1. 4.6 Congruence in Right Triangles
To Prove Triangles Congruent using the Hypotenuse Leg Theorem

2. Right Triangles…
In a Right Triangle the side opposite the Right Angle is called the Hypotenuse.
The Hypotenuse is always the largest side of the Right Triangle
The other two sides are called the Legs.
The Legs will always include the Right Angle.

3. Side Side Angle?
Remember SSA is not a Congruence Rule in All Triangles.
It does work however in a special case, Right Triangles.
It occurs when hypotenuses and one pair of legs are congruent.

4. The HL Theorem!

5. So…
To Use the HL Theorem, you must show that three conditions are met:
There are two right triangles. (Right Angles)
The triangles have congruent hypotenuses.
There is one pair of congruent legs.

6. Example 1

7. Example 1B
What two triangles are congruent by the Hypotenuse Leg (HL) Theorem? Write a Congruence Statement…
∆LMN ≅ ∆OQP

8. Example 2: Using HL Theorem

9. Ex 2B: Using HL
ΔXYZ is Isosceles. From Vertex X a perpendicular Line is drawn intersecting YZ at point M.
Explain why ΔXMY≅ΔXMZ…

10. Example 3: Using HL Theorem

11. Closure… How are SAS and HL Theorem alike? How are they Different?
How does AAS Relate to HL Theorem? (Think Isosceles Triangles…)