1. Section 4-5 Triangle Congruence AAS, and HL

2. All Angles and All Sides are Congruent SSS- Side-Side-Side Postulate
So far we can prove triangles are congruent through several postulates…
All Angles and All Sides are Congruent
SSS- Side-Side-Side Postulate
SAS- Side-Angle-Side Postulate
ASA- Angle-Side-Angle Postulate

3. AAS: Angle-Angle-Side Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the triangles are congruent.

4. Example 1:
Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

5. Example 1:

6. Example 2:
Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

7. Example 2:
In addition to the congruent segments that are marked, NP  NP. Two pairs of corresponding sides are congruent. This is not enough information to prove the triangles are congruent.

8. Example 3: Given: AD║EC, BD  BC Prove: ∆ABD  ∆EBC
Plan for proof: Notice that ABD and EBC are congruent. You are given that BD  BC. Use the fact that AD ║EC to identify a pair of congruent angles.

9. Proof: Statements: BD  BC AD ║ EC D  C ABD  EBC ∆ABD  ∆EBC
Reasons:
Given
If || lines, then alt. int. s are 
Vertical Angles Theorem
ASA Congruence Postulate

10. Hypotenuse-Leg (HL) Congruence
What is a hypotenuse?
In a right triangle, this would be the longest side. The side across from the right angle.

11. Example 4
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.
According to the diagram, the triangles are right triangles that share one leg.
It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.

12. Example 5 If possible, prove
Definition of right triangles
Are right triangles
Reflexive Prop. Of Congruence
HL Theorem

13. Assignment #
Pg. 255
“Think and Discuss” Grey Box
#1-3