Loading...
Triangle Congruence
A
B
C
D
E
F
G
H
. . . .

Congruence in Right Triangles

Theorem. Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, respectively, then the two right triangles are congruent.

Given: Right triangles DFE and PRQ with right angles EFD and QRP, respectively
DF ¯ PR ¯
DE ¯ PQ ¯
Prove: ΔDFEΔPRQ

To prove that ΔDFEΔPRQ,  construct a triangle that is congruent to both and apply transitivity.

Proof: