Construction Instructions:
Step 1: Create a quadrilateral and label it ABCD.
Step 2: Construct midpoints on each of the sides.
Step 3: Connect these midpoints to form quadrilateral EFGH.

Investigate:
Drag the vertices or sides of quadrilateral ABCD. Make sure you drag it into a variety of sizes and shapes, including concave quadrilaterals. You might want to measure lengths of sides, measures of angles, and find areas of quadrilaterals to assist in identifying various relationships.
(You will need to construct the polygon interior of each quadrilateral and measure its area)

To construct the polygon interior of a closed figure:
o Select the vertices of the closed figure, in order.
o Choose from the Construct menu, the Polygon Interior command.
o Click anywhere inside the sketch window to de-select the polygon interior.

 To measure the area of a polygon:
· Select the polygon interior.
· Choose from the Measure menu, the Area command.

Conjectures: Record your conjectures about the midpoint quadrilateral.
 

Explore More: Under what conditions is the midpoint quadrilateral (quadrilateral EFGH) a rectangle? A rhombus? A square?
 

Justify: Verify that your conjectures are true or false. Create an argument to convince your classmates that your conjectures are true (or false).
 

Think about: What would you need to do to formally PROVE one of your conjectures?