HL Congruence: The Special Case of Right Triangles

• 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.

Examples

Practice Questions:

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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