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Similar Figures ||| What is the simplified form of all of these ratios? because the ratios of their matching sides were equal. In the last example, the triangles were similar 15 10 = 12 8 = 9 6 = L O Is rectangle LMNO similar to rectangle HIJK? 10 N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? 1. Are the corresponding (matching) 10 angles the same size? Yes. N M 4 No. H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? 1. Are the corresponding (matching) 2. Are the corresponding (matching) sides in the same ratio? angles the same size? 10 Yes. N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? Which side corresponds to LM? 10 N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? Which side corresponds to MN? 10 N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? Write the unsimplified ratio of LM to HI: 10 N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? Write the ratio of MN to IJ: 10 N M 4 H K 8 I J 3 L O Is rectangle LMNO similar to rectangle HIJK? Is the ratio LM:HI equal to the ratio MN:IJ ? 10 10 8 = N M 4 4 3 H K ?? Yes No 8 I J 3 L O Now answer the question: Is rectangle LMNO similar to rectangle HIJK? 10 Yes No N M 4 H K 8 I J 3 L 4 O 1. The angles are equal, but 2. The sides are not in the same ratio. Is rectangle LMNO similar to rectangle HIJK? Now answer the question: 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? 120o 12 12 120∘ D 60o 8 C K 4 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M A 8 60∘ 1. Are the corresponding angles equal? 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 2. Do the sides form the same ratio ? A parallelogram KLMN? Is parallelogram ABCD similar to 8 60∘ Complete this ratio: B 120∘ 12 12 120∘ D 60∘ 8 C AB KL K 4 60∘ = L 120∘ 6 120∘ 6 60∘ N 4 M A 2. Do the sides form the same ratio? parallelogram KLMN? Is parallelogram ABCD similar to 8 60∘ Complete this ratio: B 120∘ 12 12 120∘ D 60∘ 8 C LM BC K 4 60∘ = L 120∘ 6 120∘ 6 60∘ N 4 M 2. Do the sides form the same ratio ? Is parallelogram ABCD similar to A Are the ratios equal ? Yes. 8 60∘ B 120∘ 12 No. 12 120∘ D 60∘ 8 C 8 4 K 4 60∘ parallelogram KLMN? = L 120∘ 6 12 6 120∘ 6 60∘ N 4 M Is parallelogram ABCD similar to A 8 60∘ B 120∘ 12 Yes. 12 120∘ D No. 60∘ 8 C K 4 60∘ parallelogram KLMN? L 120∘ 6 120∘ 6 60∘ N 4 M Is parallelogram ABCD similar to A YES!! Corresponding angles are equal AND corresponding sides are in the same ratio. 8 60∘ B 120∘ 12 12 120∘ D 60∘ 8 C K 4 parallelogram KLMN? 60∘ L 120∘ 6 120∘ 6 60∘ N 4 M Which side corresponds to YZ? CD AB AD XW Complete the ratio: YZ 2 = Solve this simple equation to find the length of YZ. YZ 2 = 16 24 YZ = 24 D A 12 C B 15 Given that trapezoid ABCD ||| trapezoid WZYX, find m. (||| means 'similar to') W m Z 16 Y X 24 D A Given that find m. 12 C B 15 Complete the ratio needed to find m: trapezoid ABCD ||| trapezoid WZYX, W m 24 16 Z 16 = Y X m goes here 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. 24 16 Z = 16 12 m m = Y X 24 D A 12 C B 15 Given that trapezoid ABCD ||| trapezoid WZYX, find YZ. W m Complete the ratio for YZ: Z 16 Y X Write a number here. YZ 24 D A 12 C B 15 W Given that trapezoid ABCD ||| trapezoid WZYX, find YZ. Complete the ratio: m Z 16 YZ 15 Y X = 24 D A 12 C B 15 Given that trapezoid ABCD ||| trapezoid WZYX, find YZ. W 15 YZ m = Z 16 24 16 YZ = Y X C Given ∆ABC ||| ∆DEF, find n. 12 10 A B F 6 n D E Complete this ratio: C Given ∆ABC ||| ∆DEF, find n. 12 10 A B 10 F n 6 n = D E C 12 Given ∆ABC ||| ∆DEF, find n. 10 A B Solve this ratio: F 6 n D E 10 n n = = 12 6 Congratulations!! You have finished. |