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Congruence in Right Triangles

Congruence in Right Triangles. Objective : Prove right triangles congruent by using the Hypotenuse-Leg Theorem. Right Triangles. leg. hypotenuse. leg. Hypotenuse-Leg Theorem.

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Congruence in Right Triangles

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  1. Congruence in Right Triangles Objective: Prove right triangles congruent by using the Hypotenuse-Leg Theorem

  2. Right Triangles leg hypotenuse leg

  3. Hypotenuse-Leg Theorem • If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. • IfΔPQR and ΔXYZ are right triangles, PR ≅ XZ and PQ ≅ XY P X R Z Q Y • ThenΔPQR ≅ ΔXYZ

  4. Remember… • To use the HL Theorem, the triangles must meet three conditions: • There are two right triangles. • The triangles have congruent hypotenuses. • There is one pair of congruent legs.

  5. Practice • Are the two triangles congruent? If so, write the congruence statement.

  6. Practice • For what values of x and y are the triangles congruent by HL?

  7. Practice • Given: ΔGKE is isosceles with base GE, and ∠L and ∠D are right angles, and K is the midpoint of LD. • Prove: LG ≅ DE

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