Question

In the figure below, points D, E, and F are the midpoints of the sides of LABC,

Suppose DF=34, AC=48, and BC=78.
Find the following lengths.

Answer 1

Answers:

• DE = 39
• AB = 68
• BE = 34

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Step-by-step explanation:

BC = 78 is parallel to the midsegment DE.

This parallel midsegment is half as long as BC, so DE = BC/2 = 78/2 = 39

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DF = 34 doubles to AB = 2*DF = 2*34 = 68, since the midsegment is half as the parallel side, so we just think in reverse of that process.

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BE = 34 for two reasons

• Quadrilateral EBFD is a parallelogram with opposite sides BE and DF that are congruent.
• E is the midpoint of AB, so BE is half as long as AB

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We don't use the info that AC = 48.