Question

Which pair of triangles can be proven congruent by the HL theorem?

2 right triangles have congruent hypotenuses.
2 triangles have one congruent angle and 2 congruent sides.
2 right triangles have congruent hypotenuses and another congruent side.
2 triangles have 3 congruent sides.

Answer 1

A pair of triangles that can be proven congruent by the HL theorem is: C. 2 right triangles have congruent hypotenuses and another congruent side.

The Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two triangles that are formed would be similar to each other, as well as the original triangle.

In Mathematics, HL is an abbreviation for hypotenuse leg and it is a theorem which states that if the hypotenuse and one leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two triangles would be congruent.

In conclusion, two (2) right-angled triangles that have congruent hypotenuses and another congruent side is a pair of triangles that can be proven congruent by the hypotenuse leg (HL) theorem.

Answer 2

C 2 right triangles have congruent hypotenuses and another congruent side

Explanation:

The HL theorem applies only to right triangles. In order for it to apply, the hypotenuse (H) must be congruent, and one legs (L) must be congruent from one triangle to the other.

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If you recognize that HL is an abbreviation for Hypotenuse-Leg, then the wording of your answer choices tells you which is correct.