? 1. a and Geometry Chapter 6 149

26 Answers for Lesson 6-7, pp Exercises 1. a. W ; Z. W(a, ); Z(c e, d) c. W(a,); Z(c e,d) d. c; it uses multiples of to name the coordinates of W and Z.. a. origin 3. a. y-axis. x-axis. Distance c. Qa, R Q c 1 e, d R d. coordinates 4. a. rt.. legs c. multiples of d. M e. N f. Midpoint g. Distance 5. a. isos.. x-axis c. y-axis d. midpts. e. sides f. slopes g. the Distance Formula Geometry Chapter 6 150

27 Answers for Lesson 6-7, pp Exercises (cont.) 6. a.. 7. a. "( 1 a) 1 c "(a 1 ) 1 c "a 1. "a 1 8. a. D( a, c), E(0, c), F(a, c), G(0, 0). c. "(a 1 ) 1 c "(a 1 ) 1 c d. e. f. g. h. i. c a 1 c a 1 c a 1 c a 1 j. sides k. DEFG 9. a. (a, ) "(a 1 ) 1 c "(a 1 ) 1 c. (a, ) c. the same point 10. Answers may vary. Sample: The Midsegment Thm.; the segment connecting the midpts. of sides of the is to the 3rd side and half its length; you can use the Midpoint Formula and the Distance Formula to prove the statement directly. Geometry Chapter 6 151

28 Answers for Lesson 6-7, pp Exercises (cont.) 11. The vertices of KLMN are L(, a c), M(, c), N(, c), and K(, a c). The slopes of KL and MN are zero, so these segments are horizontal. The endpoints of KN have equal x-coordinates and so do the endpoints of LM. So these segments are vertical. Hence opposite sides of KLMN are parallel and consecutive sides are #. It follows that KLMN is a rectangle Answers may vary. Samples are given. 1. yes; Dist. Formula 13. yes; same slope 14. yes; prod. of slopes no; may not have intersection pt. 16. no; may need measures 17. no; may need measures 18. yes; prod. of slopes of sides of A yes; Dist. Formula 0. yes; Dist. Formula, sides 1. no; may need measures. yes; intersection pt. for all 3 segments 3. yes; Dist. Formula, AB BC CD AD 4. A 5. 1, 4, 7 Geometry Chapter 6 15

29 Answers for Lesson 6-7, pp Exercises (cont.) 6. 0,,4,6, , 0.4, 1.6,.8, 4, 5., 6.4, 7.6, , 1.5, 1.8,...,9.5, , Q 1 n R, 3 Q 1 n R,..., (n 1) 30. (0, 7.5), (3, 10), (6, 1.5) 31. Q 1, 6, Q 1, 8, (3, 10), Q 5, 11, Q 7, ( 1.8, 6), ( 0.6, 7), (0.6, 8), (1.8, 9), (3, 10), (4., 11), (5.4, 1), (6.6, 13), (7.8, 14) 33. (.76, 5.), (.5, 5.4), (.8, 5.6),...,(8.5, 14.6), (8.76, 14.8) 34. 3,5, 3,5,..., Q Q 1 n 3 R 1 n 3 (n 1), 5 (n 1) 35. a. L(, d), M( c, d), N(c,0) * ) AM * ) CL. : y x; :y (x c); : y (x c) ( 1 c) 1 3 R c. P Q 3, 10 n R Q 1 n R d 1 c d c d 3 R * BN ) Q 1 n R * ) * ) AM CL AM 5 "( 1 c) 1 d d. Pt. P satisfies the eqs. for and. e. ; AP 5 $Q 3 R 1 Q d 3 R $Q 3 R Q( 1 c) 1 d R 5 Q 3 R Q 10 n R R d c 1 3 R Q 10 n R R The other distances are found similarly. ( 1 c) Q 1 n R 3 "( 1 c) 1 d 5 3 AM Geometry Chapter 6 153

30 Answers for Lesson 6-7, pp Exercises (cont.) 36. a. c. Let a pt. on line p e (x, y). Then the eq. of p is x a or y (x a). c. x 0 d. When x 0, y (x a) ( a). So p and e. q intersect at 0,. f. Let a pt. on line r e (x, y). Then the eq. of r is or y (x ). g. (0 ) h. 0, 37. Assume a. a, a R,..., a (n 1) 38. Assume a, d c. a, c, Q Q a c Q a c c a c a c a c R a,c,..., Q n a R Q n a R a (n 1), c (n 1) Q Q n a R c a c R a n Q Q d n c RR a n 39. a. The > with ases d and, and heights c and a, respectively, have the same area. They share the small right with ase d and height c, and the remaining areas are > with ase c and height ( d). So 1 ad 5 1 c. Mult. oth sides y gives ad c. a Q n a. The diagram shows that d, since oth represent the slope of the top segment of the. So y (a), ad c. c c d c n R Q d n c RR a c y 0 y 0 x a c c Geometry Chapter 6 154

31 Answers for Lesson 6-7, pp Exercises (cont.) 40. Divide the quad. into >. Find the centroid for each and connect them. Now divide the quad. into other > and follow the same steps. Where the two lines meet connecting the centroids of the 4 > is the centroid of the quad. 41. a. Horiz. lines have slope 0, and vert. lines have undef. slope. Neither could e mult. to get 1.. Assume the lines do not intersect. Then they have the same slope, say m. Then m?m m 1, which is impossile. So the lines must intersect. c. Let the eq. for / 1 e y 5 ax, and for / e y 5 a x, and the origin e the int. point. A y C B y x x a a a x y x Define C(a, ), A(0, 0), and BQa, a R. Using the Distance Formula, AC 5 "a 1, BA 5 $a 1 a4, and CB 5 1 a. Then AC 1 BA 5 CB, and m A 90 y the Conv. of the Pythagorean Thm. So / 1 # /. Geometry Chapter 6 155