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4.3 Congruent Triangles Congruence Theorem SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B D C E F Vocabulary Included Angle: In a triangle, the angle formed by two sides is the included angle for the two sides. Included Side: The side of a triangle that forms a side of two given angles. Included Angles & Sides Included Angle: A is the included angle for AB & AC. A B is the included angle for BA & BC. * C is the included angle for CA & CB. Included Side: B AB is the included side for A & B. BC is the included side for B & C. AC is the included side for A & C. * * C Congruence Theorems ASA If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent. A B SAS A D C E F B D C E F If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. Congruence Theorems AAS If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. A B HL C E D A D F B C E If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. F Are these triangles congruent? If so, why and name the triangles. B A E C F D S B A C R T S B A C R T S B A C R T S B A C R T You can only use what is marked in the picture! You can not mark anything else in the pictures EXCEPT: 1. Vertical angles 2. Shared side (by the reflexive property, any side is congruent to itself). 3. If there are parallel lines, you can mark alternate interior angles (they make a Z shape). Name the congruent triangles. A C B E D Name the congruent triangles. X W Y Z Name the congruent triangles. A D B C