Question 1193344: EF is the median of trapezoid ABCD in the figure below. Use the following theorems to answer the questions.
If three (or more) parallel lines intercept congruent line segments on one transversal, then they intercept congruent line segments on any transversal.
The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.
Suppose that AB = 11.4 and DC = 17.2.
Find MF.
Find EM.
Find EF.
Find
1/2(AB + DC).
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
No figure shown; without it we can answer some of the questions but not all.
Find MF.
We can't; point M is not defined
Find EM.
We can't; point M is not defined
Find EF.
The median of a trapezoid has a length that is half the sum of the lengths of the two bases: (11.4+17.2)/2= 14.3
Find 1/2(AB + DC).
14.3 -- we did that above
If you can use ONLY the theorems shown to find the length of EF, then draw diagonal AC to divide the trapezoid into triangles ABC and ACD, with the diagonal intersecting EF at some point P.
Then, using the stated theorem about the length joining the midpoints of a side of a triangle, EP is half of CD and PF is half of AB, so EF=EP+PF is half of (AB+CD).
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