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ABC is a triangle and AD is the median of the triangle. E is any point on the median ED. Which of the following options is correct?

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ar(ABE) = ar(ACE)

BE = CE

AB+BE = AC+CE

AE=

\frac{BC + CE}{2}

answer is A.

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Detailed Solution

Given, AD is the median of the triangle which divides the triangle in two equal triangles i.e

area (△ ABD) = area (△ ACD)

…. eq(1)

Let us Consider a point E on AD
Since CD= BD as the median divides the side BC in two equal parts,

area (△ CDE) = area (△ EBD)

…. (2)
Now, subtracting The equation 2 from equation 1 we get
Area of ⃤ ABE =Area of ⃤ ACE

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