In trapezoid ABCD, if the base DC = 16 and the base AB = 20 and E is the midpoint of AD and F is the midpoint of BC, what is the measure of EF?
18
To find the measure of EF in trapezoid ABCD, we can use the fact that E is the midpoint of AD and F is the midpoint of BC.
First, let's draw trapezoid ABCD:
A----------------B
/ \
/ \
/ \
D----------------C
Next, let's mark E as the midpoint of AD and F as the midpoint of BC:
A--------E-------B
/ \
/ \
/ \
D------------C
Since E is the midpoint of AD, we can divide AD into two equal parts:
A--------E-------B
/ | \
/ | \
/ | \
D------------C
Now, we can see that DE is equal to EF. Similarly, since F is the midpoint of BC, we can conclude that CF is also equal to EF.
Since DE and CF are equal, we can write an equation:
DE = CF
We know that DC = 16 and AB = 20.
Therefore, we can find the length of EF by subtracting the lengths of DE and CF from the total base length, AB - DC:
EF = AB - (DE + CF)
= AB - 2 * DE
Substituting the known values:
EF = 20 - 2 * DE
Since DE is equal to half of DC (because E is the midpoint of AD), we have:
DE = DC / 2
= 16 / 2
= 8
Therefore, we can substitute the value of DE into the equation for EF:
EF = 20 - 2 * DE
= 20 - 2 * 8
= 20 - 16
= 4
So, the measure of EF is 4.