What types of quadrilaterals are formed when various restrictions are placed on the diagonals?
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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.
Drag any of the red dots to change the shape or size of a figure.
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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?
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