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TOPIC 9-3: MORE SIMILAR POLYGONS TERM DEFINITION Common Ratio SKETCH The ratio of the lengths of two corresponding sides. EXAMPLE 1 Use the similar figures below to answer the questions that follow. D 10 A 8 5 B 6 C H 5 E 4 2.5 F 3 G What is the common ratio of quadrilateral ABCD to quadrilateral EFGH above? EXAMPLE 2 Show that the ratio of the perimeters is the same as the common ratio. EXAMPLE 3 What is the common ratio of quadrilateral EFGH to quadrilateral ABCD in EXAMPLE 1? EXAMPLE 4 Determine if the figures are similar. Justify your answer. 37 9 18 6 12 53 3 2 EXAMPLE 5 Use the similar figures below to answer the questions that follow. H A 2.5 z B 3 12 D x C E 10 5 F y G a) Quad EFGH Quad _________________. b) What is their common ratio?_____________ c) Find the following: x = ____________ y = ____________ z = ____________ d) What is the ratio of their perimeters?__________ e) How do b) and d) compare?__________________________ EXAMPLE 6 Use the similar figures below to answer the questions that follow. V U x R y+2 S T 18 E D 3 A 5 B 4 C a) Find the common ratio of polygon RSTUV to polygon ABCDE:___________ b) Find the values of: x = __________ y = __________ EXAMPLE 7 Quad ABCD Quad EFGH below. Answer the following questions. 21 E A 100 60 F B 9 5 D 6 C H a) Complete the following: mE = __________ 18 G c) Find the following: mG = __________ EH = __________ mB = __________ BC = __________ mH = __________ AB = __________ b) What is the common ratio of Quad ABCD to Quad EFGH?__________ EXAMPLE 8 The lengths of the sides of a triangle are in the ratio 3:5:7. Its perimeter is 120 cm. Find the length of the shortest side of the triangle. EXAMPLE 9 The measures of the angles of a triangle are in the ratios 1:2:3. Find the measure of the largest angle.