Greetings from Alaska,
These five classical constructions will illustrate the five ways to determine that a quadrilateral is a parallelogram. Students will need a compass and straightedge.
This activity pairs with section 8.3 of McDougal Littel geometry: Proving Parallelograms. I have used this as an in class activity as well as a take-home assignment.
1] Construct a parallelogram by constructing opposite sides parallel.
https://youtu.be/ynRl9KIEa8w
2] Construct a parallelogram by c