Prove like this 3: Quadrilaterals

Author:
Steve Phelps
Topic:
Quadrilaterals

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?
Image

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?
Image

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?
Image

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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