Congruence of Triangles

Core concept

Importantly, AAA (all three angles equal) does NOT guarantee congruence, only similarity — two triangles can have identical angles but be different sizes (like a small and large equilateral triangle), demonstrating why angle-only matching is insufficient to prove congruence. These congruence criteria are essential tools throughout geometry for proving that two triangles are truly identical, used extensively in more complex geometric proofs involving quadrilaterals, circles, and other shapes.