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Question

In the given figure, FECGBD and 1=2. Prove that ADEABC.

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Solution

We have,
FECGBD
EC=BD ....(i)
It is given that
1=2
AD=AE [sides opposite to equal angles are equal] ....(ii)
From (i) and (ii), we have
AEEC=ADED
DE || BC [By the converse of basic proportionality theorem]
1=3 and 2=4
Thus, in s ADE and ABC, we have
A=A
1=3
2=4
So, by AAA-criterion of similarity, we have
ADEABC


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