Examine quadrilateral ABCD, which has vertices A(1,6),B(6,6), C(5,2), and D(0,2). Which methods can be used to prove that quadrilateral ABCD is a parallelogram? Select all that apply.

Question

Prove AD≅AB and BC≅CD by using the distance formula and the definition of congruent segments. Prove AD and BC have equal slopes and are therefore parallel, by using the slope formula. Then prove AD≅BC by using the distance formula and the definition of congruent segments. Prove AD and BC have equal slopes and are therefore parallel, by using the slope formula. Then prove AB≅CD by using the distance formula and the definition of congruent segments. Prove AB∥CD and BC∥AD by using the slope formula and the relationship of the slopes of parallel lines.

Answer 1

A and B have the same y coordinate, 6, so they form a horizontal line

same with C and D with the same y=2 coordinate, forming another horizontal line, parallel to AB.

AB is parallel to CD.

Same doesn't apply to the x coordinates, only thing they have in common is AC distance is 5, just like BD

that makes AC and BD parallel.

sloppy "proof" but true.