Question

1. match the correct answers.

given: \\( \angle mno ; \angle mnp \cong \angle o n p ; m p = 2 \\) in
what is the length of \\( o p \\) ?
by which theorem?

Explanation:

Step1: Recall the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Step2: Apply the theorem

Since \( \angle MNP\cong\angle ONP\), \(NP\) is the angle - bisector of \( \angle MNO\). Also, \(MP\perp NM\) and \(OP\perp NO\).
By the Angle - Bisector Theorem, \(MP = OP\).

Answer:

The length of \(OP\) is \(2\) in. By the Angle - Bisector Theorem.