1. Section 3 - Using Similar Triangles
Goal: You will use proportions to identify similar polygons.

2. 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

3. 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

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

5. 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: _______

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

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

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

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

10. Example 6:
Find the length of

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

12. Example 8: Similar Triangles and Radiation Therapy
Video

13. Similar Triangles and Radiation Therapy

14. 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?

15. 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?

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

17. 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.