AMSCO'S Geometry. New York - Rye High School

The Parallelogram 383DEFINITIONThe distance between two parallel lines is the length of the perpendicular fromany point on one line to the other line.Properties of a Parallelogram1. Opposite sides are parallel.2. A diagonal divides a parallelogram into two congruent triangles.3. Opposite sides are congruent.4. Opposite angles are congruent.5. Consecutive angles are supplementary.6. The diagonals bisect each other.EXAMPLE 1In ~ABCD, mB exceeds mA by 46 degrees. Find mB.SolutionLet x mA.Then x 46 mB.Two consecutive angles of a parallelogram are supplementary. Therefore,mA mB 180 mB x 46x x 46 180 67 462x 46 180 1132x 134x 67Answer mB 113ExercisesWriting About Mathematics1. Theorem 10.2 states that two consecutive angles of a parallelogram are supplementary. Iftwo opposite angles of a quadrilateral are supplementary, is the quadrilateral a parallelogram?Justify your answer.2. A diagonal divides a parallelogram into two congruent triangles. Do two diagonals divide aparallelogram into four congruent triangles? Justify your answer.