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Question

In given figure, FECGBD and 1=2. then prove that ADEABC.
1008982_fa3ca3a636e94c7f9ad9c0d3b93fef40.png

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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=ADBD

DE||BC [By the converse of basic proportionality theorem]

1=3 and 2=4

Thus, in sADE and ABC, we have

A=A

1=3

2=4

So, by AAA-criterion of similarity, we have

ADEABC [Hence proved]

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