Right Triangle Congruence

Leg-Leg Congruence

If the legs of a right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

In the figure, $\overline{AB}\cong \overline{XY}\text{and}\overline{BC}\cong \overline{YZ}$ .

So, $\Delta ABC\cong \Delta XYZ$ .

Hypotenuse-Angle Congruence

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the triangles are congruent.

In the figure, $\overline{AC}\cong \overline{XZ}\text{and}\angle C\cong \angle Z$ .

So, $\Delta ABC\cong \Delta XYZ$ .

Leg-Angle Congruence

If one leg and an acute angle of a right triangle are congruent to one leg and the corresponding acute angle of another right triangle, then the triangles are congruent.

In the figure, $\overline{AB}\cong \overline{XY}\text{and}\angle C\cong \angle Z$ .

So, $\Delta ABC\cong \Delta XYZ$ .

Hypotenuse-Leg Congruence

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

In the figure, $\overline{AB}\cong \overline{XY}\text{and}\overline{AC}\cong \overline{XZ}$ .

So, $\Delta ABC\cong \Delta XYZ$ .