1.Obj. 26 Parallelograms The student is able to (I can): Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems. Prove that a given quadrilateral is a parallelogram.

2. parallelogramA quadrilateral with two pairs of parallel sides. A parallelogram has the following properties: Opposite sides are parallel. (Definition) Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. 3. 2 pairs of sides If a quadrilateral has two pairs of parallel sides, then it is a parallelogram T>>EI>>MTI ME, TE IM 4. Opp. sides If a quadrilateral is a parallelogram, then opposite sides are congruent. KGINKI NG, GK IN 5. Opp. angles If a quadrilateral is a parallelogram, then opposite angles are congruent. K>>GO>>NK N, O G 6. Cons. angles supp. If a quadrilateral is a parallelogram, then consecutive angles are supplementary.1 42 3m1 + m2 = 180 m2 + m3 = 180 m3 + m4 = 180 m4 + m1 = 180 7. Diagonals bisect If a quadrilateral is a parallelogram, then its diagonals bisect each other. TU>>S >>ENTS NS, ES US 8. ExamplesFind the value of the variable: 1. x = 5x + 32x + 152. x = (x + 84)3. y =y(3x) 9. ExamplesFind the value of the variable: 1. x = 4 5x + 32x + 15 5x + 3 = 2x + 15 3x = 122. x = 42 (x + 84)3x = x + 84 2x = 843. y = 54 3(42) = 126 y = 180 - 126y(3x) 10. Conditions for Parallelograms If one pair of opposite sides of a quadrilateral is congruent and parallel then the quadrilateral is a parallelogram. parallel, We can also use the converses of the theorems from the previous section to prove that quadrilaterals are parallelograms. ParallelogramOpposite sides Opposite angles Cons. s supp. Diagonals bisect