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State whether the following statement is true or false:

A 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

Given, a triangle with a median.
Question Image

Δ A B C

, AD is the median.
Now, area of triangle=

12

base

\times

height

⇒ a r Δ A B D = 12 B D A E ⇒ a r Δ A B D = 12 D C A E [D is the midpoint of BC, BD=DC] ⇒ a r Δ A B D = a r Δ A C D

Thus, the median of the triangle divides it into two triangles of equal area.
Hence, the given statement is true.
Hence, the correct option is 1.

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