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Name: ______________________ Class: _________________ Date: _________ Geometry Chapter 6 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Determine whether each pair of figures is similar. Justify your answer. ____ 1. a. b. c. d. ΔDEF ∼ ΔCBA because the corresponding angles are congruent. ΔDEF is not similar to ΔCBA because the corresponding angles are not congruent. ΔDEF ∼ ΔCBA because the ratio of the corresponding sides is proportional and the corresponding angles are congruent. ΔDEF is not similar to ΔCBA because the ratio of the corresponding sides is not proportional. 1 ID: A Name: ______________________ ____ ID: A 2. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation. D: (x, y) → (4x, 4y) A(2, 1), B(4, 1), C(4, − 3) a. b. c. d. This is a dilation –12). This is a dilation This is a dilation C’(1, –0.75). This is a dilation –0.75). about (0, 0) with a scale factor of 0.25; A’(8, 4), B’(16, 4), C’(16, about (0, 0) with a scale factor of 4; A’(8, 4), B’(16, 4), C’(16, –12). about (0, 0) with a scale factor of 0.25; A’(0.5, 0.25), B’(1, 0.25), about (0, 0) with a scale factor of 4; A’(0.5, 0.25), B’(1, 0.25), C’(1, Short Answer Solve each proportion. 3. x+1 14 = x−1 20 2 Name: ______________________ ID: A Identify the similar triangles. Find x. 4. Determine whether each pair of triangles is similar. Justify your answer. 5. Find x and the measures of the indicated parts. 6. AB 7. EB and ED 3 Name: ______________________ ID: A 8. BC and AC 9. BD and CE BD = 4x CE = 2x + 2 10. Find x so that QS Ä PT. PQ = 8, QR = 5, RS = 15, ST = x + 3 4 Name: ______________________ ID: A 11. Determine whether QS Ä PT. Justify your answer. PQ = 18, QR = 6, RS = 12, ST = 36 Find the perimeter of the given triangle. 12. ABC, if ABC ∼ PQR, perimeter of PQR = 36, AC = 12, PR = 6 13. PQR, if PQR ∼ PST, QR = 15, ST = 10, PS = 9, and PT = 8 5 Name: ______________________ ID: A 14. Find PS if ABC ∼ PQR, AD is an altitude of PQR, AD = 12, AC = 16, and PR = 10. ABC, PS is an altitude of 15. Find AB if BD and QS are altitudes and PQR. ABC ∼ 16. Are the two triangles similar? How do you know? Which theorem or postulate proves the two triangles are similar? 17. 6 Name: ______________________ ID: A 18. 19. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. D: (x, y) → (3x, 3y) J(1, 4), K(6, 4), L(6, 1), M(1, 1) 7 ID: A Geometry Chapter 6 Review Answer Section MULTIPLE CHOICE 1. ANS: B 2. ANS: B MSC: DOK 2 SHORT ANSWER 3. ANS: 17 −3 4. ANS: ΔABC ∼ ΔEDF; x = 3 5. ANS: yes; ΔEDF ∼ ΔBCA by SAS Similarity 6. ANS: x = 7, AB = 20 7. ANS: x = 3, EB = 15, ED = 42 8. ANS: x = 6, BC = 10, AC = 12 9. ANS: x = 5, BD = 20, CE = 12 10. ANS: 21 11. ANS: PQ ST yes, = =3 QR SR 12. ANS: 72 13. ANS: 40.5 14. ANS: 7.5 15. ANS: 6 16. ANS: yes, by AA∼ MSC: DOK 2 17. ANS: AA Postulate MSC: DOK 2 1 ID: A 18. ANS: AA∼ Postulate MSC: DOK 2 19. ANS: J´(3, 12), K´(18, 12), L´(18, 3), M´(3, 3) MSC: DOK 2 2