sketchometry.org Explore the Midpoint Quadrilateral of a Quadrilateral Explore the Midpoint Quadrilateral of a Quadrilateral Prerequisites and Objectives > Students know special quadrilaterals such as rectangle, square, trapezoid, kite, rhombus, and parallelogram. > Students construct the midpoints of the sides of a quadrilateral and investigate the midpoint quadrilateral. > Students explain why this quadrilateral is a parallelogram. sketchometry Instructions Students should know > how to construct a quadrilateral/polygon, > how to construct the midpoint of a line segment, > how to show grid lines and PropertiesShow Grid > how to snap to the grid. PropertiesSnap to grid Further Explorations > Students compare this result with the midpoint quadrilateral of a kite. > Students investigate midpoint quadrilaterals of other special quadri- laterals. Explore the Midpoint Quadrilateral of a Quadrilateral Construction > Choose any four points and connect them to obtain a quadrilateral. > Construct the midpoints E, F, G, and H of the sides of the quadrilateral. > Draw the midpoint quadrilateral EFGH. Exploration > Drag any of the vertices A, B, C, and D and observe the midpoint quadri- lateral EFGH. Describe its shape. > Write down your observation in your study journal. > Support your conjecture with a proof. Hint: Draw the diagonals of quadri- lateral ABCD as auxiliary lines. > Draw special types of quadrilaterals ABCD (square, rectangle, parallelo- gram, rhombus) by placing the vertices of these quadrilaterals on grid points. Describe what kind of midpoint quadrilaterals you get. > Write your results in your study journal together with sketches and proofs. sketchometry.org – Center for Mobile Learning with Digital Technology – University of Bayreuth – Result Sheet Explore the Midpoint Quadrilateral of a Quadrilateral > Which special shape does the midpoint quadrilateral of a quadrilateral have? Write down your conjecture. > Draw the diagonals of the quadrilateral ABCD. Consider the triangles ACD and CAB. Then consider the triangles DBC and BDA. Write down a proof of your above conjecture. > Draw special types of quadrilaterals (square, rhombus, parallelogram, rectangle) by placing the vertices of the quadrilateral ABCD on grid points. Describe what kind of midpoint quadrilaterals you get. sketchometry.org – Center for Mobile Learning with Digital Technology – University of Bayreuth.