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HL Postulate

HL Postulate. Lesson 3.8. 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.

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HL Postulate

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  1. HL Postulate Lesson 3.8

  2. 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!

  3. 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

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

  5. Given circle O YO ⊥ YX ZO ⊥ ZX Conclude: YX  ZX Y X O Z • StatementReason • 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

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

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