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.

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HL Postulate

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Hl postulate

HL Postulate

Lesson 3.8


Hl postulate

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!


Hl postulate

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


Hl postulate

A

B

D

C

C

Leg, right angle, hypotenuse,

S AS


Hl postulate

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


Hl postulate

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

  • Right angle

  • One leg

  • Hypotenuse


  • Login