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Name _________________________________ Period_________ Date________________ Adapted from Corbin/Lyons Dilations & Similarity #1 1. What does similarity mean? ______________________ 2. What does the symbol ∼ mean? _________________________ y 5 A′ 3. Name the transformation(s) that show that ABC ABC . A x 4. Using the Pythagorean Theorem, find the measurement ̅̅̅̅̅. ̅̅̅̅ and 𝐴′𝐶′ of 𝐴𝐶 B′ B C C′ -5 -5 5 5. Replace the side lengths that correspond to each segment to show the ratios are proportional. AB AB BC BC AC AC BC BC AB AB AC AC 6. The pair of triangles in the figure is similar. What is the value of x? 20 in. x 3 in. y 4 in. Proportion _______________ 16 in. 7. Using the same figure above, what is the value of y? Proportion _________________ Solution__________ Solution____________ ̅? 8. ∆ 𝐽𝐾𝐿 is similar to ∆ 𝑅𝑆𝑇. What is the value of 𝐽𝐿 J R 10 Proportion _______________ K L 10 S Solution____________ T 8 ̅̅̅̅ = 15, 𝐴𝐶 ̅̅̅̅ = 9, 𝑎𝑛𝑑 𝐴𝐷 ̅̅̅̅ = 5, then find 𝐴𝐹 ̅̅̅̅ . 9. ∆ 𝐴𝐵𝐶 ~∆ 𝐴𝐷𝐹 (~ means “similar to”). If 𝐴𝐵 A D F Proportion _________________ B Solution__________ C 10. Polygon 𝐴𝐵𝐶𝐷 is similar to polygon 𝐸𝐹𝐻𝐺. Using the values in this diagram, find x. 20 A B 15 E F x y 12 H G Proportion _________________ D 10 Solution__________ C 11. Using the diagram above, find the value for y. Proportion _________________ Solution__________ 12. At the same time of day, a man who is 6 feet tall casts an 8-foot shadow and his son casts a 4 foot shadow. What is the height of the man’s son? Proportion _________________ Solution__________ 13. Draw two similar quadrilaterals and label the sides and the angles to show they are similar.