1. SOLUTION EXAMPLE 2 Standardized Test Practice Corresponding side lengths are proportional. KL NP = LM PQ KL 12m = 10m 5m5m KL= 24 Write a proportion. Substitute given values. Solve the proportion.

2. EXAMPLE 2 Standardized Test Practice ANSWER The length of KL is 24 meters. The correct answer is C.

3. 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.

4. SOLUTION EXAMPLE 3 Using Indirect Measurement You can use a proportion to find the height of the tree. Tree’s height Alma’s height = Length of tree’s shadow Length of Alma’s shadow Write a proportion. Substitute given values. x feet 5 feet = 14feet 7 feet x 10 = Solve the proportion. ANSWER The tree is 10 feet tall.

5. 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. Original Image (x, y) A (–1, –1 ) B( 0, 1 ) C( 2, 2 ) D( 3, 0 ) Graph the image of the quadrilateral. ( 3 x, 3 y) A’ (– 3, – 3 ) B’( 0, 3 ) C’( 6, 6 ) D’( 9, 0 )

6. GUIDED PRACTICE 2. At the right, ABCD, FGHJ. Find the value of x. for Examples 2, 3 and 4 x= 8 ANSWER

7. GUIDED PRACTICE for Examples 2, 3 and 4 What If? Suppose the tree in Example 3 casts a shadow of 18 feet, a 6 foot tall person casts a 9 foot shadow, and the triangles are similar. Find the height of the tree. 3. ANSWER The tree is 12 feet tall.

8. GUIDED PRACTICE 4. Graph RST with vertices R(1, 1), S(3, 2), and T(2, 3). Then graph its image after a dilation using a scale factor of 2. for Examples 2, 3 and 4 ANSWER