Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
If …
Then …
To prove the HL Theorem you will need to draw auxiliary lines to make a third triangle.
Proof of Theorem 4-6: Hypotenuse-Leg Theorem
Given:
Prove:
Proof: On
Mark point S so that
Since corresponding parts of congruent triangles are congruent,
To use the HL Theorem, the triangles must meet three conditions.
Conditions