1. 4.4 – Prove Triangles Congruent by HL
Geometry
Ms. Rinaldi

2. Right Triangles
In a right triangle, the sides next to the right angle are called the legs. The side opposite the right angle is called the hypotenuse.
hypotenuse
leg
leg

3. Hypotenuse-Leg (HL) Congruence Postulate *Only for RIGHT Triangles*B
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
If it’s a right triangle,
Hypotenuse
Leg
Then C A S T R

4. Decide whether the congruence statement is true.
EXAMPLE 1
Use HL
Decide whether the congruence
statement is true.
Explain your reasoning. A B D C
SOLUTION
It’s a right triangle
(H)
(L)
So by HL,

5. Decide whether the congruence statement is true.
EXAMPLE 2
Use HL
Decide whether the congruence
statement is true.
Explain your reasoning. A C B D
SOLUTION
It’s a not a right triangle, so HL does not apply.
Also, you have an Angle-Side-Side, but ASS is not a congruence postulate, so there is not enough information.

6. EXAMPLE 3
Use HL
Decide whether the congruence
statement is true.
Explain your reasoning.

7. Decide whether the congruence statement is true.
EXAMPLE 4
Use HL
Decide whether the congruence
statement is true.
Explain your reasoning. C D F A B E

8. State the third congruence that must be given to prove that
EXAMPLE 5
Use HL
State the third congruence that must be given to prove that
using the indicated postulate. B
Given: Angle A and D are right angles.
Use the HL Congruence Postulate. A C E F D