Challenge: Skills and Applications For use with pages P( 1, 4) R( 3, 1)
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1 LESSON 8.4 NME TE hallenge: Skills and pplications For use with pages 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. In the diagram, is a parallelogram. a. Name three triangles that are similar to EF. (For each triangle, give the vertices in the correct, corresponding order.) E F b. Write a paragraph proof for our result. G H In Eercises 8, refer to the diagram. Find the coordinates of the missing point so that the similarit statement is true. (There ma be more than one correct answer.). Given PQR ~ STU, find the coordinates of U. 4. Given PQR ~ VST, find the coordinates of V.. Given PQR ~ SWT, find the coordinates of W. 6. Given PQR ~ TSX, find the coordinates of X. 7. Given PQR ~ YTS, find the coordinates of Y. 8. Given PQR ~ TZS, find the coordinates of Z. P( 1, 4) R(, 1) 9. etermine if the following conjecture is true or false. If it is true, write a paragraph proof; if it is false, sketch or describe a countereample. If the corresponding angles of quadrilaterals and EFGH are congruent, then ~ EFGH. 10. To estimate the radius of the sun, a student punches a tin hole in a piece of paper and allows the sun to shine through the hole, forming an image on a screen 00 cm awa. If the image has a radius of 0.6 cm and the student knows that the sun is 10,000,000 km awa, what is the student s estimate of the radius of the sun? (Illustration is not to scale.) Q( 1, 1) S(0, 0) T(6, 0) Lesson 8.4 r 10,000,000 km 00 cm 0.6 cm image 6 Geometr hapter 8 Resource ook opright Mcougal Littell Inc. ll rights reserved.
2 nswer Ke hapter 8 Lesson 8.4 hallenge: Skills and pplications 1. a. VWX ~ ZYX b. Sample answer: Since VW YZ, the lternate Interior ngles Theorem gives V Z and W Y. So, b the Similarit Postulate, VWX ~ ZYX.. a. EH, GH, GF b. Sample answer: Prove EF ~ EH: Since is a parallelogram,. So, b the orresponding ngles Postulate, EF. lso, b the Refleive Propert of ongruence, E E. So b the Similarit Postulate, EF ~ EH. Prove EF ~ GH: Since is a parallelogram, and. So b the orresponding ngles Postulate, E GH and FE H. So, b the Similarit Postulate, EF ~ GH. Prove EF ~ GF: Since is a parallelogram,. So, b the lternate Interior ngles Theorem, E GF. lso, b the Vertical ngles Theorem, FE FG. So, b the Similarit Postulate, EF ~ GF.. 6, 4, 6, , 9, 0, , 6 1, 4 1, , 4, 0, , 9, 6, , 6 1, 4 1, false; Sample answer: Let be a square and let EFGH be a nonsquare rectangle ,000 km
3 LESSON 8.4 NME TE Practice For use with pages The triangles shown are similar. List all the pairs of congruent angles and write the statement of proportionalit. 1.. S. R Q R T M T W V U L O T N etermine whether the triangles can be proved similar. If the are similar, write a similarit statement. If the are not similar, eplain wh. 4. Y. H G 6. X M T X N Z L M 7 18 N R J T K 7. P E Q U T V S M N O R The triangles are similar. Find the value of the variables Write a paragraph or a two-column proof. 1. Given: is a right triangle. is an altitude. Prove: ~ Lesson 8.4 opright Mcougal Littell Inc. ll rights reserved. Geometr 7 hapter 8 Resource ook
4 nswer Ke hapter 8 Lesson 8.4 Practice 1. Q, R, T; ~ QRT. S UTV, W UVT, TUV SUW; SUW ~ TUV. R M, L MON, MNO RTL, RLT ~ MON 4. not enough information. es; LMN ~ HG 6. es; XTR ~ KJ 7. es; QNM ~ PNO 8. es; ~ E 9. es; RSV ~ RTU 10., , Statements Reasons 1. is a right. 1. Given. is an altitude.. Given.. ef. of altitude 4. is a right. 4. lines intersect to form right... ll right are Refleive Prop. of ongruence 7. ~ 7. ~ Postulate
5 nswer Ke hapter 8 Lesson 8.4 Practice 1. Q, R, T; ~ QRT. S UTV, W UVT, TUV SUW; SUW ~ TUV. R M, L MON, MNO RTL, RLT ~ MON 4. not enough information. es; LMN ~ HG 6. es; XTR ~ KJ 7. es; QNM ~ PNO 8. es; ~ E 9. es; RSV ~ RTU 10., , Statements Reasons 1. is a right. 1. Given. is an altitude.. Given.. ef. of altitude 4. is a right. 4. lines intersect to form right... ll right are Refleive Prop. of ongruence 7. ~ 7. ~ Postulate
6 Lesson 8. LESSON 8. NME TE Practice For use with pages re the triangles similar? If so, state the similarit and the postulate or theorem that justifies our answer. 1.. F G. I L H J E K M P N raw the given triangles roughl to scale. Then, name a postulate or theorem that can be used to prove that the triangles are similar. 4. In, m 8 and m 94. In XYZ, m Y 94 and m Z 48.. The ratio of to XY is :. In, m 7, and in XYZ, m Y 7. The ratio of to YZ is :. 6. In, m 0, 4, and 9. In XYZ, m Y 0, XY and YZ 4.. Use the diagram shown to complete the statements. 7. m GE? 8. m EG? F? 10. G? EG? 1. Name the three pairs of triangles that are similar in the figure. E F 10 G Write a paragraph or a two-column proof. 1. Given: is equilateral. 14. Given: is a trapezoid E, F, EF are midsegments. with and as bases. Prove: ~ FE Prove: E ~ E E F E 7 Geometr hapter 8 Resource ook opright Mcougal Littell Inc. ll rights reserved.
7 nswer Ke hapter 8 Lesson 8. Practice 1. es; ~ E; Similarit Postulate. no. es; MP~ LMN; SS Similarit Theorem 4.. X X 8 94 Similarit Postulate SS Similarit Theorem 6. X Y 4. Z Y 48 SS Similarit Theorem 9 Z 1. ~ GF, ~ EF, ~ GE 1. Statements Reasons 1. is equilateral. 1. Given.. ef. of equilateral. E, F, and EF. Given are midsegments. 4. EF 1,, 4. Midsegment F 1 Thm.. ~ FE. SSS Similarit Thm. 14. Statements Reasons 1. is a trapezoid. 1. Given. and are bases.. Given.. ef. of base of trapezoid 4. E E 4. orresponding Postulate. E E. orresponding Postulate 6. E E 6. Similarit Postulate 7 7 Y Z
8 LESSON 8.7 NME TE Practice For use with pages 06 1 Identif the dilation, and find its scale factor. Then, find the values of the variables. 1. P. P 9 1. P 8 4 P 6 4. P 4. P z P P Use the origin as the center of the dilation and the given scale factor to find the coordinates of the vertices of the image of the polgon.. k 6. k N H I Lesson 8.7 M 1 1 L 7. You are making hand shadows on a wall using a flashlight. You hold our hand 1 foot from the flashlight and feet from the wall. Your hand is parallel to the wall. If the measure from our thumb to ring finger is 6 inches, what will be the distance between them in the shadow? G 1 1 J opright Mcougal Littell Inc. ll rights reserved. Geometr 10 hapter 8 Resource ook
9 nswer Ke hapter 8 Lesson 8.7 Practice 1. The dilation has center and scale factor ; 0, 10.. The dilation has center 9 and scale factor 7 4, 7 4 ;.. The dilation has center and scale factor ; 1, 1, z The dilation has center and scale factor ; M, 4, N 4, 8, L 4, G,, H 0, 1, I 0, 1., J 1, in.
10 LESSON 11. NME TE Practice For use with pages The polgons shown are similar. Find the ratio (shaded to unshaded) of their perimeters and of their areas Solve.. The perimeter of an equilateral triangle is 48 centimeters. smaller equilateral triangle has a side length of 6 centimeters. What is the ratio of the areas of the larger triangle to the smaller triangle? 6. The ratio of the areas of two similar triangles is 84:40. What is the ratio of the lengths of corresponding sides? 7. pentagon has an area of 18 square centimeters. similar pentagon has an area of 180 square centimeters. What is the ratio of the perimeters of the smaller pentagon to the larger pentagon? 8. The dimensions of a rectangle are 8 centimeters b 1 centimeters. What are the dimensions of a similar rectangle with eactl double the area? 9. Find the ratio of the areas of the triangles. 10. Find the ratio of area I to area II I II Lesson Floor plan The floor plan has a scale of 1 inch to 18 feet. a. What is the scale area of the kitchen? What is the actual area? b. What is the scale area of the bedroom? What is the actual area? in in. 4 in. dining room living 8 in. room bath kitchen bedroom opright Mcougal Littell Inc. ll rights reserved. 8 in. Geometr 4 hapter 11 Resource ook
11 nswer Ke hapter 11 Lesson 11. Practice 1. 1 :; 1:. 14:11; 196:11. :; 9: 4. :4; :16. 64:9 6. 1: : 8. 8 cm b 1 cm : :9 11. a in. ; 16 ft 1 b in. ; 16 ft
9.3. Practice C For use with pages Tell whether the triangle is a right triangle.
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1 = 1, b d and c d. Chapter 7. Worked-Out 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)
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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
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hapter 0 opright b Mcougal Littell, a division of Houghton Mifflin ompan. Prerequisite Skills (p. 648). Two similar triangles have congruent corresponding angles and proportional corresponding sides..
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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
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hapter 7 Maintaining Mathematical 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) = 1 7 7 1 x = 3 1 1 x = x 1 = 1 x = 3. 3(x 5) + 8(x 5) =
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