The **Right Triangle Leg Leg Congruence Theorem** is a theorem for right triangles that says if the two corresponding shorter legs of two right triangles are congruent, then the two triangles are congruent. For instance, if the length of the shorter legs of the two triangles is 5, and the other leg is 12, then we are sure that the two triangles are congruent. Yes, they are in fact the triangles with side lengths 5, 12 and 13.

**Theorem**

Given two triangles and right angled at and respectively. If and , then triangle is congruent to triangle .

**Proof**

(Given)

(All right angles are congruent, Postulate 4).

(Given)

Therefore, by SAS Triangle congruence, triangle and triangle are congruent.

Note that the Leg Leg Congruence Theorem is also related to the Hypotenuse-Leg Theorem.