Kites and trapezoids

The class wrapped up working with parallelograms today. The class spent about 20 minutes completing questions and discussing problems. We then went through responses. I displayed a page of responses from a randomly chosen student and then the class commented or questioned the results. There were some good discussions and some ideas were clarified and some misunderstandings identified.

We then dove into working with kites and trapezoids. I had three examples of each on the board. For the trapezoids, I was sure to include one example of an isosceles trapezoid. I then had students refer to the quadrilateral properties grid and asked them to consider the examples and try to complete the grid columns for kites and trapezoids.

I walked around and answered questions students had. I also asked students their reasoning and thinking about their entries. The main focus I was trying to have students consider the properties that parallelograms always have and what this would mean for kites and trapezoids. Students seemed to struggle with the connections but finally started to realize that if a parallelogram always had diagonals that bisected each other then kites and trapezoids could never have this property.

The properties that parallelograms sometimes have were a bit trickier. For example, all side lengths are congruent is always true for a rhombus; kites and trapezoids can never have all side lengths congruent. On the other hand, a rhombus always has diagonals that are perpendicular but this does not preclude a kite from also always having perpendicular diagonals.

I referenced traditional kites that students may have used as children to make connections to the diagonal structures that are present in a kite.

I passed out a sheet that contained definitions and theorems concerning kites and trapezoids. This sheet also provided a couple of worked examples and a few problems. Their homework is to complete the problems for next class, which will provide additional problem and work practice.