Q. 114.1( 12 Votes )
In the adjoining figure, D and E are points on the sides AB and AC of ∆ABC such that ar(∆BCE) = ar(∆BCD).
Show that DE ‖ BC.
A triangle ABC in which points D and E lie on AB and AC of ∆ABC such that ar(∆BCE) = ar(∆BCD).
To prove: DE ‖ BC
Here, from the figure we know that BCE and BCD lie on same base BC and
It is given that area(∆BCE) = area(∆BCD)
Since two triangle have same base and same area they should equal altitude(height)
That means they lie between two parallel lines
That is DE ‖ BC
DE ‖ BC
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