ABCD is a trapezoid with median EF. a. AB = 15, DC = 11, then EF = ? b. EF = 14, DC = 10, then AB = ? c. EF = 18, AB = (5n - 9), and DC = (2n + 3). Fin

Question

im confused on what im supposed to do to answer this question. please help

Answer 1

You should definitely draw a picture for this one, if a picture isn't already given. Your trapezoid has two parallel sides. In order for this problem to work, make sure the two parallel sides are AB and CD. The median (or midsegment) of the trapezoid connects the midpoints of the other two sides, and there are two important properties. The midsegment is always parallel to the two parallel bases of the trapezoid, AND the midsegment is always the average of the lengths of the two parallel bases. For instance, if the length of AB was 1 and the length of CD was 3, then the length of the midsegment EF would be the average of 1 and 3, which is 2.

 

In part a, the length of AB is 15 and the length of DC is 11. You just have to find the median, which will be the average of 15 and 11.

 

In part b, they give you the median and one of the parallel sides. Don't just find the average, you have to find the length of the OTHER parallel base.

 

In part c it's the same as part a, except the values are replaced with algebraic expressions. Do the same thing - find the average. Your answer will be an algebraic expression!

 

Let me know if you need more help.