Compass construction of a parallelogram #1

Compass Construction of a parallelogram #1
This is the first of a five part series of parallelogram constructions intended for high school geometry.

We use the McDougal Littel textbook pictured in the video.
Section 8.3 illustrates the five methods for proving that a quadrilateral is a parallelogram. My students perform all five of these constructions on a double sided sheet op paper. All five constructions together taught live require about a half hour of instruction time.

Definition: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram
Construction #1 - Construct a quadrilateral with both pairs of opposite sides parallel.

Theorem 8.7. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Construction #2 - Construct a quadrilateral with both pairs of opposite sides congruent.

Theorem 8.8. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Construction #3 - Construct a quadrilateral with both pairs of opposite angles congruent.

Theorem 8.9. If ONE pair of opposite sides of a quadrilateral is both congruent AND parallel, then the quadrilateral is a parallelogram
Construction #4 - Construct a quadrilateral with one pair of opposite sides bot parallel and congruent.

Theorem 8.10. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Construction #5 - Construct a quadrilateral with diagonals that bisect each other.