This active exploration works with physical geoboards or calculator/ online apps. Students from 6th-10th grade can find this material new and engaging, with upper elementary students, this may work after a quadrilaterals unit with strong guidance.
Students first explore using geoboards by creating examples of squares and trapezoids and looking at basic properties of their diagonals. (Are the diagonals congruent? Parallel? Intersection? Bisecting each other?")
Students are then instructed to make an example on the geoboard of each relevant vocabulary word, including parallelogram, congruent, bisect, and more.
The second page is a table for students to explore which theorems result in parallelograms. Students are given a statement. They build at least two quadrilaterals that match the statement and use those to hypothesize whether the statement always, sometimes, or never results in a parallelogram. The statements cover a variety of answers, including all theorems found in section 6.3 of Holt Geometry.
No answer key is included. This activity is best seen as an exploration where students should be coming up with the answers and explaining to each other rather than thinking the answers are easy and simple.