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because the ratios of their matching sides made a proportion. In the last example, the triangles were similar What is the simplified form of all of these ratios? 15 10 Their ratios were all equal. = 12 8 = 9 6 = L 4 O Is rectangle LMNO similar to rectangle HIJK? 10 10 N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? 1. Are the corresponding (matching) 10 angles congruent (the same size)? 10 Yes. N M 4 No. 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? 1. Are the corresponding (matching) 2. Do the corresponding (matching) sides form a proportion (make equal fractions)? angles congruent (the same size)? 10 10 Yes. N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? Which side corresponds to LM? 10 10 N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? Which side corresponds to MN? 10 10 N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? Write the ratio of LM to HI: 10 10 N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? Write the ratio of MN to IJ: 10 10 N M 4 3 H K 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? Use cross multiplication to determine if the ratio LM:HI is equal to the ratio MN:IJ. 10 10 10 8 ? N M 4 4 3 3 H K Yes No 8 8 I J 3 L 4 O Is rectangle LMNO similar to rectangle HIJK? 10 • 3 = 30 8 • 4 = 32 if the ratio LM:HI is equal to the ratio MN:IJ. Use cross multiplication to determine 10 10 30 ≠ 32 N M 4 3 H K NO! 8 8 I J 3 L 4 O Now answer the question: Is rectangle LMNO similar to rectangle HIJK? 10 10 Yes No N M 4 3 H K 8 8 I J 3 L 4 O Now answer the question: Is rectangle LMNO similar to rectangle HIJK? 2. The sides do not make a proportion. 1. The angles are congruent. 10 10 NO! N M 4 3 H K 8 8 I J 3 A 8 60∘ B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 120∘ D 60∘ 8 C K 4 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M A 8 60∘ 1. Are the corresponding angles congruent? B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 120∘ Yes. No. D 60∘ 8 C K 4 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M A 8 60∘ 2. Do the sides form a proportion? Complete this ratio: B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 120∘ D 60∘ 8 C 8 K 4 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M A Complete this proportion: 8 60∘ 2. Do the sides form a proportion? B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 120∘ D 60∘ 8 C 8 4 K 4 60∘ = L 120∘ 6 120∘ 6 60∘ N 4 M A Are the cross-products equal? 8 60∘ 2. Do the sides form a proportion? B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ Yes. No. 12 12 120∘ D 60∘ 8 C 8 4 K 4 60∘ = L 120∘ 6 12 6 120∘ 6 60∘ N 4 M What is the cross-product? A 8 60∘ 2. Do the sides form a proportion? B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 120∘ D 60∘ 8 C 8 4 K 4 60∘ = L 120∘ 6 12 6 120∘ 6 60∘ N 4 M A 8 60∘ B Is parallelogram ABCD similar to parallelogram KLMN? 120∘ 12 12 Yes. No. 120∘ D 60∘ 8 C K 4 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M Which side corresponds to YZ? CD AB AD XW Complete the proportion: YZ 2 = equivalent fractions to solve for YZ. Use cross multiplication or YZ 2 = 16 24 YZ = 24 D A 12 C B 15 Given that trapezoid ABCD ~ trapezoid WZYX, find m. W m Z 16 Y X 24 D A 12 C B 15 Complete the proportion used to find m: Given that trapezoid ABCD ~ trapezoid WZYX, find m. W m 16 24 Z 16 = Y X 24 D A 12 C B 15 Given that trapezoid ABCD ~ trapezoid WZYX, find m. W m Use cross multiplication or equivalent fractions to find m. 16 24 Z = 16 m 12 m = Y X 24 D A 12 C B 15 trapezoid ABCD ~ trapezoid WZYX, find YZ. Given that W Complete the ratio for YZ: m Z 16 Y X YZ 24 D A 12 C B 15 trapezoid ABCD ~ trapezoid WZYX, find YZ. Given that W Complete the proportion: m Z 16 Y X YZ 15 = 24 D A 12 C B 15 trapezoid ABCD ~ trapezoid WZYX, find YZ. Given that Use cross-multiplication to find YZ. W 15 YZ m = Z 16 24 16 Y YZ = X C Given ∆ABC ~ ∆DEF Find n. 12 10 A B 11 F 6 n D E 5.5 Complete this proportion: C Given ∆ABC ~ ∆DEF Find n. 12 10 A B 11 10 n F 6 n = D E 5.5 Solve this proportion: C n = Given ∆ABC ~ ∆DEF Find n. 12 10 A B 11 10 n F 6 n = D E 5.5 12 6 How long is side JL? How long is side JK? 15 GOOD JOB! 10 15 How long is side KG? Complete the proportion: 15 t = t = Solve the proportion for t: 15 t = 10 6 |