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## Congruent Triangles !

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**Congruent Triangles !**By: Jackie Bruno and Breanna Brukalo and Erika Lanham**Aim: To review Congruent Triangles !**Do Now: Define -Congruent -Congruent line segments -Midpoint -Angle Bisector -Complimentary and Supplementary angles -Vertical angles**Congruent Triangles**Two triangles that correspond in congruent sides and angles. Two triangles are congruent if they agree in all three sides OR 2 pairs of sides and an included angle OR two angles and an included side**Reasons !**• A bisector divides a line into 2 congruent parts • A midpoint divides a line into 2 congruent parts • Perpendicular lines forms right angles • Supplements of congruent angles are congruent • Vertical angles are congruent • When congruent segments added to congruent segments, the sum is congruent. • Halved of congruent parts are equal • Corresponding parts of congruent triangles are congruent • Does anyone have anymore to add?**Reasons!**• There are a few reasons you can give to say that two triangles are congruent: • Angle Side Angle • Side Angle Side • Angle Angle Side • Side Side Side • You may be thinking there is another reason. • Angle Angle Angle? • Well this would be incorrect. You cannot prove two triangles congruent by the reasoning that their angles are all congruent.**Can you prove these triangles to be congruent?**Prove triangles APQ and BPQ to be congruent. S**Since these triangles share a common side PQ, in this**situation, you use AAS. This happens because 2 corresponding angles are equal and a 3rd side PQ, shared by both triangles. Therefore the other 3 corresponding parts must also be equal.