A median of a triangle divides it into two
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Show that a median of a triangle divides it into two triangles of equal area
Answered by admin @
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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