Question

Prove that median of a traingle divides it into 2 traingles of equal areas

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer:

Hope the above answer helps you