1. EQ: How do you show 2 triangles are similar?
7.3
OBJ: Show that two triangles are similar using the AA Similarity Postulate
EQ: How do you show 2 triangles are similar?

2. Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

4. Determine whether the triangles are similar. If they are similar,
Example 1
Use the AA Similarity Postulate
Determine whether the triangles
are similar. If they are similar,
write a similarity statement.
Explain your reasoning.
SOLUTION
If two pairs of angles are congruent, then the triangles are similar. 1.
G  L because they are both marked as right angles.

5. Find mF to determine whether F is congruent to J.
Example 1
Use the AA Similarity Postulate 2.
Find mF to determine whether F is congruent to J.
mF + 90° + 61° = 180°
Triangle Sum Theorem
mF ° = 180°
Add.
mF = 29°
Subtract 151° from each side.
Both F and J measure 29°, so F  J.
ANSWER
By the AA Similarity Postulate, FGH ~ JLK

6. Are you given enough information to show that RST is similar to
Example 2
Use the AA Similarity Postulate
Are you given enough information to show that RST is similar to
RUV? Explain your reasoning.
SOLUTION
Redraw the diagram as two triangles: RUV and RST.
RST  RUV.
R  R by the Reflexive Property of Congruence.
Using AA Similarity Postulate, RST ~ RUV.

7. Checkpoint
Use the AA Similarity Postulate
Determine whether the triangles are similar. If they are similar, write a similarity statement. 1.

8. Checkpoint
Use the AA Similarity Postulate
Determine whether the triangles are similar. If they are similar, write a similarity statement. 1. 8

9. Checkpoint
Use the AA Similarity Postulate
Determine whether the triangles are similar. If they are similar, write a similarity statement. 2.
ANSWER
yes; GLH ~ GKJ 9

10. Checkpoint
Use Similar Triangles
Write a similarity statement for the triangles. Then find the value of the variable. 3. 10

11. 5 = 15 3 y 5y = 3(15) 5y = 45 Y = 9 Checkpoint
Use Similar Triangles
Write a similarity statement for the triangles. Then find the value of the variable. 3.
5 = 15 y
5y = 3(15)
5y = 45
Y = 9 11

12. Homework
Worksheet 7.3A
Quiz