Question

If the opposite angles of a quadrilateral ABCD are NOT equal, which of the following can be true?If the opposite angles of a quadrilateral ABCD are NOT equal, which of the following can be true?

Answer 1

Answer:

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Step-by-step explanation:

Given:- Quadrilateral ABCD

angle A = angle C; angle B = angle D... [1]

To prove:- The given figure is a parallelogram

angle A + angle B + angle C + angle D = 360*

angle A + angle D + angle A + angle D = 360* (from [1])

angle A + angle D = 180*... [2]

AB || DC (from [2] as angle A and angle D become co-interior angles)

Similarly, we can prove that AD || BC

Hence proved - The given quadrilateral ABCD is a parallelogram by definition.

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