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Congruence in Right Triangles

Congruence in Right Triangles. hypotenuse. legs. Right Triangles. The side opposite the right angle is the longest side and is called the hypotenuse . The other two sides are called legs. B. Y. C. Z. A. X. Theorem 4-6 Hypotenuse-Leg (HL) Theorem

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Congruence in Right Triangles

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  1. Congruence in Right Triangles

  2. hypotenuse legs Right Triangles • The side opposite the right angle is the longest side and is called the hypotenuse. • The other two sides are called legs.

  3. B Y C Z A X Theorem 4-6 Hypotenuse-Leg (HL) 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. ABC  XYZ

  4. Why? DGF  DEF

  5. What additional information do you need to prove the triangles congruent by HL?

  6. When proving triangles are congruent by HL, the following conditions must be met: • The hypotenuses are congruent. • At least one set of legs is congruent. • You have two right triangles.

  7. C A B D Since BC ≅AD, <ABC and <DBC are right angles. Since <ABC and <DBC are right angles, Then ΔABC and Δ DBC are right triangles.

  8. Statements Reasons

  9. Statements Reasons

  10. Homeworkp. 2195 - 10, 14 - 15, Write as a proof: 28 - 29

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