Students will use Cabri® Jr. software on their TI-83/84 calculator to connect consecutive midpoints of different quadrilaterals and analyze and determine characteristics of the new quadrilateral formed.
Before the Activity
Students should be familiar with Cabri Jr. on their calculator. Students should have received instruction in coordinate geometry and also about the definitions and properties of quadrilaterals.
During the Activity
Go to Apps and open up Cabri Jr. Create four segments whose endpoints intersect to form a non-special quadrilateral. Plot the midpoints of all four sides of the quadrilateral and then use these consecutive midpoints as endpoints to create four new segments to form a second quadrilateral in the interior of the original quadrilateral.
Measure lengths and slopes of the four new segments to analyze the new quadrilateral. Sketch a drawing on paper and write down information to support your conclusion. It should be a parallelogram!
Repeat the construction (connecting consecutive midpoints) with the parallelogram as the original figure. What is the new quadrilateral? Clear the drawing and start over by constructing a rectangle. Repeat previous directions with the rectangle as the original figure. What shape is constructed in the interior of the rectangle? How about the next quadrilateral formed?
Connect consecutive midpoints of other different special quadrilaterals (rhombus, kite, square, etc.) and analyze to decide what the new quadrilateral is.
After the Activity
Request students to make a table with the first column listing all the different quadrilaterals and the second column giving the quadrilateral formed when consecutive midpoints of the first quadrilateral are connected.