Which is the hypotenuse-leg theorem?

A. If the hypotenuse and one leg of a right triangle are similar to the corresponding parts of another right triangle, then the triangles are congruent.
B. If the hypotenuse is congruent to the corresponding part of another right triangle, then the triangles are congruent.
C. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are equilateral.
D. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

It should be D.

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

The correct option is D. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

To understand why this is the correct answer, let's explain the Hypotenuse-Leg Theorem:

The Hypotenuse-Leg Theorem (HL) is a congruence criterion for right triangles. It states that if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

To prove that two triangles are congruent using the Hypotenuse-Leg Theorem, you need to show that the hypotenuse and one leg of each triangle are congruent.

Here's an example:

Let's say we have two right triangles, Triangle ABC and Triangle DEF. We want to prove that Triangle ABC is congruent to Triangle DEF.

To use the Hypotenuse-Leg Theorem, we need to show that the hypotenuse and one leg of Triangle ABC are congruent to the corresponding parts of Triangle DEF.

1. We observe that the hypotenuse of Triangle ABC is congruent to the hypotenuse of Triangle DEF. Let's denote this as AB ≅ DE.

2. We also observe that one leg of Triangle ABC is congruent to one leg of Triangle DEF. Let's denote this as AC ≅ DF.

3. Since both the hypotenuse and one leg are congruent, we can apply the Hypotenuse-Leg Theorem and conclude that Triangle ABC is congruent to Triangle DEF.

Therefore, the correct answer is D. If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.