NAME _____________________________________________ DATE ____________________________ PERIOD _____________
6-3 Enrichment
Tests for Parallelograms
By definition, a quadrilateral is a parallelogram if and only if both pairs of opposite sides are parallel. What conditions
other than both pairs of opposite sides parallel will guarantee that a quadrilateral is a parallelogram? In this activity,
several possibilities will be investigated by drawing quadrilaterals to satisfy certain conditions. Remember that any test
that seems to work is not guaranteed to work unless it can be formally proven.
Complete.
1. Draw a quadrilateral with one pair of opposite sides congruent. Must it be a parallelogram?
2. Draw a quadrilateral with both pairs of opposite sides congruent. Must it be a parallelogram?
3. Draw a quadrilateral with one pair of opposite sides parallel and the other pair of opposite sides congruent. Must it be
a parallelogram?
4. Draw a quadrilateral with one pair of opposite sides both parallel and congruent. Must it be a parallelogram?
5. Draw a quadrilateral with one pair of opposite angles congruent. Must it be a parallelogram?
6. Draw a quadrilateral with both pairs of opposite angles congruent. Must it be a parallelogram?
7. Draw a quadrilateral with one pair of opposite sides parallel and one pair of opposite angles congruent. Must it be a
parallelogram?