Download Angle-Angle (AA) Triangle Similarity

Name ______________________________
Angle-Angle Triangle Similarity
Module 2 Lesson 15
Learning Target: I can use the angle-angle criterion for two triangles to be similar.
Opening Exercise
If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of
corresponding sides.
Angle-Angle (AA) Triangle Similarity
1. Explain why the triangles are similar and write a similarity statement.
2. Explain why the triangles are similar and write a similarity statement.
3. Given: 𝐸𝐵 ⊥ 𝐴𝐵 and 𝐷𝐶 ⊥ 𝐴𝐶.
Prove ∆ABE ~ ∆ACD, and then find CD.
4. The triangles shown below are similar. Use what you know about similar triangles to find the
missing side lengths 𝑥 and 𝑦.
5. The triangles shown below are similar. Write an explanation to a student, Claudia, of how to find
the lengths of 𝑥 and 𝑦.
Name ______________________________
Angle-Angle Triangle Similarity
Module 2 Lesson 15
Problem Set
1. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing
angle and side length measures.
28
20
3
8
6
44.42°
57.12°
7
78.46°
57.12°
2. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing
angle and side length measures.
3. In the figure below, △ 𝐿𝑀𝑁~ △ 𝑀𝑃𝐿.
a. Classify △ 𝐿𝑀𝑃 based on what you know about similar triangles and justify your reasoning.
b. If 𝑚∠𝑃 = 20°, find the remaining angles in the diagram.
̅̅̅̅, ̅̅̅̅
4. In the diagram below of ∆𝑃𝑅𝑇, Q is a point on ̅̅̅̅
𝑃𝑅 , S is a point on 𝑇𝑅
𝑄𝑆 is drawn, and ∠𝑅𝑃𝑇 ≅
∠𝑅𝑆𝑄. Which reason justifies the conclusion that ∆𝑃𝑅𝑇~∆𝑆𝑅𝑄?
5. In the diagram of ∆𝐴𝐵𝐶 and ∆𝐸𝐷𝐶 below, ̅̅̅̅
𝐴𝐸 and ̅̅̅̅
𝐵𝐷 intersect at C, and ∠𝐶𝐴𝐵 ≅ ∠𝐶𝐸𝐷.
Which method can be used to show that ∆𝐴𝐵𝐶 must be similar to ∆𝐸𝐷𝐶?
6. The diagram below shows ∆𝐴𝐵𝐶, with ̅̅̅̅̅̅
𝐴𝐸𝐵 , ̅̅̅̅̅̅
𝐴𝐷𝐶 , and ∠𝐴𝐶𝐵 ≅ ∠𝐴𝐸𝐷. Prove that ∆𝐴𝐵𝐶 is
similar to ∆𝐴𝐷𝐸.
7. In the diagram below,
,
,
, and
. Prove that
.
8. In the accompanying diagram,
.
and
and
intersect at point T. Prove that
Name ______________________________
Angle-Angle Triangle Similarity
Given the diagram below and ̅̅̅̅
𝐷𝐸 ∥ ̅̅̅̅
𝐾𝐿, find 𝐹𝐸 and 𝐹𝐿.
Module 2 Lesson 15
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