What you’ll learn
Understand angle-angle similarity.
Key idea
Two equal corresponding angle pairs determine triangle similarity; angle equality alone does not determine size.
AA determines shape, not equal size; congruence requires additional length evidence.
Worked example
Classify examples and non-examples for the concept 'Understand angle-angle similarity'.
Triangles P and Q each have corresponding angles 25,35,120 degrees; their side lengths are not specified. Classify similarity by AA with evidence.
- Two corresponding angle pairs equal 25 and 35 degrees; each third angle is 180-25-35=120 degrees.
- AA establishes the same shape and proportional sides, but does not determine a unit scale or guarantee congruence.
Answer: Similar — corresponding pairs 25 and 35 match, which suffices for AA without equal side lengths.
Quick Check
Classify examples and non-examples for the concept 'Understand angle-angle similarity'.
Triangles P and Q each have corresponding angles 35,30,115 degrees; their side lengths are not specified. Classify similarity by AA with evidence.