Triangles on the same Base and Between the same Parallels

If the two triangles are on the same base and their opposite vertex is on the parallel line then their area must be equal.

Here, ABC and DBC are the two triangles having common base i.e. BC and between the two parallel lines i.e. XY and BC.

ar (ABC) = ar (DBC)

Area of Triangle

Area of triangle  =\dfrac{1}{2}\times\ \text{base}\times\ \text{height}

Median of a Triangle

The line segment from any vertex of the triangle to the midpoint of the opposite side is the Median.

There are three medians of a triangle and the intersection of all the three medians is known as the Centroid.

The median divides the triangle into two equal parts.

In ∆ABC AE, CD and BF are the three medians and the centroid is the point O.

AE divides the triangle into two equal parts i.e. ∆ACE and ∆AEB,

CD divides the triangle into two equal parts i.e. ∆CBD and ∆CDA

BF divides the triangle into two equal parts i.e. ∆BFA and ∆BFC.

A Parallelogram and a Triangle on the same base and also between same parallel.

If a triangle is on the base which is same with a parallelogram and between the same parallel line then the area of the triangle is half of the area of the parallelogram.

Here ∆ ABC and parallelogram ABCE are on the same base and between same parallel lines i.e. XY and BC so 

\mathrm{ar\ (\triangle ABC)=\dfrac{1}{2}\ ar(ABCE)}

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