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Congruent Triangles Toolkit 4.1-4.3 Today’s Goals: To recognize congruent figures. To prove two triangles congruent. Congruent Polygons If two polygons are congruent, then all the angles are congruent And all the sides are congruent. Ex.1: Naming Congruent Parts TJD RCF. List the congruent corresponding parts. Sides: TJ RC Angles: T R JD CF DT FR J C D F D F R J C T Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. CF Ex. 2: Finding Congruent Triangles Ex.3: Proving Triangles Congruent Use the information given in the diagram. Give a reason why each statement is true. Given PQ PS, QR SR Reflexive Property b) PR PR Given c) Q S, QPR SPR 3rd Angles Thm. d) QRP SRP Definition of e) PQR PSR Congruent Triangles a) Shortcuts to Proving Two Triangles Congruent Enrichment Activity Work with your partners… Side-Side-Side (SSS) If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. Use SSS to Prove Congruency ABC ______ Included Angle The angle between two sides (segments). B is included between AB and CB. B A C Side-Angle-Side (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. ABC ____ Use SAS to Prove Congruency ABC ____ Ex.4: Using SSS or SAS RS TK. What other information do you need to prove RSK TKS? To prove using SSS: RK TS To prove using SAS: RSK TKS Ex.5: Are the Triangles Congruent? From the information given, can you prove RED CAT ? No, not enough information to prove RED CAT. T is not included between CA and CT. Ex. 6: From the given information, can you prove that AEB DBC? Explain. Given: EB CB AE DB Two-Column Proof Can you use SSS or SAS to prove congruency? Given: FG || KL, FG KL Prove: FGK KLF Angle-Side-Angle (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. ABC XZY ASA ABC CDA Angle-Angle-Side (AAS) If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. ABC YXZ AAS ABC DEC SUMMARY: Determine if you can prove the triangles congruent. Which method would you use?