Mid-points of any quadrilateral

This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright & copy ; 1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

ABCD is a quadrilateral. P, Q, R and S are the mid-points of AB, BC, CD and DA respectively.

Drag the points B, C , D and observe PQRS. What kind of quadrilateral must PQRS be? Compare the areas of PQRS and ABCD. What can you say? Prove your conjectures.

Run Applet 1

Further question

If ABCD is a trapezium, what kind of quadrilateral is PQRS?

Run Applet 2

Further question

If ABCD is a paralleologram, what kind of quadrilateral is PQRS?

Run Applet 3

Further question

If ABCD is a rhombus, what kind of quadrilateral is PQRS?

Run Applet 4

Further question

If ABCD is a rectangle, what kind of quadrilateral is PQRS?

Run Applet 5

Further question

If ABCD is a square, what kind of quadrilateral is PQRS?

Run Applet 6

Further question

PQRS is a quadrilateral, A is a free point, B, C, D and D' are points obtained by reflections.

When will A and D' merge? Drag A, P, Q, R and S to investigate.

If PQRS is fixed, what can you say about the length of AD' when A is dragged? Can you prove the result? Press the "Hint" button for the hints.

Run Applet 7