Asked by Ian
I will prove that quadrilateral EFGH is a rectangle by demonstrating that _
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GPT-5 mini
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I will prove that quadrilateral EFGH is a rectangle by demonstrating that all four of its interior angles are right angles.
Equivalent (also sufficient) ways to prove EFGH is a rectangle:
- Show EFGH is a parallelogram and one angle is 90° (a parallelogram with one right angle is a rectangle).
- Show opposite sides are parallel and adjacent sides are perpendicular (EF ∥ GH, FG ∥ EH, and EF ⟂ FG).
- Show the diagonals bisect each other and are equal in length (diagonals that bisect each other and are congruent characterize a rectangle).
Any one of these statements (or directly proving each angle = 90°) completes the proof.
Equivalent (also sufficient) ways to prove EFGH is a rectangle:
- Show EFGH is a parallelogram and one angle is 90° (a parallelogram with one right angle is a rectangle).
- Show opposite sides are parallel and adjacent sides are perpendicular (EF ∥ GH, FG ∥ EH, and EF ⟂ FG).
- Show the diagonals bisect each other and are equal in length (diagonals that bisect each other and are congruent characterize a rectangle).
Any one of these statements (or directly proving each angle = 90°) completes the proof.
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