To prove that quadrilateral ABCD is a parallelogram, we can use the definition of a parallelogram as a quadrilateral with opposite sides that are both congruent and parallel.
Given that the opposite sides (AB and CD) of the quadrilateral are congruent, we can infer that AB = CD.
Given that the adjacent angles (ABD and BCD, and CDA and DAB) of the quadrilateral are congruent, we can infer that angle ABD = angle BCD and angle CDA = angle DAB.
Given that the adjacent sides (AB and BC, and CD and DA) of the quadrilateral are congruent, we can infer that AB = BC and CD = DA.
To prove that the quadrilateral is a parallelogram, we need to show that the opposite sides are parallel. We can use the fact that if a pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
Since AB = CD and BC = DA, and AB || CD, we can conclude that quadrilateral ABCD is indeed a parallelogram.
Prove that quadrilateral ABCD is a parallelogram. How do you know that the figure is a parallelogram?
Opposite sides of the figure are congruent.
Adjacent angles of the figure are congruent
Adjacent sides of the figure are congruent.
Adjacent sides of the figure are parallel
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