Question

prove that median of a triangle divides into two equal parts of equal area​

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)=

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)

Step-by-step explanation:

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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)=  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.