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Can you conclude that this parallelogram is a rectangle explain

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Concept:

– In a parallelogram, if one angle is a right angle, all angles are right angles, so the figure is a rectangle.
– Equivalently, a parallelogram is a rectangle iff its diagonals are equal in length.
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Example:

– Let A(0,0), B(4,0), D(0,3).
Then C = B + D – A = (4,3).

– AB is along the x-axis and AD is along the y-axis, so AB ⟂ AD; angle A = 90°.
– Therefore ABCD is a rectangle (all angles are 90°, opposite sides are parallel and equal).
– Brief explanation: – In a parallelogram, a right angle at one vertex forces all angles to be right angles, yielding a rectangle.

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