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2 1 2 3 4 5 Similarity, Congruence & Proof Unit 2 Content Map and Standards Similarity vs Congruence Transformations (Shutter) Properties of Algebra (Flip Book) Properties of Equality (Think Map) Triangle Congruence Rules & Non Rules (6 door) Triangle Congruence Standards: MCC9-12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Essential Question: • Under what conditions are similar figures congruent? • How do I know which method to use to prove two triangles congruent? Eight Door Foldable MCC9-12.G.SRT.5 (front – closed) Can I prove these triangles congruent? Side-Angle-Side (SAS) Hypotenuse-Leg (HL) Angle-Side-Side (SS) Note: whole sheet of regular paper landscape Side-Side-Side (SSS) Angle-Side-Angle (ASA) Angle-Angle-Side (AAS) Angle-Angle-Angle (AAA) Can I prove these triangles congruent? MCC9-12.G.SRT.5 (top left door opened) Two triangles are congruent if and only if sides corresponding __________________ and corresponding angles __________________ are congruent. You only need ___________ three sets of corresponding parts congruent in order to prove two triangles are congruent. correct Do you have the _________________ information? Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 SSS (top right door opened) Three pairs of congruent ____________________ Y sides. _ _E _S Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 SAS (second left door opened) Two pairs of Y _________________ congruent sides and the E included _________________ angle. S _ _ _ Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 ASA (second right door opened) Two pairs of congruent ___________________ angles and the included ___________________ side. _Y _E _S Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 HL (third left door opened) Two pairs of Y ___________________ congruent sides of a E ___________________ right triangle. S _ _ _ Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 AAS (third right door opened) Two pairs of congruent ___________________ angles and the Non-included ___________________ side. _Y _E _S Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 SS (bottom left door opened) Triangles may _N ______ NOT be congruent. 0 _ _! NOT prove triangle **You can ______ Similarity or __________________ ____________________ Congruence with this postulate. Closed Closed Closed Closed Closed Closed Closed MCC9-12.G.SRT.5 AAA (bottom right door opened) NOT prove You can _______ N ___________________. Congruence _ 0 can _ Similarity ! _ **You ________ prove triangular ___________________ (AA Similarity Postulate). Closed Closed Closed Closed Closed Closed Closed Summarizer (back – closed) Compare and Contrast each of the rules for congruence. Also compare them with the “non-rules” for congruence. Student Template • Print next two “Slides” and copy them double sided Side-SideSide (SSS) Compare and Contrast each of the rules for congruence. Also compare them with the “non-rules” for congruence. Can I prove these triangles congruent? MCC9-12.G.SRT.5 Angle-SideAngle (ASA) Side-AngleSide (SAS) Angle-AngleSide (AAS) HypotenuseLeg (HL) Angle-AngleAngle (AAA) Angle-SideSide (SS) Two triangles are congruent if and only if corresponding __________________ and corresponding __________________ are congruent. Three pairs of ____________________ sides. You only need ___________ sets of corresponding parts congruent in order to prove two triangles are congruent. Do you have the _________________ information? _ _ _ _ _ _ _ _ _ Two pairs of _____________________ sides and the _____________________ angle. Two pairs of ____________________ angles and the ____________________ side. Two pairs of _____________________ sides of a _____________________ triangle. Two pairs of ____________________ angles and the ____________________ side. Triangles may ______ be congruent. You can ______ prove ___________________. **You can ____ prove triangle __________________ or __________________ with this postulate (see HL for the only time this works). **You ________ prove triangle ____________________________ (AA Similarity Postulate). _ _ _ _ _ _ _ _ _ _ _ _