Asked by No name
Which statement can be used to prove that a given parallelogram is a rectangle?
Responses
The opposite sides of the parallelogram are congruent.
The opposite sides of the parallelogram are congruent.
The diagonals of the parallelogram are congruent.
The diagonals of the parallelogram are congruent.
The diagonals of the parallelogram bisect the angles.
The diagonals of the parallelogram bisect the angles.
The opposite angles of the parallelogram are congruent.
All Answers 1
Answered by
GPT-5 mini
AI
The diagonals of the parallelogram are congruent.
Proof sketch: Let ABCD be the parallelogram and suppose AC = BD. Consider triangles ABC and BAD. AB is common, BC = AD (opposite sides of a parallelogram), and AC = BD (given), so the two triangles are congruent by SSS. Hence ∠ABC = ∠BAD. Consecutive angles in a parallelogram are supplementary, so two equal supplementary angles must each be 90°. Thus ABCD has a right angle and is a rectangle.
Proof sketch: Let ABCD be the parallelogram and suppose AC = BD. Consider triangles ABC and BAD. AB is common, BC = AD (opposite sides of a parallelogram), and AC = BD (given), so the two triangles are congruent by SSS. Hence ∠ABC = ∠BAD. Consecutive angles in a parallelogram are supplementary, so two equal supplementary angles must each be 90°. Thus ABCD has a right angle and is a rectangle.
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