Triangle Congruence Obj: learn all the ways to prove triangles are congruent To Identify- SSS, AAS, SAS, or ASA

Definitions Congruent Triangles- triangles w/ same size and shape Transformations- Dilate, slide, flip or turn Congruence transformations- transformations that do not change the congruence (slide, flip or turn)

Corresponding Parts of Congruent Triangles M R Q P L  P N  R M  Q

Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent.

Example: Draw and label the picture, and find x O A G D T C 14 18 21

Theorem: Congruence of triangles is reflexive, symmetric, and transitive

Side Side Side (SSS) Where you show all corresponding sides of a triangle are congruent to the corresponding sides of another triangle. One way to prove 2 triangles are congruent

Side Angle Side - (SAS) If 2 sides and an included angle of 1 triangle are congruent to 2 sides and included angle of another triangle, then triangles are congruent Notice: The angle is between the 2 sides

Angle Side Angle -(ASA) If 2 angles and an included side of 1 triangle are congruent to 2 angles and included side of another triangle, then the triangles are congruent. Notice: The side is between the angles

AAS - (Angle Angle Side) If 2 angles and a non-included side of 1 triangle are congruent to the corresponding 2 angles and side of a 2nd triangle, then the 2 triangles are congruent Notice: Side is not included!!!

Recap of Showing Triangles Congruent SSS SAS AAS ASA ASS Just say "No" to

Proof: Statement Justification C A E 2 1 D B 1.) Given 2.) Definition of vertical angles 3.) Definition of bisector 4.) ASA 5.) CPCTC

Your Turn: 3.) reflexive 4.) SAS S T P R 2 1 Statement Justification 1.) Given 3.) reflexive 4.) SAS

Homework Skills: Pg 236 1 – 9, 16 Pg 243 1 – 15 odd, 20, 21 Proofs Pg 238 24 - 27 Pg 244 25 – 29 Pg 255 31 - 34