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Prove like this 3: Quadrilaterals

Author:Steve Phelps

PROVE

Given Segment BE is congruent to segment ED and that angle DEB is right, what kind of quadrilateral could this be, and how do you know?
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No Constraints

This figure has no constraints (givens). Drag the points around. Could this figure ever be a trapezoid? Under what conditions? How do you know? Could this figure ever be an isosceles trapezoid? Under what conditions? How do you know? Could this figure ever be a kite? Under what conditions? How do you know? Could this figure ever be a parallelogram? Under what conditions? How do you know? Could this figure ever be a rectangle? Under what conditions? How do you know? Could this figure ever be a rhombus? Under what conditions? How do you know? Could this figure ever be a square? Under what conditions? How do you know?
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One Constraints

This figure has one constraint (givens): Segment BE is congruent to segment ED. In other words, we say E is the _______ of segment BE. Drag the points around. Could this figure ever be a trapezoid? Under what conditions? How do you know? Could this figure ever be an isosceles trapezoid? Under what conditions? How do you know? Could this figure ever be a kite? Under what conditions? How do you know? Could this figure ever be a parallelogram? Under what conditions? How do you know? Could this figure ever be a rectangle? Under what conditions? How do you know? Could this figure ever be a rhombus? Under what conditions? How do you know? Could this figure ever be a square? Under what conditions? How do you know?
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Two Constraints

This figure has one additional constraint (givens): Segment BD is perpendicular to segment AC. Drag the points around. Could this figure ever be a trapezoid? Under what conditions? How do you know? Could this figure ever be an isosceles trapezoid? Under what conditions? How do you know? Could this figure ever be a kite? Under what conditions? How do you know? Could this figure ever be a parallelogram? Under what conditions? How do you know? Could this figure ever be a rectangle? Under what conditions? How do you know? Could this figure ever be a rhombus? Under what conditions? How do you know? Could this figure ever be a square? Under what conditions? How do you know?

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