Section 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

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. AB and DE BC and EF AC and DF 12 2 10 2 8 2 = = = 18 3 15 3 12 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: _______

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

Example 5: ∆ WXY ~ ∆ PQR. Find the perimeter of ∆ WXY.

Example 6: Find the length of .

Example 7: Use proportions with geometric figures In the diagram, . Find and . On Your Own 2: In the example above . Find AC. AC

Example 8: Similar Triangles and Radiation Therapy Video

Similar Triangles and Radiation Therapy

Example 9: The blueprint shows a scale drawing of a cell phone. The length of the antenna on the blueprint is 5 centimeters. The actual length of the antenna is 2 centimeters. What is the scale of the blueprint?

Example 10: You buy a 3-D scale model of the Reunion Tower in Dallas, TX. The actual building is 560 feet tall. Your model is 10 inches tall, and the diameter of the dome on your scale model is about 2.1 inches. What is the diameter of the dome on the actual building?

Activity: Gridding a Canvas 4 x 5 cm 16 x 20 in

Gridding Artwork on a Canvas Elijah printed off a picture 11.4 x 15.2 mm he wanted to recreate on the 16 by 20 in canvas on the right.