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Published byKendall Hutcheon Modified over 2 years ago

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HL Postulate Lesson 3.8

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

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B A D CC Leg, right angle, hypotenuse, S AS

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Y X O Z Given circle O YO ⊥ YX ZO ⊥ ZX Conclude: YX ZX StatementReason 1.Circle OGiven 2.OY OZRadii of circle are congruent (L) 3.YO ⊥ YX, ZO ⊥ ZXGiven 4. OYX & OZX are rt s ⊥ ⇒ right ( ) 5.OX OXReflexive (H) 6. △ OYX △ OZXHL (2, 4, 5) 7.YX ZXCPCTC

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Remember, you still have three things to prove congruent: 1. Right angle 2. One leg 3. Hypotenuse

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