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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

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 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