G.6 Proving Triangles Congruent Visit www.worldofteaching.com For 100’s of free powerpoints.

Objective: Students will be able to determine triangle congruence Objective: Students will be able to determine triangle congruence. EQ: What strategies do you use when determining triangle congruence?

The Idea of Congruence Two geometric figures with exactly the same size and shape. A C B D E F

Do you need all six ? NO ! SSS SAS ASA AAS

The triangles are congruent by SSS. Side-Side-Side (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. B A C Side E Side F D Side AB  DE BC  EF AC  DF ABC   DEF The triangles are congruent by SSS.

Side-Angle-Side (SAS) The triangles are congruent by SAS. If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. included angle B E Side F A C Side D AB  DE A   D AC  DF Angle ABC   DEF The triangles are congruent by SAS.

Angle-Side-Angle (ASA) The triangles are congruent by ASA. If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent. included side B E Angle Side F A C D Angle A   D AB  DE  B   E ABC   DEF The triangles are congruent by ASA.

Angle-Angle-Side (AAS) The triangles are congruent by AAS. If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent. Non-included side B A C Angle E D F Side Angle A   D  B   E BC  EF ABC   DEF The triangles are congruent by AAS.

Name That Postulate (when possible) SAS ASA SSA AAS Not enough info!

Reflexive Sides and Angles Vertical Angles, Reflexive Sides and Angles When two triangles touch, there may be additional congruent parts. Vertical Angles Reflexive Side side shared by two triangles

Name That Postulate SAS SAS SSA AAS Vertical Angles Reflexive Property (when possible) Vertical Angles Reflexive Property SAS SAS Vertical Angles Reflexive Property SSA AAS Not enough info!

Reflexive Sides and Angles When two triangles overlap, there may be additional congruent parts. Reflexive Side side shared by two triangles Reflexive Angle angle shared by two

Let’s Practice B  D AC  FE A  F Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B  D For SAS: AC  FE A  F For AAS: