LA Congruence Theorem says: If one leg and an acute angle of one right triangle are congruent to one leg and an acute angle of another right triangle, then the two right triangles are congruent.
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LL Congruence theorem says: If the two legs of one right triangle are congruent to the two legs of another right triangle, then the two right triangles are congruent.
The side-angle-side congruence theorem states that if you know that the lengths of two sides of two triangles are congruent and also that the angle between those sides has the same measure in both triangles, then the two triangles are congruent.
Excuse me, but two triangles that have A-A-S of one equal respectively to A-A-S of the other are not necessarily congruent. I would love to see that proof!
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