The Show and Hide buttons allow three different quadrilaterals and their measurements to appear or disappear on the screen, with the following properties:

• Show/Hide Perpendicular Bisectors: Draws a quadrilateral for which the diagonals bisect one another and meet at a right angle.
• Show/Hide Perpendicular Bisectors Congruent: Same as above, but the diagonals are also equal in length.
• Show/Hide Congruent Bisectors: The diagonals have equal length and bisect one another.

Click Show Perpendicular Bisectors. Notice that the measurements of the four interior segments are displayed.

• Given the measurements of the half-diagonals, what can you conclude about the side lengths of the quadrilateral that is formed?
• Drag any of the red points to change the size and shape of the quadrilateral. Does the relationship between the side lengths change?
• What types of quadrilaterals can be formed if the diagonals are perpendicular bisectors?

Conduct a similar investigation for Perpendicular Bisectors Congruent and for Congruent Bisectors. What types of quadrilaterals are formed in each of these cases?