Answer variants:
bisected angles
corresponding pair of sides
\(ON\)
\(OM\)
[Given]
\(\angle PON\)
\(OM\) is the angle bisector of \(\angle POQ\). \(NP\) and \(NQ\) meet \(OA\) and \(OB\) respectively at \(62^\circ\). Complete the missing fields to prove that the triangles \(OPN\) and \(OQN\) are congruent to each other.
Proof:
We know that
is the angle bisector of \(\angle POQ\).
is the angle bisector of \(\angle POQ\).
Hence, \(= \angle QON\).
[Since the angles mentioned in the previous step are ]
Now, let us consider the triangles OPN and OQN.
\(\angle OPN = \angle OQN =\) \(62^\circ\)
Also, is common to both the triangles \(OPN\) and \(OQN\).
Here, Two corresponding pair of angles and one are equal.
Thus by congruence criterion, \(OPN\) \(\cong\) \(OQN\).