Use Exercise 33 and the following drawing to complete the proof of this theorem: “The length of the median of a trapezoid is onehalf the sum of the lengths of the two bases”.
Given:  Trapezoid


Prove: 

33. Use Theorem
Given: 


Prove: 

To prove:
Given:
We need to prove, “The length of the median of a trapezoid is onehalf the sum of the lengths of the two bases”.
In a trapezoid ABCD,
Property used:
MeansExtremes Property:
In a proportion, the product of the means equals the product of the extremes; that is, if
If a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.
Proof:
Consider a trapezoid ABCD.
Given that
We know that the median of the trapezoid is parallel to each base.
We know that, if a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side
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