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State true or false.
The median of a triangle divides it into two triangles of equal areas.

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True

False

answer is A.

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Detailed Solution

Suppose ABC = triangle, where,
AD = medians.
Now, in

△ ABD

and

△ ADC

,
Vertex is common Where, bases
BD = DC
Now plot a perpendicular AT on the base BC

AE ⊥ BC

Here, area of triangle ABD can be given as,

A = \frac{1}{2} \times base \times altitude of △ ADB

A = \frac{1}{2} \times BD \times AE

A = \frac{1}{2} \times DC \times AE (since, BD = DC)

Now,
DC = base of

△ ADC

AE is altitude of

△ ADC

A = \frac{1}{2} \times base DC \times altitude of △ ACD

A = area △ ACD

A = area △ ACD

A = area △ ACD

So, we can say that median of a triangle divides the triangle into two triangles of same areas. Correct option is 1.

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