Question

In trapezoid ABCD, identify DC. HELP ASAP!!

Answer 1

Answer:

option (a) is correct.

the value of line segment DC is 19 .

Step-by-step 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

$GH=\frac{1}{2}(AB+DC)$

Substitute known values,

$16=\frac{1}{2}(13+DC)$

$\Rightarrow 32=(13+DC)$

$\Rightarrow DC=19$

Thus, the value of line segment DC is 19 .

Hence, option (a) is correct.