Question

the following points and lines exist in a plane.
. $overleftrightarrow{ab}$ intersects $overleftrightarrow{pq}$ at point $m$;
. point $c$ is on $overleftrightarrow{ab}$;
. point $r$ is on $overleftrightarrow{pq}$;
. $\triangle cmr$ is a right triangle.
which statement describes the relationship between $overleftrightarrow{ab}$ and $overleftrightarrow{pq}$?
a. $overleftrightarrow{ab}$ and $overleftrightarrow{pq}$ are skew
b. $overleftrightarrow{ab}$ and $overleftrightarrow{pq}$ are collinear
c. $overleftrightarrow{ab}perpoverleftrightarrow{pq}$
d. $overleftrightarrow{ab}paralleloverleftrightarrow{pq}$

Explanation:

Step1: Recall line - relationship definitions

Skew lines are non - coplanar, but the two lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{PQ}$ are in the same plane. Collinear means the two lines are the same line, but they intersect at a single point $M$, so they are not collinear. Parallel lines do not intersect, but $\overleftrightarrow{AB}$ and $\overleftrightarrow{PQ}$ intersect.

Step2: Analyze right - triangle condition

Since $\triangle CMR$ is a right triangle and points $C$ is on $\overleftrightarrow{AB}$, point $R$ is on $\overleftrightarrow{PQ}$, and they intersect at $M$, the angle formed by the two lines at the intersection is a right angle. Perpendicular lines form a right angle at their intersection.

Answer:

C. $\overleftrightarrow{AB}\perp\overleftrightarrow{PQ}$