Question

In trapezoid ABCD, identify DC. HELP ASAP!!

Answer 1

option (a) is correct.

the value of line segment DC is 19 .

Explanation:

Given a trapezoid ABCD with AB║DC and AB = 13 , GH = 16

We have to find the length of DC.

mid segment is a line joining mid points of two non parallel sides of a trapezoid.

Trapezoid mid segment theorem states that the mid segment of a trapezoid is equal to half of sum of its two parallel sides.

Since, G is mid point of side AD as AG = GD (given)

also, H is mid point of side BC as BH = HC (given)

Thus, GH is the mid segment of the trapezoid ABCD.

AB║DC , GH ║DC AB║GH

Thus, using trapezoid mid segment theorem, we have

`GH=(1)/(2)(AB+DC)`

Substitute known values,

`16=(1)/(2)(13+DC)`

`\Rightarrow 32=(13+DC)`

`\Rightarrow DC=19`

Thus, the value of line segment DC is 19 .

Hence, option (a) is correct.