7. EXAMPLE 1 Identifying Similar Polygons STEP 1 Decide whether corresponding angles are congruent. Each angle measures 90 . Tell whether the television screens are similar. A E B F C G D H
8. STEP 2 Decide whether corresponding side lengths are proportional. EXAMPLE 1 Identifying Similar Polygons 30 inches 18 inches 40 inches 24 inches = ? 5 3 = 5 3 ANSWER Yes, quadrilateral ABCD ~ quadrilateral EFGH .
9. SOLUTION EXAMPLE 2 Standardized Test Practice Corresponding side lengths are proportional. Write a proportion. Substitute given values. Solve the proportion. KL NP = LM PQ KL 12 M = 10M 5 M KL = 24
10. EXAMPLE 3 Using Indirect Measurement Height Alma is 5 feet tall and casts a 7 foot shadow. At the same time, a tree casts a 14 foot shadow. The triangles formed are similar. Find the height of the tree.
11. SOLUTION EXAMPLE 3 Using Indirect Measurement You can use a proportion to find the height of the tree. Write a proportion. Substitute given values. Solve the proportion. Tree’s height Alma’s height = Length of tree’s shadow Length of Alma’s shadow x feet 5 feet = 14feet 7 feet x 10 = ANSWER The tree is 10 feet tall.
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17. EXAMPLE 4 Dilating a Polygon Quadrilateral ABCD has vertices A (– 1, – 1), B (0, 1), C (2, 2), and D (3, 0). Dilate using a scale factor of 3 . SOLUTION Original Image (x, y) A (–1, –1 ) B ( 0, 1 ) C ( 2, 2 ) D ( 3, 0 ) ( 3 x , 3 y ) A ’ (– 3, – 3 ) B ’ ( 0, 3 ) C ’ ( 6, 6 ) D ’ ( 9, 0 )
18. EXAMPLE 4 Dilating a Polygon Quadrilateral ABCD has vertices A (– 1, – 1), B (0, 1), C (2, 2), and D (3, 0). Dilate using a scale factor of 3 . SOLUTION Graph the quadrilateral. Find the coordinates of the vertices of the image. Graph the image of the quadrilateral. Original Image (x, y) A (–1, –1 ) B ( 0, 1 ) C ( 2, 2 ) D ( 3, 0 ) ( 3 x , 3 y ) A ’ (– 3, – 3 ) B ’ ( 0, 3 ) C ’ ( 6, 6 ) D ’ ( 9, 0 )
