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  • The median of a triangle divides it into two (A) triangles of equal area (B) congruent triangles (C) right triangles (D) isosceles triangles

The median of a triangle divides it into two

(A) triangles of equal area
(B) congruent triangles
(C) right triangles
(D) isosceles triangles

Answers (1)

Answer: [A]

Solution: 

Let AN be the median of \triangle ABC

`

We have drawn AM perpendicular to BC

We know that median bisects a line into 2 equal parts.

Hence BN = NC …(i)

Now, area of a triangle is given as = \frac{1}{2} (Base) (Height)

Area of   \triangle ABN= \frac{1}{2} (BN)(AM)        …(ii)

(AM is the perpendicular distance between point A and BN. Hence AM is the height of  \triangle ABN )

Area of  \triangle ACN = \frac{1}{2}(CN)(AM)

(AM is the perpendicular distance between point A and CN. Hence AM is the height of  \triangle ACN )

From (i), we have BN = NC

Area of \triangle ACN = \frac{1}{2}(BN)(AM)     …(iii)

Comparing equations (ii) and (iii), we get

Area of   \triangle ABN  =  Area of  \triangle ACN 

Hence the median of a triangle divides it into two triangles of equal area.

Hence, option (A) is the correct answer. 

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