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
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.