In trapezoid ABCD, identify DC. HELP ASAP!!
1 answer:
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.
<u>Trapezoid mid segment theorem states that the mid segment of a trapezoid is equal to half of sum of its two parallel sides.</u>
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
Substitute known values,
Thus, the value of line segment DC is 19 .
Hence, option (a) is correct.
You might be interested in
Answer:
= 12
Step-by-step explanation:
The shape ABCDEF is an irregular polygon.
The sum of the interior angles of any regular or irregular polygon = (n - 2) x 180 (where n is the number of sides of the polygon).
Therefore, the sum of the interior angles of shape ABCDEF = (6 - 2) x 180 = 720°
So to find the value of , we need to add together all the interior angles and equal it to 720, then solve for
.
Before we do that, we need to determine angle F.
From inspection, we can see that angle F and 52° are a linear pair. We know that a linear pair of angles add up to 180°, so F + 52 = 180 ⇒ F = 180 - 52 = 128°
Therefore:
A + B + C + D + E + F = 720
(10 - 5) + 108 + (8
- 3) + (14
- 25) + 133 + 128 = 720
Collect like terms:
10 + 8
+ 14
- 5 + 108 - 3 - 25 + 133 + 128 = 720
Combine like terms:
32 + 336 = 720
Subtract 336 from both sides:
32 = 384
Divide both sides by 32:
= 12