If FE is a midsegment of ABCD, find DF.
A. 2
B. 3
C. 5
D. 6

C

Step-by-step explanation:

Remark

A midsegment is 1/2 the size of the side that it is parallel to.

Equation

6x - 6 = 2*(x + 3)                    Remove the brackets

6x - 6 = 2x + 6                       Subtract 2x from both sides

6x - 2x - 6 = 6                        Combine

4x - 6 = 6                               Add 6 to both sides

4x = 6 + 6                              Combine

4x = 12                                   Divide by 4

x = 12 / 4

x = 3

Find DF

But that's not the answer.

DF = x + 2

DF = 3 + 2

DF = 5

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.