Question

lesson extra practice: points, lines, and planes
use the diagram.

1. give two other names for \\(overrightarrow{cd}).
2. give another name for plane m.
3. name three points that are collinear. then name a fourth point that is not collinear with these three points.
4. name a point that is not coplanar with points a, c, and e.

use the diagram.

1. what is another name for \\(overrightarrow{pq})?
2. what is another name for \\(overrightarrow{rs})?
3. name all rays with endpoint t. which of these rays are opposite rays?
4. in the diagram, draw planes m and n that intersect in line k.

Explanation:

Step1: Recall line - naming rules

A line can be named using any two points on the line. For $\overleftrightarrow{CD}$, two other names could be $\overleftrightarrow{DC}$ and $\overleftrightarrow{BD}$ (assuming $B$ is also on the line).

Step2: Recall plane - naming rules

A plane can be named by any three non - collinear points on the plane. Another name for plane $M$ could be plane $ABC$ (assuming $A$, $B$, and $C$ are non - collinear points on plane $M$).

Step3: Recall collinear and non - collinear points

Three collinear points could be $A$, $C$, $B$ (assuming they are on the same line). A non - collinear point to these three could be $D$.

Step4: Recall coplanar points

A point not coplanar with $A$, $C$, and $E$ could be $D$ (assuming $D$ is outside the plane containing $A$, $C$, and $E$).

Step5: Recall line - naming for $\overleftrightarrow{PQ}$

Another name for $\overleftrightarrow{PQ}$ could be $\overleftrightarrow{QP}$.

Step6: Recall line - naming for $\overleftrightarrow{RS}$

Another name for $\overleftrightarrow{RS}$ could be $\overleftrightarrow{SR}$.

Step7: Recall ray and opposite - ray concepts

Rays with endpoint $T$ are $\overrightarrow{TP}$, $\overrightarrow{TQ}$, $\overrightarrow{TR}$, $\overrightarrow{TS}$. Opposite rays are $\overrightarrow{TP}$ and $\overrightarrow{TQ}$, $\overrightarrow{TR}$ and $\overrightarrow{TS}$ (assuming appropriate orientation).

Step8: Recall plane - intersection concept

To draw planes $M$ and $N$ that intersect in line $k$, draw two flat surfaces (representing planes) that cross each other along a straight line (representing line $k$).

Answer:

1. $\overleftrightarrow{DC}$, $\overleftrightarrow{BD}$
2. plane $ABC$
3. Collinear points: $A$, $C$, $B$; Non - collinear point: $D$
4. $D$
5. $\overleftrightarrow{QP}$
6. $\overleftrightarrow{SR}$
7. Rays with endpoint $T$: $\overrightarrow{TP}$, $\overrightarrow{TQ}$, $\overrightarrow{TR}$, $\overrightarrow{TS}$; Opposite rays: $\overrightarrow{TP}$ and $\overrightarrow{TQ}$, $\overrightarrow{TR}$ and $\overrightarrow{TS}$
8. Draw two flat surfaces crossing along a straight line.