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Triangle Congruence
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Congruence in Right Triangles

Theorem. Leg-Acute Angle (LA) Congruence Theorem
If one leg and one acute angle of a right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the two right triangles are congruent.

Given: Right triangles HIJ and KLM with right angles HIJ and KLM, respectively
IJ ¯ LM ¯
HJIKML
Prove: ΔHIJΔKLM

Proof: