1. Warm-Up
Determine if the following triangles are congruent and name the postulate/definitions/properties/theorems that would be used to prove them congruent (if possible)...

4. Triangle Congruence Theorems
By using the three postulates we discovered yesterday we can prove that there are 2 other ways to make triangles congruent.

5. (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.

6. (HL) Hypotenuse - Leg  Theorem
If the hypotenuse and a leg of a right Δ are  to the hypotenuse and a leg of a second Δ, then the 2 Δs are .
The hypotenuse and one leg (HL) of the first right triangle
are congruent to the corresponding parts of the second right triangle.

7. Are the triangles congruent
Are the triangles congruent? If so, by what method would each of the triangles be proven congruent?

8. Name the additional equal corresponding part(s) needed to prove the triangles are congruent by the indicated postulate or theorem.

9. Name the additional equal corresponding part(s) needed to prove the triangles are congruent by the indicated postulate or theorem.

10. A B

11. C F

12. F F

13. F B

14. E E

15. Statements
Reasons

16. Statements
Reasons M

17. Example : Statements Reasons
Given: B is the midpoint to AE and CD. Prove: ∆ABD  ∆EBC

18. Summary: Draw pictures for each…
Reflexive Property
Vertical Angles are congruent
Definition of Congruent Segments
Definition of Perpendicular
Definition of Midpoint
SSS Postulate
ASA Postulate
SAS Postulate
AAS Theorem
HL Theorem