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Transcript
Triangle Congruence Theorems Geometry Notes – 4.2/4.3 Mr. Belanger Importance • Used to prove triangles congruent • Gives many options for proving congruence • Will continue to be used following this chapter SSS Congruence Theorem Side – Side – Side Congruence: If three corresponding sides in two triangles are congruent, then the triangles are congruent. SAS Congruence Theorem Side – Angle – Side Congruence: If, in two triangles, two sides and the included angle (formed by the two sides) are congruent, then the triangles are congruent. ASA Congruence Theorem Angle – Side – Angle Congruence: If, in two triangles, two angles and the side connecting them are congruent, then the triangles are congruent. AAS Congruence Theorem Angle – Angle – Side Congruence: If, in two triangles, two angles and the non-included (not between) side are congruent, then the triangles are congruent. Examples: Try to decide if the triangles are congruent and if so, why? SAS Examples: Try to decide if the triangles are congruent and if so, why? NO! AAA not a congruence theorem Examples: In triangle ADB and ADC, angle A is congruent to both, side AD is congruent to both and sides BD = CD. It’s obvious that ADB and ADC are not congruent. Be careful about just matching up any three parts like SSA. It has to be one of the four theorems. Examples: Are the triangles congruent? Yes, AAS Now memorize these four theorems!