Question

show that a median of a triangle divides it into two triangle of equal areas
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Answer 1

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

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.

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.

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

×base×altitude of△ADB=

$\frac{1}{2} \times bd \times ae$

$\frac{1}{2} ×DC×AE(∵BD=DC)$

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

$\frac{1}{2} × base DC × altitude of △ACD$

= area△ACD

area△ACD⇒area(△ABD) = area(△ACD)

area(△ACD)Hence the median of a triangle divides it into two triangles of equal areas.

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