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6.3-6.4 Review and Answers January 14, 2010 Bell Ringers ‐ January 13 1. The ratio of the 2 side lengths is given. Solve for the variable AB : AC is 7 : 8 B 14a A C 48 3. The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles. 1 : 1 : 2 2. Solve for x and Dind m∠1 and m∠2. 2 1º x + 1 7 º 5x + 1 1 4. Solve for y and Dind m∠3 and m∠4 4 4x + 24º 3 18x ‐ 18º 6.3-6.4 Review and Answers January 14, 2010 1. List all pairs of congruent angles for the Digures. Then, write the ratios of the corresponding sides in a statement of proportionality. S ∆RST ~ ∆WVU V R T W U ∠R ≅ ∠W RS ST TR = = WV VU UW ∠S ≅ ∠V ∠T ≅ ∠U 2. Determine whether the polygons are similar. If they are, write a similarity statement and Dind the scale factor. D B 5 3 A Yes, ∆ABC ~ ∆FDE 15 C 4 15 = 5 9 F 3 1 12 4 9 3 = 3 1 E 12 = 3 1 3. The polygons are similar as indicated. Find the value of x. BCDE ~ KLMJ B C J K 12 12 D E 8 8 12 = 12 x M x L 8x = 144 x = 18 1 6.3-6.4 Review and Answers January 14, 2010 P 4. In the diagram, WXYZ ~ MNOP a) Find the scale factor of WXYZ to MNOP. 8 = 10 M X W 4 5 x y Z 10 zº 12 8 Y O 135º N b) Find the values x, y, and z. 4 5 12 x = 4x = 60 x = 15 y=8 z = 135º c) Find the perimeter of WXYZ. 12 + 8 + 12 + 8 = 40 d) Find the perimeter of MNOP. 15 + 10 + 15 + 10 = 50 e) Find the ratio of the perimeter of MNOP to the perimeter of WXYZ. 40 = 50 4 5 2 6.3-6.4 Review and Answers January 14, 2010 5. Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. G M K N H ∠GKH ≅ ∠NKM ∠G ≅ ∠N ∆GHK ~ ∆NMK (Vertical Angles ≅ Thm) (Alternate Interior Angles Thm) (Angle ‐ Angle Similarity Postulate) 6. Determine whether the triangles can be proved to be similar. If they are write a similarity statement. Explain your reasoning. Q R U T S ∠S ≅ ∠S (ReDlexive POC) ∠SRT ≅ ∠SQU (Corresponding Angles Thm) ∆SRT ~ ∆SQU (AA Similarity Postulate) 3 6.3-6.4 Review and Answers January 14, 2010 7. The perimeter and the ratio of the length to the width of a rectangle are given. Find the length and width of the rectangle. Perimeter: 480 ft. l : w = 5 : 1 P = 2l + 2w 480 = 2(5x) + 2(x) 480 = 10x + 2x 480 = 12x 40 = x l = 5x = 5(40) = 200 w = 1x = 1(40) = 40 8. Find the geometric mean of the two numbers. Write as a proportion and then solve for the geometric mean. a) 3 and 15 3 x = x 15 2 x = 45 x = √(45) x = √(9 * 5) = 3 √(5) b) 4 and 6 4 x = x2 = 24 x 6 x = √(24) x = √(4 * 6) = 2 √(6) 4