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HL Postulate - PowerPoint PPT Presentation

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

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!

1

2

B

D

3

4

C

<1  <2

Thus <3  <4

So BC  CD, AC  AC

Then triangle ABC  Triangle ADC SSS

B

D

C

C

Leg, right angle, hypotenuse,

S A S

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