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Answer variants:
bisected angles
\(\angle PON\)
common
angle bisector
corresponding pair of sides
\(\angle OPN\)
\(OM\) is the angle bisector of \(\angle POQ\). \(NP\) and \(NQ\) meet \(OA\) and \(OB\) respectively at \(69^\circ\). Complete the missing fields to prove that the triangles \(OPN\) and \(OQN\) are congruent to each other.
Proof:
We know that \(OM\) is the .
Hence, \(= \angle QON\).
[Since the angles mentioned in the previous step are ]
Now, let us consider the triangles OPN and OQN.
\(= \angle OQN =\) \(69^\circ\) [Given]
Also, \(ON\) is to both the triangles \(OPN\) and \(OQN\)
Here, one and two corresponding pair of angles are equal.
Thus by congruence criterion, \(OPN\) \(\cong\) \(OQN\).
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