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Question
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
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Solution
Let ABCD is a parallelogram.
Given: ∠1 = ∠2
Now, ABCD is a parallelogram.
So, ∠1 = ∠4 [Alternate angles] ...(i)
Also, ∠2 = ∠3 [Alternate angles] ...(ii)
Now, ∠1 = ∠2 ...[Given]
Hence, ∠3 = ∠4 ...[From equation (i) and (ii)]
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