Use the definition of a parallelogram to complete the biconditional statement.

A parallelogram is a quadrilateral with two pairs of parallel sides.

A quadrilateral is a parallelogram _[blank]_.

Which answer correctly fills in the blank in the previous sentence?

if it has two pairs of parallel sides and is a polygon

if and only if it has two pairs of parallel sides

because it has only four sides and two of them are parallel

if it has only two pairs of parallel sides

if and only if it has two pairs of parallel sides

Step-by-step explanation:

The definition says that a paralellogram is a quadrilateral with two pairs of parallel sides. That means that  the only way to have a paralellogram is to have a quadrilateral with two pairs of parallel sides. If we have a quadrilateral with only one pair of parallel sides, then it is not a parallelogram.

This translates to the following statement "a quadrilateral is a parallelogram if and only if it has two pairs of parallel sides". Meaning that if we have a parallelogram we know we have a quadrilateral with two pairs of parallel sides and if we have a quadrilateral with two pairs of parallel sides we have a parallelogram.

2160ft3

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)