Question

assume that lines ac and bd are parallel. complete each statement. in terms of m and a number in degrees, p = ? in terms of m and number in degrees, n = ? therefore, in terms of m, n = ? these statements prove which theorem? a p = 90 - m; n = 90 - m; n = p; if parallel lines have a transversal, then vertical angles are congruent b p = 90 - m; n = 90 - m; n = m; if parallel lines have a transversal, then corresponding angles are congruent c p = 90 - m; n = 90 - m; n = p; if parallel lines have a transversal, then alternate interior angles are congruent d p = 90 - m; n = 90 - m; n = m; if parallel lines have a transversal, then same side interior angles are congruent

Explanation:

Step1: Find the value of p

Since the angle formed by the horizontal - like line and AC is a right - angle (implied by the perpendicular symbol), and one part of this right - angle is m. Using the fact that the sum of angles in a right - angle is 90 degrees, we have $p = 90 - m$.

Step2: Use the property of parallel lines

Lines AC and BD are parallel. The angle corresponding to p and n are alternate interior angles. By the property of parallel lines with a transversal, alternate interior angles are congruent. So $n=p$. Since $p = 90 - m$, then $n = 90 - m$.

Step3: Identify the theorem

The key property used here is that if parallel lines have a transversal, then alternate interior angles are congruent.

Answer:

C. $p = 90 - m$; $n = 90 - m$; $n = p$; If parallel lines have a transversal, then alternate interior angles are congruent