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.