1. 4.6: Congruence in Right Triangles

2. Right Triangles
Learning Target: To prove right triangles congruent by the HL Theorem.

3. Right Triangles Hypotenuse: the longest side of a right triangle
Legs: The sides of a right triangle that are not the hypotenuse

4. Theorem 
Theorem 4.6: Hypotenuse-Leg (HL) Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
To use the HL Theorem, you must show that three conditions are met:
There are two right triangles
The triangles have congruent hypotenuses
There is one pair of congruent legs

5. Using the HL Theorem

6. Using the HL Theorem
Statements
Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5.

7. Using the HL Theorem
Statements
Reasons 1. 2. 3. 4. 1. 2. 3. 4.

8. 4.6: Congruence in Right Triangles
(4.6): Pg. 237; 1-4, 7, 8, 10, 11, 14
p. 234: 1, 3, 5, 8, 9
4.6: Congruence in Right Triangles

9. Review: Solving Systems

10. Review: Solving Systems

11. Review: Solving Systems
Find the values of x and y that make the following triangles congruent.
2y+3
x+y x 12