1. 6-2B Proving Quadrilaterals Are Parallelograms
How do you show that a quadrilateral is a parallelogram? What are the conditions?

2. Properties of Parallelograms
The opposite sides of a parallelogram are parallel (by definition).
The opposite angles of a parallelogram are congruent.
The opposite sides of a parallelogram are congruent.
The consecutive angles of a parallelogram are supplementary.
The diagonals of a parallelogram bisect each other.

3. Write the Converse of the definition
The opposite sides of a parallelogram are parallel (by definition).
A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition).
Draw a parallelogram on a piece of graph paper.
How do you check for 2 pairs of parallel sides?

4. Write the converse of:
The opposite angles of a parallelogram are congruent.
If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
1. Measure the angles of your parallelogram.

5. Write the Converse of
The opposite sides of a parallelogram are congruent.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
1. Measure the length of the sides of your quadrilateral. Write down the measurements.

6. Write the Converse of
The consecutive angles of a parallelogram are supplementary.
If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.
1. Add up the measures of the consecutive angles. Are they supplementary?

7. Write the Converse of
The diagonals of a parallelogram bisect each other.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Draw diagonals in your quadrilateral.
Measure the diagonals.
Measure each part of the diagonals and write down the measurement.

8. Is the quadrilateral a parallelogram?
Yes, diagonals bisect each other.
Yes, Opposite sides are congruent.
70°
110°
?? The congruent sides may not be parallel.
Yes, consecutive angles are supplementary.

9. Conditions for a Parallelogram
A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition).
If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

10. Assignment 6-2B
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