Six Properties of Parallelograms

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Six Properties of Parallelograms 5-2 Proving Quadrilaterals are Parallelograms Six Properties of Parallelograms Opposite sides are parallel. (definition) Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. Consecutive (same-side interior) angles are supplementary. Either diagonal separates the parallelogram into two congruent triangles.

Definition used to prove that Quadrilaterals are Parallelograms If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

Theorems used to prove that Quadrilaterals are Parallelograms If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

(More) Theorems used to prove that Quadrilaterals are Parallelograms If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Homework Section 5.2 Classroom Exercises (p. 173) #1-9 Section 5.2 Written Exercises (p. 174-175) #1-7, 10, & 19-22