Parallelograms

ParallelogramsDefinitionsQuadrilateral- polygon with 4 sides

Parallelogram- quadrilateral with both pairs of opposite sides parallel

Opposite sides- do not share a vertexOpposite angles- do not share a sideTheorem 6-3Opposite sides of a parallelogram are congruent.

Theorem 6-4Consecutive angles of a parallelogram are supplementary

Why is this true? What kinds of angles are these (think about parallel lines cut by a transversal)?

Theorem 6-5Opposite angles of a parallelogram are congruent.Theorem 6-6Diagonals of a parallelogram bisect each other.Problem 3 (p.362)Given:KP=y+10MP=2x-8LP=xNP=y+2Find x and y.Find KM and LN.

y=14, x = 16, KM=48, LM=32

Theorem 6-7If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.Complete the following questions about the diagram below.If RS= 12, then ST= ______?If AB= 8, then BC= ______?If AC= 20, then AB= ______?If AC= 10x, then BC=______?

RSTCBAProblemFind x and y. x=1.5; y=7Find DF and CADF=10, CA=12

Answer True or False(Remember, for a statement to be true, it must be true ALL of the time!)1. Every parallelogram is a quadrilateral.True2. Every quadrilateral is a parallelogram.False3. All the angles of a parallelogram are congruent.False4. All sides of a parallelogram are congruent.False5. In RSTU, RS || TU.True6. In ABCD, if m