AA Similarity Conjecture

• AA Similarity Conjecture states - If two angles of one Triangle are Congruent to two angles of another (triangle), then the triangles are similar.

Example of AA Similarity Conjecture

• ∠A and ∠B of Triangle ABC are Congruent to ∠D and ∠E of Triangle DEF. So, the two triangles are similar.

Solved Example on AA Similarity Conjecture

∠CFD = 40°, find ∠FAE.

Choices:
A. 65°
B. 50°
C. 40°
D. 70°
Correct Answer: B
Solution:
Step 1: ∠CDF ≅ ∠AEF = 90°
Step 2: ∠CFD ≅ ∠AFE [Vertically opposite angles.]
Step 3: ΔAEF ~ ΔCDF [AA similarity conjecture.]
Step 4: ∠FCD = 180° - (∠CFD + ∠CDF) [Triangle Sum Theorem.]
Step 5: ∠FCD = 180° - (40° + 90°) [Substitute.]
Step 6: ∠FCD = 50° [Simplify.]
Step 7: ∠FAE ≅ ∠FCD [Corresponding angles of similar triangles are congruent.]
Step 8: ∠FAE = 50°

Related Terms for AA Similarity Conjecture

• Angle
• Angle-Angle-Side (AAS)
• Angle-Side-Angle (ASA)
• Congruent
• Conjecture
• Similarity
• Triangle

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