Question

In figure, side of is produced on both sides such that . Prove that .

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Medium

Solution

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In
  (linear pair angles)

  …(i)
Also   …(ii)
But   (given) …(iii)
From (iii), eqn (i) becomes
  …(iv)
Now from (ii) and (iv), we have

i.e.,
  (converse of isosceles theorem)
Hence proved.

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