Question

Prove that median of triangle divides it into two triangle of equal area


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Answer 1

Answer:

Consider triangle ABC with the mid point D on the side BC and height AE

BD = DC ( D is the midpoint of side BC) ---------------------------------------1

Now consider triangle ABD 

Area of triangle ABD = 1/2 * base * height

                                  = 1/2 * BD * AE ------------------------------------------2

Consider triangle BDC

Area of triangle BDC = 1/2 *base * height

                                  = 1/2 * DC * AE ------------------------------------------3

From 1, 2 and 3 we come to know that,

 Area of triangle ABD = Area of triangle DBC

Therefore a median divides a triangle into two triangles of equal area.

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Step-by-step explanation:

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