Question(1) For each of the following descriptions, rewrite the statement using geometric notation and draw each figure. (a) Point $B$ on ray $W Q$. (b) Line $R N$ bisects line segment $Q T$. (C) Line $F G$ is parallel to line $T R$. (2) Point $M$ is on $\overline{Q R} . Q R=20 \mathrm{~cm}$. If $M R=12 \mathrm{~cm}$, then what is $Q M$ ? (3) Draw a counterexample for each conditional statement. (a) If $\overline{F G} \cong \overline{G H}$, then point $G$ is on $\overline{F H}$. (b) If $\overleftrightarrow{A B}$ and $\overline{C D}$ are not parallel, then they must intersect.

Studdy Solution
(b) Provide a counterexample for the statement: "If $\overleftrightarrow{AB}$ and $\overline{CD}$ are not parallel, then they must intersect."
Consider $\overleftrightarrow{AB}$ and $\overline{CD}$ as skew lines in 3D space. Draw the counterexample where the lines are not parallel and do not intersect.
\begin{array}{c} \begin{tikzpicture} \draw (0,0) -- (4,0); \draw (1,-1) -- (1,3); \node at (0,-0.3) {A}; \node at (4,-0.3) {B}; \node at (1,-1.3) {C}; \node at (1,3.3) {D}; \end{tikzpicture} \end{array}
Solution:
1. (a) Point $B$ on ray $\overrightarrow{WQ}$: $B \in \overrightarrow{WQ}$ (b) Line $RN$ bisects line segment $\overline{QT}$: $RN \text{ bisects } \overline{QT}$ (c) Line $FG$ is parallel to line $TR$: $FG \parallel TR$
2. $QM = 8 \, \mathrm{cm}$
3. (a) Counterexample for $\overline{FG} \cong \overline{GH}$ with $G$ not on $\overline{FH}$. (b) Counterexample for $\overleftrightarrow{AB}$ and $\overline{CD}$ not parallel and not intersecting.