A surveyor needs to measure the distance, AB, across the lake. beginning at E, he locates the midpoint, C, of AE and the midpoint, D, of BE. He then measures CD. What is AB?

A surveyor needs to measure the distance AB across the lake beginning at E he locates the midpoint C of AE and the midpoint D of BE He then measures CD What is class=

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Answer:

158 m

Step-by-step explanation:

According to the midpoint theorem, the segment joining midpoints of two segments in a triangle is parallel to the third side and is half of the length of third side.

In the given figure,

AEB is the triangle,

In which C and D are the midpoints of the segment of the segments EB and EA respectively,

Thus, by the midpoint theorem,

DC ║ AB and DC = [tex]\frac{AB}{2}[/tex]

Or AB = 2DC

Given, DC = 79 m,

Hence, AB = 2(79) = 158 m.

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