Question

state and prove that a median of triangle divides it into two triangles of equal area . how many medians can be drawn in a triangle name the point of intersection.. plzz give me the answer..​

Answer 1

Answer:

you can draw three medians in a triangle

and the point of interaction of medians is known as centroid.

Answer 2

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)=  

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.  

solution

Step-by-step explanation: