Transcript Slide 1

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
B
1
2
3
4
Given:
D
C
AB  AD
<1  <2
Thus <3  <4
So BC  CD, AC  AC
Then triangle ABC  Triangle ADC SSS
A
B
D
CC
Leg, right angle, hypotenuse,
S
A
S
Given circle O
Y
X
O
Z
YO ⊥ YX
ZO ⊥ ZX
Conclude: YX  ZX
Statement
Reason
1. Circle O
Given
2. OY  OZ
Radii of circle are congruent (L)
3. OX  OX
Reflexive (H)
4. OYX  OZX
⊥ ⇒ right  ()
5. △OYX  △OZX
HL (2, 3, 4)
6. YX  ZX
CPCTC
Remember, you still have three things to
prove congruent:
1. Right angle
2. One leg
3. Hypotenuse