Question

determine which lines, if any, must be parallel. select all that apply. explain your reasoning. the lines are parallel by the lines perpendicular to a transversal theorem. the lines are parallel by the perpendicular transversal theorem. the lines are parallel by the linear pair perpendicular theorem. only one right angle is marked at each intersection.

Explanation:

Step1: Recall parallel - line theorems

If two lines are perpendicular to the same line, then they are parallel. In the given figure, lines $b$ and $c$ are both perpendicular to line $a$.

Step2: Apply the theorem

By the Lines Perpendicular to a Transversal Theorem (which states that if two lines are perpendicular to the same transversal, then the two lines are parallel), lines $b$ and $c$ are parallel.

Answer:

C. $b$ and $c$
The lines are parallel by the Lines Perpendicular to a Transversal Theorem.