Question

The median of a triangle divided it into two ( A median is a line segment from a vertex to the midpoint of the opposite side. )

(a) triangles of equal area

(b) congruent traingles

(c) isosceles triangles

(d) right triangles

Answer 1

(a) triangles of equal area

Let PQR be a triangle and let PS be one of its medians.
In △PQS and △PRS the vertex is common and these bases QS and RS are equal.

Draw PT⊥QR.

Now area(△PQS)=$\frac{1}{2}$​×base×altitudeof△PQS

=$\frac{1}{2}$​×QS×PT

=$\frac{1}{2}$​×RS×PT(∵QS=RS)

but RS and PT is the base and altitude of △PRS

=$\frac{1}{2}$​× base RS × altitude of △PRS

=area△PRS

⇒area(△PQS)=area(△PRS)

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