Answer variants:
\(\angle OQN\)
angle bisector
\(\angle QON\)
common
corresponding pair of angles
bisected angles
\(OM\) is the angle bisector of \(\angle POQ\). \(NP\) and \(NQ\) meet \(OA\) and \(OB\) respectively at \(29^\circ\). 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, \(\angle PON = \) .
[Since the angles mentioned in the previous step are ]
Now, let us consider the triangles OPN and OQN.
\(\angle OPN =\) \(=\) \(29^\circ\) [Given]
Also, \(ON\) is to both the triangles \(OPN\) and \(OQN\)
Here, two and one corresponding pair of sides are equal.
Thus by congruence criterion, \(OPN\) \(\cong\) \(OQN\).