Question

Complete the proof that m∠P+m∠T+m∠PQT=180° without using the Triangle Angle Sum Theorem.

Answer 1

Looking at the table of statements and reasons, the missing reason has the statement "

Let's compare the relative position of these two angles in the image below:

These two angles are on opposite sides of the transversal line QT, and in the region between the lines QS and PT, therefore they are alternate interior angles.

Since the lines QS and PT are parallel, alternate interior angles are congruent, so we have

Therefore the reason for statement 3 is the "Alternate Interior Angles Theorem".