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.


Answer :

Given


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


Proof:


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


Hence proved


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