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Triangle Congruence: Hypotenuse-Leg Theorem Explanation

Understand the HL Postulate for congruent right triangles with detailed examples and proof steps. Learn how to apply this theorem effectively in geometry. Practice with interactive games.

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Triangle Congruence: Hypotenuse-Leg Theorem Explanation

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  1. Warm Up

  2. http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431621.htmlhttp://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431621.html

  3. 3.8 HL Postulate 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!

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

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

  6. Given circle O YO ⊥ YX ZO ⊥ ZX Conclude: YX = ZX Y X O Z • Statement Reason • Circle O Given • OY = OZ Radii of circle are congruent (L) • OX = OX Reflexive (H) • <OYX = <OZX ⊥ ⇒ right < (<) • △OYX = △OZX HL (2, 3, 4) • YX = ZX CPCTC

  7. Remember, you still have three things to prove congruent: • Right angle • One leg • Hypotenuse

  8. http://www.classzone.com/books/geometry_concepts/page_build2.cfm?id=game&ch=5&CFID=40580573&CFTOKEN=83522164http://www.classzone.com/books/geometry_concepts/page_build2.cfm?id=game&ch=5&CFID=40580573&CFTOKEN=83522164

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