Two line segments can be drawn to intersect in various ways—they could be perpendicular, they could bisect one another, or both. Depending on the arrangement of these segments, various quadrilaterals can be formed by connecting the endpoints of the segments.
This activity allows you to discover what types of quadrilaterals can be formed when the diagonals meet in a certain way.
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The Show and Hide buttons allow four different quadrilaterals to appear or disappear on the screen, with the following properties:
- Show/Hide Perpendicular Diagonals: The diagonals will always meet at a right angle.
- Show/Hide Perpendicular Diagonals, One Bisected: The diagonals will always meet at a right angle, and one of the diagonals will be cut in half by the other.
- Show/Hide Congruent Diagonals: The diagonals will always have equal length.
- Show/Hide Bisected Diagonals: The diagonals will divide one another in half.
Drag any of the red dots to change the shape or size of a figure.
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Click Show Perpendicular Diagonals. Drag the red buttons to change the size and shape of the quadrilateral (but notice that the diagonals always meet at a right angle). What types of quadrilaterals can be formed such that the diagonals are perpendicular?
- Can a rectangle be formed?
- Can a trapezoid be formed?
- Can any other shapes be formed?
Use the Show buttons to make other quadrilaterals appear. What types of quadrilaterals can be formed for each of the given constraints on the diagonals?
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