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3.2 Congruent Triangles October 09, 2015 Congruent Polygons Congruent Triangles Congruent Triangles = All pairs of corresponding parts are congruent. F C E B • All corresponding sides are congruent A All triangles have 6 parts D A 3 Sides • All corresponding angles are congruent 3 Angles C B 3.2 Proving Triangles Congruent Side Angle Side Angle Side Angle Ways to Prove Triangles Congruent (3 Postulates) Sides 1.) SideSideSide (SSS) Postulate Angles If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. H A Side Angle Side Angle Side Angle Reflexive Property Any segment or angle is congruent to itself. C B F G The reflexive property creates a copy of a segment or angle for you to use in two different triangles. U W N P Q X Y M I P 1 3.2 Congruent Triangles October 09, 2015 Ways to Prove Triangles Congruent (3 Postulates) A 2.) SideAngleSide (SAS) Postulate D If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent. Side Angle Side Angle Side Angle F A C B E G D C B E J H Included angle = The angle formed between the two congruent sides. K Ways to Prove Triangles Congruent (3 Postulates) H A 3.) AngleSideAngle (ASA) Postulate If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. Side Angle Side Angle Side Angle Included side = The side between the two congruent angles. C B F G V M W O E Y X N N M P A Given: D midpoint of Ways to Prove Triangles Congruent (3 Postulates) Prove: Summary Statements 1.) SSS (SideSideSide) Reasons B D C 2.) SAS (SideAngleSide) 3.) ASA (AngleSideAngle) 2