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Transcript
4.3-‐4.5 Proving Triangles are Congruent Side-Side-Side (SSS) Theorem: If all 3 sides are congruent, then the 2 triangles are congruent. Decide whether the triangles are congruent. Explain your reasoning. 1 Side-Angle-Side (SAS) Postulate: If 2 sides and the included angle are congruent, then both triangles are congruent. 2 Angle-Side-Angle Theorem: If 2 angles and the included side are congruent, then the 2 triangles are congruent. Angle-Angle-Side Theorem: If 2 consecutive angles, followed by a side are congruent, then the 2 triangles are congruent. 3 Hypotenuse-Leg Theorem: In a right triangle if the corresponding hypotenuse and leg are congruent, then the 2 triangles are congruent. 4 5 You may not use the following to prove 2 triangles are congruent!! 1. "Angle,Angle, Angle or A.A.A": No calling triple A for help! 2. "Angle, Side, Side or A.S.S": No Swearing! 6 Decide whether the 2 triangles are congruent. If they are, tell why. 7 Decide whether the 2 triangles are congruent. If so, tell why. a. b. 8 Decide whether the 2 triangles are congruent. If so, tell why. a. b. 9 Overlapping triangles are when the 2 triangles share a common side or angle. Example: 1 Keys to solve overlapping triangles! 1. Use 2 colored pencils to outline the 2 triangles. 2. Redraw each triangle individually and label all angles and sides with given information. 3. Look at the 2 triangles and see if you can prove that they are congruent using: SAS, SSS, ASA, AAS, or HL T Z V X Y W 10 Try two more! Are they congruent?? a. b. 11