# HL Postulate - PowerPoint PPT Presentation

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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

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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!

A

1

2

B

D

3

4

C

<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 AS

Given circle O

YO ⊥ YX

ZO ⊥ ZX

Conclude: YX  ZX

Y

X

O

Z

• StatementReason

• Circle OGiven

• OY  OZRadii of circle are congruent (L)

• OX  OXReflexive (H)

• OYX OZX⊥ ⇒ right  ()

• △OYX  △OZXHL (2, 3, 4)

• YX  ZXCPCTC

• Remember, you still have three things to prove congruent:

• Right angle

• One leg

• Hypotenuse