6Theorem 6-8If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
7Example 1For value of x will quadrilateral MNPL be a parallelogram?If the diagonals bisect each other, then the quadrilateral is a parallelogram.2y – 7 = y + 2y – 7 =y = 93x = y3x = 9x = 3
8Example 2aAngles A and C are congruent. ∠ADC and ∠CBA are congruent by the Angle Addition Postulate. Since both pairs of opposite angles are congruent, ABCD is a parallelogram.
9Example 2bThis cannot be proven because there is not enough information given. It is not stated that the single-marked sides are congruent to the double-marked sides. If opposite sides are congruent, then the quadrilateral is a parallelogram.
10Quick Check 2aSince one pair of opposite sides are both parallel and congruent, we can use Theorem 6-8 to prove PQRS is a parallelogram.
11Quick Check 2bNot enough information is given. It is not stated that the single-marked segments are congruent to the double-marked segments. If diagonals bisect each other, then the quadrilateral is a parallelogram.