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# Geometry PowerPoint PPT Presentation

Geometry. 6.3 Tests for Parallelograms. Proving a Quadrilateral is a Parallelogram. Only one of the following needs to be shown: 1) Show that both pairs of opposite sides are parallel. 2) Both pairs of opposite sides are congruent. 3) Both pairs of opposite angles are congruent.

Geometry

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## Geometry

6.3

Tests for Parallelograms

### Proving a Quadrilateral is a Parallelogram

• Only one of the following needs to be shown:

• 1) Show that both pairs of opposite sides are parallel.

• 2) Both pairs of opposite sides are congruent.

• 3) Both pairs of opposite angles are congruent.

• 4) The diagonals bisect each other.

• 5) A pair of opposite sides is both parallel and congruent.

### Example 1

• Determine if the following quadrilaterals are parallelograms, if yes explain.

### Example 2

• Find x and y so that the quadrilateral is a parallelogram.

### Example 3

• Graph quadrilateral QRST with vertices Q(-1,3), R(3,1), S(2, -3), and T(-2,-1). Determine if it is a parallelogram using the slope formula.

• Worksheet