What you’ll learn
Prove AA similarity.
Key idea
A common angle and a justified parallel-line corresponding angle can give two pairs without assuming similarity.
Two justified corresponding pairs establish shape and vertex order, not congruence.
Worked example
Complete missing statements or reasons in a proof for 'Prove AA similarity'.
Triangles ABC/DEF have A=D=60, B=E=30 degrees. Complete the similarity conclusion, vertex order and proof reason.
- Two stated corresponding angle equalities determine the vertex order A-D, B-E, C-F.
- AA establishes similarity; third angles both 90; no side equality is assumed.
Answer: Triangle ABC similar to DEF by AA — A-D and B-E give two corresponding pairs, leaving C-F=90.
Quick Check
Complete missing statements or reasons in a proof for 'Prove AA similarity'.
Triangles ABC/DEF have A=D=60, B=E=30 degrees. Complete the similarity conclusion, vertex order and proof reason.