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.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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