Question

Consider the quadrilateral ABCD. Which information could be used to prove that the quadrilateral ABCD is a parallelogram?

A) apply the distance formula to show that diagonals AC and BD are congruent.
B) Apply the distance formula to show that segments AB and AD are congruent and segments CD and BC are congruent
C) Apply the slope formula to show that segments AB and CD are perpendicular and segments AD and BC are perpendicular.
D)Apply the slope formula to show that segments AB and CD have the same slope and segments AD and BC have the same slope

Answer 1

For all you other k12 ppl dreading this ... the answer is D

Answer 2

Correct choice is D

Explanation:

A) This option is false, because diagonals AC and BD of the parallelogram heedn't be congruent.

B) This option is false, because if quadrilateral ABCD has two pairs of congruent sides, then this quadrilateral is kite (not parallelogram).

C) This option is false, because two pairs of opposite parallelogram's sides cannot be perpendicular.

D) This option is true, because parallelogram is a quadrilateral with two pairs of parallel opposite sides. So, if segments AB and CD have the same slope and segments AD and BC have the same slope, then AB║CD and AD║BC and ABCD is a parallelogram.