1. 4.4 Hypotenuse-Leg (HL) Congruence Theorem
Essential Question: Can I prove two right triangles are congruent using SSA?

2. REVIEW
AAS
ASA

3. Methods of Proving Triangles Congruent
If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Methods of Proving Triangles Congruent
SSS
SAS
ASA
AAS

4. Parts of Right Triangles
Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs.
hypotenuse
leg
leg

5. Examples: Tell whether the segment is a leg or a hypotenuse.

6. SSA won’t prove two triangles congruent unless. . .

7. by a special case of SSA called Hypotenuse-Leg.
A X
B C Y Z
. . . using a right triangle.
by a special case of SSA called Hypotenuse-Leg.

8. Hypotenuse- Leg (HL) Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.
A X
B C Y Z

9. HL (Hypotenuse - Leg) is not like any of the previous congruence postulates... actually if it was given a name it would be ASS or SSA and earlier we found that this was NOT a congruence postulate. 
HL works ONLY BECAUSE IT IS A RIGHT TRIANGLE!!!!!

10. Determine if the triangles are congruent.HL
SAS NO HL

11. Summary Triangles are congruent by…
SSS
AAS
SAS
ASA HL

12. Triangles are not congruent by…
ASS or SSA
AAA