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CHAPTER:- AREA OF PARALLELOGRAM AND TRIANGLES CLASS 9
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Consider △AOC and △AOC
∠EBC=∠BCA and ∠BEC=∠ECA as they are alternate angles
Hence, as two angles are equal the third angle is also equal.
∠AOC=∠BOE
So, △AOC and △AOC are similar by AAA
And also,
∠AOB=180
∘
−∠AOC=∠COE
Now, consider △AOB and △EOC
sides AO is proportional to OE
sides CO is proportional to OB
and ∠AOB=∠COE
Hence, △AOB and △EOC are similar by SAS
So,
∠ABC=∠BCE and ∠BAE=∠AEC property of similar triangles
So, AB∣∣CE
Hence, ABEC is a parallelogram.
Hope this will help you.......
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