Question

in the figure below, points t, r, x, y, and z lie in plane p. points q and s do not lie in plane p. in each part below, fill in the blanks to write a true statement. (a) suppose line $overleftrightarrow{qt}$ is drawn on the figure. then $overleftrightarrow{qt}$ and blank are distinct lines that intersect. (b) another name for plane p is plane blank. (c) blank and x are distinct points that are collinear. (d) y, blank, blank, and blank are distinct points that are coplanar.

Explanation:

Step1: Recall line - intersection concept

Two lines intersect if they have a common point. Since $Q$ is outside plane $P$ and $T$ is in plane $P$, a line like $\overleftrightarrow{RT}$ (any line in plane $P$ that intersects $\overleftrightarrow{QT}$) can be considered. Let's take $\overleftrightarrow{RT}$.

Step2: Recall plane - naming convention

A plane can be named by any three non - collinear points in the plane. Points $T$, $X$, and $Y$ are non - collinear points in plane $P$, so plane $P$ can be named plane $TXY$.

Step3: Recall collinear points concept

Collinear points lie on the same line. Points $X$ and $Y$ lie on the same line in plane $P$, so $Y$ and $X$ are collinear.

Step4: Recall coplanar points concept

Coplanar points lie in the same plane. Points $Y$, $X$, $Z$, and $T$ all lie in plane $P$, so we can choose $X$, $Z$, $T$.

Answer:

(a) $\overleftrightarrow{RT}$
(b) $TXY$
(c) $Y$
(d) $X$, $Z$, $T$