1. Similar Triangles

2. Similar figures have the same shape but not necessarily the same size.
When naming similar figures, list the letters of the corresponding vertices in the same order. ∆ABC ~ ∆DEF.
Two figures are similar if
The measures of their corresponding angles are equal.
The ratios of the lengths of the corresponding sides are proportional.

3. Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.
82◦
Corresponding angles D E F
Corresponding sides A B C
55◦
43◦

4. = = = = G A C H F B Small Large
Determine if the shapes are proportional. Do not rely on a visual G A
4 in C
28 in
16 in
1. Highlight corresponding sides
7 in
10 in H
2. Set up proportions F
40 in
3. Simplify B
Small
4 in
10 in
7 in = =
Large
40 in
28 in
16 in
1 in
1 in
1 in = =
4 in
4 in
4 in

5. The traffic light is about 30 feet tall.
City officials want to know the height of a traffic light. Estimate the height of the traffic light.
27.25 15
48.75 h =
Write a proportion. 27 15 49 h
Use rounded numbers to estimate. ≈
h ft 9 5 49 h ≈
Simplify.
9h ≈ 245
Solve proportions.
27.25 ft
48.75 ft
h ≈ 27
The traffic light is about 30 feet tall.

6. Assignment

7. You will need two different colored highlighters
Date ____________
Similar Triangles
You will need two different colored highlighters

8. Similar figures have the __________ shape but not necessarily the same size.
When naming similar figures, list the letters of the corresponding vertices in the _______________________. ∆ABC ~ ∆DEF.
Two figures are similar if
The measures of their corresponding angles are __________.
The ratios of the lengths of the corresponding sides are _________________.

9. Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.
82◦
Corresponding angles D E F
Corresponding sides A B C
55◦
43◦

10. = = = = G A C H F B Small Large
Determine if the shapes are proportional. Do not rely on a visual G A C 1. H 2. F 3. B
Small = =
Large = =

11. City officials want to know the height of a traffic light
City officials want to know the height of a traffic light. Estimate the height of the traffic light. = ≈
h ft ≈ ≈
27.25 ft
48.75 ft