ANGLE-ANGLE-SIDE TRIANGLE CONGRUENCE CRITERIA (AAS): Given two triangles △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′𝐶′. If 𝐴𝐵 = 𝐴′𝐵′ (Side), 𝑚∠𝐵 = 𝑚∠𝐵′ (Angle), and 𝑚∠𝐶 = 𝑚∠𝐶′ (Angle), then the triangles are congruent.
HYPOTENUSE-LEG TRIANGLE CONGRUENCE CRITERIA (HL): Given two right triangles △ 𝐴𝐵𝐶 and △ 𝐴′𝐵′𝐶′ with right angles 𝐵 and 𝐵′. If 𝐴𝐵 = 𝐴′𝐵′ (Leg) and 𝐴𝐶 = 𝐴′𝐶′ (Hypotenuse), then the triangles are congruent.
The AAS and HL criteria implies the existence of a congruence that maps one triangle onto the other.
Triangles that meet either the Angle-Angle-Angle or the Side-Side-Angle criteria do not guarantee congruence.
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