6.2 and 6.3: Quadrilaterals and Parallelograms By Brit Caswell

A parallelogram is a quadrilateral where both sets of opposite sides are parallel.

If a quadrilateral is a parallelogram, Then its opposite sides are congruent. (6.3) Then its consecutive angles are supplementary. (6.4) Then its opposite angles are congruent. (6.5) Then its diagonals bisect each other. (6.6)

Theorem 6.7 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Find the values of x and y.

Find the values of x and y.

Proving that a Quad. Is a Parallelogram We can take the converse of the statements from section 6.2 and prove that a quadrilateral is a parallelogram.

(6.8) If both pairs of opposite sides of a quadrilateral are congruent…. (6.9) If an angle of a quadrilateral is supplementary to both of its consecutive angles…. (6.10) If both pairs of opposite sides of a quadrilateral are congruent… (6.11) If the diagonals of a quadrilateral bisect each other… Then the quadrilateral is a parallelogram.

Theorem 6.12 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.