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HL Postulate Lesson 3.8

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**This only works with right triangles!**

Postulate: If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent. HL This only works with right triangles!

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**Then triangle ABC Triangle ADC SSS**

1 B 2 D 3 4 C Given: AB AD <1 <2 Thus <3 <4 So BC CD, AC AC Then triangle ABC Triangle ADC SSS

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A B D C C Leg, right angle, hypotenuse, S A S

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**Given circle O YO ⊥ YX ZO ⊥ ZX Conclude: YX ZX Y O X Z**

Statement Reason Circle O Given OY OZ Radii of circle are congruent (L) YO ⊥ YX, ZO ⊥ ZX Given OYX & OZX are rt s ⊥ ⇒ right () OX OX Reflexive (H) △OYX △OZX HL (2, 4, 5) YX ZX CPCTC

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**Remember, you still have three things to prove congruent:**

Right angle One leg Hypotenuse

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Congruence in Right Triangles

Congruence in Right Triangles

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