Prove like this 3: 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](https://beta.geogebra.org/resource/pqy8wt37/qBAXwSXkMVa0WnLK/material-pqy8wt37.png)
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](https://beta.geogebra.org/resource/gseaqb5e/ky9VWCLtOj2E2hSW/material-gseaqb5e.png)
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](https://beta.geogebra.org/resource/dbe4tweh/o7IMHPDNw525UYoe/material-dbe4tweh.png)
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?