Question

If two lines are parallel, we can conclude that:

• A. Alternate angles are equal
• B. Corresponding angles are equal
• C. Co-interior angles are supplementary
• D. All of the above

Answer 1

The correct option is D (All of the above)

Since, we have properties of angles associated with parallel lines ($l$ and $m$) cut by the transversal ($t$):

Alternate angles: Since, we have the rule of the alternate angles are equal, if and only if the lines are parallel, In this case as obvious that the lines are parallel.
From above figure, we can write alternate angles as $\angle 3=\angle 5,\angle 4=\angle 6$ and $\angle 1=\angle 7,\angle 2=\angle 8$.
Similar way, for Corresponding angles:
From the figure the corresponding angles written as $\angle 2=\angle 6,\angle 1=\angle 5,\angle 4=\angle 8$ and $\angle 3=\angle 7$ as the lines are parallel.
Co-interior angles: The sum of co-interior angles are supplementary, if the lines are parallel.
Thus, $\angle 4+\angle 5={180}^{\circ }$ and
$\angle 3+\angle 6={180}^{\circ }$
Hence, property of parallel lines include,
Alternate angles are equal, corresponding angles are equal, co-interior angles are supplementary. So, all of the options are correct.