Question

line m is constructed as the first step to prove the triangle angle - sum theorem. which of the following must be true in order to complete the proof? a m || n b bc = ac c m∠1 + m∠2 = 90 d m∠1 = m∠2

Explanation:

Step1: Recall Triangle Angle - Sum proof

To prove the Triangle Angle - Sum Theorem, we often use the property of parallel lines and alternate - interior angles. When a line is constructed parallel to one side of a triangle, we can use angle - relationships.

Step2: Analyze the options

If \(m\parallel n\), we can use the properties of parallel lines. For example, alternate - interior angles are equal. This helps in showing that the sum of the interior angles of a triangle is \(180^{\circ}\). If \(m\parallel n\), we can relate the angles of the triangle to a straight - line angle (which is \(180^{\circ}\)).

Answer:

A. \(m\parallel n\)