6.3 Using Similar Triangles Goal: You will use proportions to identify similar polygons.

Two polygons are similar if: congruent corresponding angles are ______________, and corresponding side lengths are _____________. Corresponding angles: Corresponding sides: You write ∆ ABC “is similar to” ∆ DEF as ____________________________ similar A  D, B  E, C  F AB  DE, BC  EF, AC  DF ABC  DEF

Use similarity statements Example 1: ∆ ABC ~ ∆ DEF. a. List all pairs of congruent angles. b. Check that the ratios of corresponding side lengths are equal. c. Write the ratios of corresponding side lengths in a statement of proportionality. A  D, B  E, C  F AB and DE BC and EF AC and DF 12 2 10 2 8 2 = = = 18 3 15 3 12 3 So… AB  DE , BC  EF, and AC  DF because the ratio of each corresponding side length is equal to 2/3.

Scale Factor: The ratio of any two corresponding lengths in two similar figures

Example 2: Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor. Step 1: Identify pairs of congruent angles _____________________________________ Step 2: Show that the corresponding side lengths are proportional Similarity statement: ________________ Scale factor: _______ A  J , B  K, C  L, and D  M Is AB  JK? BC  KL? CD  LM? DA  MJ? 4 ABCD  JKLM 7

Use similar polygons Example 3: In the diagram, ∆ BCD ~ ∆ RST. Find the value of x Example 3:

Use similar polygons Example 4: a. Find the scale factor. b. Find x.

8 4 6 4 3 2 5 10 Perimeter of KLMN 4 + 3 + 5 + 2 14 1 = = Perimeter of PQRS 8 + 6 + 10 + 4 28 2 4 1 5 1 8 2 10 2 3 1 2 1 4 6 2 2

Find perimeters of similar figures Example 5: A larger cement court is being poured for a basketball hoop in place of a smaller one. The court will be 20 feet wide and 25 feet long. The old court was similar in shape, but only 16 feet wide. a. Find the scale factor of the new court to the old court. b. Find the perimeters of the new court and the old court.

Example 6: ∆ WXY ~ ∆ PQR. Find the perimeter of ∆ WXY.

Example 7: In the diagram, ∆FGH ~ ∆JGK. Find the length of the altitude .