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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

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

This only works with right triangles!


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


A

B

D

C

C

Leg, right angle, hypotenuse,

S A S


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



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