1. HL Postulate
Lesson 3.8

2. This only works with right triangles!
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!

3. Then triangle ABC  Triangle ADC SSS1 B 2 D 3 4 C
Given: AB  AD
<1  <2
Thus <3  <4
So BC  CD, AC  AC
Then triangle ABC  Triangle ADC SSS

4. A B D C C
Leg, right angle, hypotenuse,
S A S

5. Given circle O YO ⊥ YX ZO ⊥ ZX Conclude: YX  ZX Y O X Z
Statement Reason
Circle O Given
OY  OZ Radii of circle are congruent (L)
YO ⊥ YX, ZO ⊥ ZX Given
OYX & OZX are rt s ⊥ ⇒ right  ()
OX  OX Reflexive (H)
△OYX  △OZX HL (2, 4, 5)
YX  ZX CPCTC

6. Remember, you still have three things to prove congruent:
Right angle
One leg
Hypotenuse