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G.6 Proving Triangles Congruent 1 Visit www.worldofteaching.com For 100’s of free powerpoints. 2 Objective: Students will be able to determine triangle congruence. EQ: What strategies do you use when determining triangle congruence? 3 The Idea of Congruence Two geometric figures with exactly the same size and shape. F B A C E D 4 Do you need all six ? NO ! SSS SAS ASA AAS 5 Side-Side-Side (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Side Side 1. AB DE 2. BC EF 3. AC DF Side ABC DEF The triangles are congruent by SSS. 6 Side-Angle-Side (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 Side Side 1. AB DE 2. A D 3. AC DF Angle ABC DEF The triangles are congruent by SAS. Angle-Side-Angle (ASA) 7 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 1. A D 2. AB DE 3. B E Angle Side Angle ABC DEF The triangles are congruent by ASA. Angle-Angle-Side (AAS) 8 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 1. A D 2. B E 3. BC EF Angle Side Angle ABC DEF The triangles are congruent by AAS. 9 Name That Postulate (when possible) SAS SSA Not enough info! ASA AAS Vertical Angles, Reflexive Sides and Angles 10 When two triangles touch, there may be additional congruent parts. Vertical Angles Reflexive Side side shared by two triangles 11 Name That Postulate (when possible) Reflexive Property SAS Vertical Angles AAS Vertical Angles SAS Reflexive Property SSA Not enough info! 12 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 triangles Let’s Practice 13 Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AC FE For AAS: A F