Properties of Parallelograms

• Investigate the properties.• Use the properties to create and solve

equations• Prove theorems about parallelograms.• Use coordinates to prove theorems

algebraically• Describe properties of parallelograms using

transformations.

What do you think?

List of Relationships

Vocabulary

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Theorem 8.3: If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Find the value of each variable in the parallelogram.

Theorem 8.4: If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Find the value of each variable in the parallelogram.

Theorem 8.5: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Find the value of x in WXYZ.

Theorem 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Find the intersection of diagonalsThe vertices of ABCD are A(1, 6), B(5, 6),C(3, 2), and D(3, 2). The diagonals of ABCD intersect at point P. What are the coordinates of P?

Find the indicated measure in PQRS.

1. PR 2. ST 3. mSRQ 4. mPQR