HL Congruence: The Special Case of Right Triangles

HL congruence applies only to right triangles: if the hypotenuse and one leg match, the triangles are congruent. It is the one case where two sides and a non-included angle are enough, because the right angle removes the ambiguity.

• Ensure that both triangles in question are right triangles.
• Identify and compare the lengths of the hypotenuses and one of the legs of both triangles.
• If both the hypotenuse and one leg are of equal length in the two triangles, then they are congruent by the HL theorem.

Worked examples: HL congruence

Practice questions on HL congruence

1. Are right triangles with a hypotenuse of (17 text{ cm}) and one leg of (8 text{ cm}), and another triangle with a hypotenuse of (17 text{ cm}) and one leg of (8 text{ cm}) congruent by the HL Congruence theorem?
2. Are right triangles with a hypotenuse of (20 text{ cm}) and one leg of (16 text{ cm}), and another triangle with a hypotenuse of (20 text{ cm}) and one leg of (15 text{ cm}) congruent by the HL Congruence theorem?

1. Yes
2. No

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