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Name: ____________KEY_________________ CP Geometry Chapter 6 Review 1. Find the measure of the largest angle of a triangle is the measures of its interior angles are in the ratio 3:5:7. 2. ANS: ______84°__________ Find the measure of the vertex angle of an isosceles triangle if the measures of the vertex angle and a base angle have the ratio 4:3. 3. ANS: ______72°__________ The measures of a pair of consecutive angles of a parallelogram have the ratio 5:7. Find the measure of each angle of the parallelogram. 4. Solve for x. ANS: ____75°, 105°______ 5. a. 2 8 x = 24 6 x d. 4 1 x=5 x 3 x 3 b. 2 x x = ±10 x 50 e. 3 x4 x 7 c. 2x 5 9 x = 5.875 3 4 x = 7, -3 If KW EG , find the length of the indicated segments. E a. HE = 20, KE = 12, WG = 9, HG = __15____ K b. KH = 7, KE = 14, HG = 12, HW = ___4______ c. HW = 4, WG = 12, HE = 28, KH = __7_______ G W d. KH = 9, KE = 12, HG = 42, WG = ___24______ e. KH = 2x - 15, KE = x, HW = 1, HG = 4. Find KH and KE. ____3; 9_____________ 6. 7. 8. SHE . Name three pairs of congruent angles and three equal ratios. GA AL GL _____ G S ; A H ; L E ; _______________________________ SH HE SE The ratio of two similar polygons is 3:5. If the length of the shortest side of the smaller polygon is 24, find the length of the shortest side of the larger polygon. ____40___________ GAL ZAP MYX . If ZA = 3, AP = 12, ZP = 21 and YX = 20, find the lengths of the remaining sides of MYX . ___MY = 5; MX = 35_____________________ H 9. Quadrilateral ABCD is similar to quadrilateral RSTW. The lengths of the sides of quadrilateral ABCD are 3, 6, 9, and 15. If the length of the longest side of quadrilateral RSTW is 20, find the perimeter of RSTW. ______ 44_______________ 10. RST JKL a. RA and JB are medians to sides ST and KL , respectively. RS = 10 and JK = 15. If the length of JB exceeds the length of RA by 4, find the length of medians JB and RA . RA = 8; JB = 12 b. SH and KO are altitudes to sides RT and JL , respectively. If SH = 12, KO = 15, LK = 3x -2, and TS = 2x + 1, find the lengths of LK and TS . __ LK = 17.5; TS = 14____ c. The perimeter of RST is 25 and the perimeter of JKL is 40. If ST = 3x + 1 and KL = 4x + 4, find the lengths of ST and KL . ____ ST = 10; KL = 16____ d. The ratio of RST to JKL is 3:x. The length of altitude SU is x - 4 and the length of altitude KV is 15. Find the length of altitude SU . _____ 5_______ Given: XW = XY, HA WY , KB WY Prove: HWA KYB 11. Statement 1. XW = XY, HA WY , KB WY 2. W Y HAW , KBY are rt. 3. 4. HAW KBY 5. HWA KYB X K H W 12. A Given: EF is the midsegment of Prove: (EI)(CG) = (CI)(EF) ABC F I 13. C G Statement Given: HW TA W HY AX T H Prove: Statement 1. EF is midsegment ABC 2. EF AC 3. FEI GCI 4. EIF CIG 5. EIF CIG EI CI 6. EF CG 7. (EI)(CG) = (CI)(EF) B A 2. 3. 4. 5. BAT Def. of lines Rt. angles are AA Sim. Post. Y B E Reason 1. Given A AX AT HY HW X Y 1. HW TA ; HY AX 2. W ATX ; Y AXT 3. AXT HYW AX AT 4. HY HW Reason 1. Given 2. Def. of midsegment 3. 4. 5. 6. PAI VAT AA Sim. Post. CSSTP 7. Cross Prod. = Reason 1. Given 2. PAI 3. AA Sim. Post. 4. CSSTP