Question

29. Show that a median of a triangle divides it into two triangles of equal areas ​

Answer 1

Answer:

Let ABC be a triangle and Let AD be one of its medians.

In △ABD and △ADC the vertex is common and these bases BD and DC are equal.

Draw AE⊥BC.

Now area(△ABD)= 1÷2 ×base×altitude of△ADB

= 1÷2×BD×AE

= 1÷2×DC×AE ( ∵ BD=DC)

but DC and AE is the base and altitude of △ACD

= 1 ÷ 2 × base DC × altitude of △ACD

=area△ACD

⇒area(△ABD)=area(△ACD)

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