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)...

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

(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.

(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.

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

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

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

A B

C F

F F

F B

E E

Statements Reasons

Statements Reasons M

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

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