Q. 175.0( 7 Votes )

In the given figu

Answer :

Given: ∆ ABC and ∆ DBC have the same base BC.

AD and BC intersect at O.


To show:


First, we construct the altitudes, AE and DF, of ∆ ABC and ∆ DBC, respectively.



Consider, ∆ AOE and ∆ DOF,


DFO = AEO [Right angles]


DOF = AOE [Vertically Opposite angles]


So, by AA criterion,


∆AOE ∆DOF


Ratio of all the corresponding sides of ∆ AOE and ∆ DOF are equal.


……….(i)


Now, we know that



……….(ii)


Similarly, ……….(iii)


Dividing (ii) by (iii),




[From (i)]


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