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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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Congruent Polygons Have congruent corresponding parts. Have congruent corresponding parts. When naming congruent polygons, always list corresponding vertices.

Congruent Polygons Have congruent corresponding parts. Have congruent corresponding parts. When naming congruent polygons, always list corresponding vertices.

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