Question

assume the two lines $overline{ab}$ and $overline{xy}$ intersect as in the diagram below. which of the following statements are true? check all that apply. $angle ary$ and $angle xrb$ are vertical angles. $angle ary$ and $angle xrb$ are complementary. $overline{ab}$ and $overline{xy}$ are perpendicular. $angle ary$ and $angle xrb$ are supplementary.

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. $\angle ARY$ and $\angle XRB$ are vertical angles because they are opposite each other at the intersection of lines $\overline{AB}$ and $\overline{XY}$.

Step2: Recall complementary - angle definition

Complementary angles add up to $90^{\circ}$. $\angle ARY$ and $\angle XRB$ are vertical angles and are equal, not complementary.

Step3: Recall perpendicular - line definition

Since the angle at the intersection of $\overline{AB}$ and $\overline{XY}$ is shown as a right - angle (the small square at the intersection point), $\overline{AB}$ and $\overline{XY}$ are perpendicular.

Step4: Recall supplementary - angle definition

Supplementary angles add up to $180^{\circ}$. $\angle ARY$ and $\angle XRB$ are vertical angles and are equal, not supplementary.

Answer:

• $\angle ARY$ and $\angle XRB$ are vertical angles.
• $\overline{AB}$ and $\overline{XY}$ are perpendicular.