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Transcript
4.2 Congruence and Triangles Essential Question: How can you prove triangles congruent? Congruent Two figures are congruent if they have the exact same size and shape. When two figures are congruent the corresponding parts are congruent (angles and sides). Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Properties of Congruent Triangles Congruence of triangles is reflexive, symmetric, and transitive. 4.3 SSS and SAS SSS: Side-Side-Side: If three sides of one triangle are congruent to three of a second triangle, then the two triangles are congruent. SAS: Side-Angle-Side: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then two triangles are congruent. 4.4 ASA and AAS ASA: Angle-Side-Angle: If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then two triangles are congruent. AAS: Angle-Angle-Side: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. 4.5 Using Congruent Triangles CPCTC: Corresponding Parts of Congruent Triangles are Congruent: