- Diagonals are perpendicular
- Diagonals are congruent
- Diagonals bisect each other
Students drew a parallelogram on a grid and then were asked to determine whether or not each statement was true for their parallelogram. I reminded students that they would need to find the slopes of the diagonals and then multiply these values together to see if the product equaled -1. For the second statement they needed to calculate the length of each diagonal using the distance formula/Pythagorean theorem. For the third statement, they would need to find the midpoint of each diagonal and see if the midpoints were the same.
At this point I let the class work. I knew there would be issues since students, generally, are not comfortable finding slopes, lengths, and midpoints. I walked around and helped students, reminding them of how slopes were calculated. This process took almost the entire class. I had intended this to be a work day with the expectation that students would need help. Having the statements as drivers for why to calculate slopes, lengths, and midpoints definitely helped. It wasn't a matter of why were we calculating these values but, rather, how do I go about calculating these values.
We shared out findings about the slope relationships at the end of class. A few students had diagonals that ended up being perpendicular while the majority did not. We were able to conclude that parallelogram diagonals are not always perpendicular but they can be perpendicular sometimes. Many students had not finished calculating the lengths or midpoints for the diagonals. I asked them to attempt to finish these calculations for next class.
We'll continue practicing work with parallelograms before diving into the sub-categories of rhombuses, rectangles, and squares.
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