Question

Jason is trying to prove that this quadrilateral is a rhombus. Using the slope formula, he finds that opposite sides of the polygon are parallel. Since all of the sides appear to be congruent, Jason concludes that ABCD is a rhombus. Is Jason's reasoning correct? Why or why not

Answer 1

Opposite sides being parallel proves that hte figure is a parallelogram.  The sides only appear to be equal so his conclusion is not valid. He would need to show that  2 adjacent sides of the parallelogram are equal ( using the distance formula)  to prove that it is a rhombus.

Answer 2

No, it is not.

Explanation:

Proving the opposite sides are parallel is the correct first step. If the quadrilateral is not a parallelogram, it cannot be a rhombus.

After knowing the quadrilateral is a parallelogram, we must know whether the sides are congruent. To do this, we must use the distance formula to find the length of each side.