Question

Johnny is wanting to prove that parallelogram ABCD is a rectangle. He shows that opposite sides are congruent and opposite parallel. Can he conclude ABCD is a rectangle ? Why or why not. Explain your reasoning in complete sentences.

Answer 1

No, because the statement explains a parallelogram also.

Explanation:

A rectangle is a quadrilateral that has four sides which has a set of equal opposite sides that are parallel to each other. The sum of all angles in a rectangle =
`360^(0)`

No, he can not conclude that ABCD is a rectangle with the statement because the statement is applicable to a parallelogram also. He could add that opposite sides are straight and parallel. So that:

<ABC = CDA =
`90^(0)` (right angle property)

<DAB = <BCD =
`90^(0)` (right angle property)