Question

name:____ date:__ period:__ seat#____
point: a dot that has not dimension. only place.
point a
line: two points that have one dimension. it extends without end.
line l, line ab (\\(overline{ab}\\)), or line ba (\\(overline{ba}\\))
plane: three or more connected points that have two dimensions.
plane m, or plane abc
use the diagram to provide two other names for \\(overrightarrow{pq}\\) and plane r.
compare collinear points and coplanar points.
name the intersection of \\(overrightarrow{pq}\\) and line k.
name the intersection of plane a and plane b.
name the intersection of line k and plane a.
provide the collinear points.
name four points.
name two lines.
name the plane that contains point a, b and c.
name the intersection of the two planes.

Explanation:

Step1: Recall line - naming rules

A line can be named using any two points on it. For $\overline{PQ}$, other names could be $\overline{QP}$, line $P$ and $Q$, or line $Q$ and $P$. For a plane, it can be named by three non - collinear points on it or by a single capital letter. For plane $R$, other names could be plane $VST$ (assuming $V$, $S$, and $T$ are non - collinear points on the plane as shown in the diagram).

Step2: Recall collinear and coplanar points

Collinear points are points that lie on the same straight line. Coplanar points are points that lie on the same plane. Collinear points are a subset of coplanar points since a line lies on a plane, but not all coplanar points are collinear.

Step3: Find intersections

For the intersection of $\overline{PQ}$ and line $K$, we look for the common point, which is point $M$. The intersection of two planes is a line. For plane $A$ and plane $B$, the intersection is the line passing through the common points (not clearly labeled in the general case but conceptually a line). The intersection of line $K$ and plane $A$ is point $M$.

Step4: Identify points, lines, and planes

Four points could be named as $A$, $B$, $C$, $D$ (assuming these are points in the diagram). Two lines could be named as line $AB$ and line $CD$. The plane that contains point $A$, $B$, and $C$ could be named as plane $ABC$. The intersection of the two planes (in the last diagram) is a line passing through the common points of the two planes.

Answer:

1. Other names for $\overline{PQ}$: $\overline{QP}$, line $P$ and $Q$; Other names for plane $R$: plane $VST$ (assuming appropriate points).
2. Collinear points lie on the same line, coplanar points lie on the same plane. Collinear $\subseteq$ Coplanar.
3. Intersection of $\overline{PQ}$ and line $K$: point $M$. Intersection of plane $A$ and plane $B$: a line. Intersection of line $K$ and plane $A$: point $M$.
4. Four points: $A$, $B$, $C$, $D$ (example). Two lines: line $AB$, line $CD$ (example). Plane containing $A$, $B$, $C$: plane $ABC$. Intersection of two planes: a line.