Question

Show that a median of a triangle divides it into two triangles of equal area​

Answer 1

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)=

2

1

×base×altitude of△ADB

=

2

1

×BD×AE

=

2

1

×DC×AE(∵BD=DC)

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

=

2

1

× 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.

Answer 2

Answer:

Step-by-step explanation:

A median of a triangle divides a side into two equal parts. Consider the two equal sides as the bases of a new triangle . The height remains the same. Hence by the equation of the area of triangle $1/2 bh$ b and h are equal and area remains the same. Hence proved