Question

geometry - chapter 1: tools of geometry
chapter 1.1: points, lines, and planes
name:
apply the vocabulary from this lesson to answer each question.

1. give an example from your classroom of three collinear points.
2. make use of the fact that endpoint is a compound of end and point and name the endpoint of \\(\overline{st}\\)

use the figure to name each of the following.

1. name 5 different points.
2. name 2 different lines.
3. name 2 different planes.
4. name 3 noncollinear points
5. what are two other ways to name \\(\overline{bd}\\)?
6. name a pair of opposite rays with endpoint c.

draw and label each of the following.

1. a segment with endpoints m and n
2. a ray with endpoints f that passes through g
3. a pair of opposite rays that both contain r
4. a line containing x and y

use the figure to name each of the following.

1. a line that contains a and c
2. a plane that contains a, d, and c

sketch a figure that shows each of the following.

1. three coplanar lines that intersect in a common point
2. two lines that do not intersect

use the figure to name each of the following.

1. three collinear points
2. four coplanar points
3. a plane containing l

Explanation:

1. Collinear points lie on the same line; classroom examples are common fixed points on a straight object.
2. A segment $\overline{ST}$ has its first labeled point as the endpoint.
3. Identify distinct labeled points in the first figure.
4. Lines are defined by 2 collinear points in the first figure.
5. Planes are flat surfaces labeled in the first figure.
6. Noncollinear points do not lie on the same line in the first figure.
7. A line can be named by any 2 points on it, in either order.
8. Opposite rays share an endpoint and form a straight line from point $C$.
9. A segment has two distinct endpoints connected by a straight line.
10. A ray has an endpoint and extends infinitely through a second point.
11. Opposite rays share endpoint $R$ and form a straight line.
12. A line extends infinitely in both directions through two points.
13. Identify the line containing points $A$ and $C$ in the second figure.
14. The plane containing $A, D, C$ is the labeled flat surface in the second figure.
15. Coplanar lines lie on the same flat surface and meet at one common point.
16. Non-intersecting lines can be parallel (coplanar) or skew (noncoplanar).
17. Collinear points lie on the same straight line in the third figure.
18. Coplanar points lie on the same flat surface in the third figure.
19. The plane containing $L$ is the labeled flat surface in the third figure.

Answer:

1. Example: The three screw holes along the top edge of a whiteboard (any valid classroom collinear points work)
2. $S$
3. $A, B, C, D, E$
4. $\overleftrightarrow{BD}, \overleftrightarrow{AN}$
5. Plane $Y$, Plane $N$
6. $A, B, E$
7. $\overleftrightarrow{DB}, \overleftrightarrow{BC}$ (or $\overleftrightarrow{CD}$, since all are on the same line)
8. $\overrightarrow{CB}$ and $\overrightarrow{CD}$
9. (Draw a straight line segment with endpoints labeled $M$ and $N$)
10. (Draw a ray with endpoint $F$, extending infinitely through a point labeled $G$, written as $\overrightarrow{FG}$)
11. (Draw a straight line with endpoint $R$, and label opposite rays e.g., $\overrightarrow{RP}$ and $\overrightarrow{RQ}$ where $P-R-Q$ are collinear)
12. (Draw a line extending infinitely in both directions through points labeled $X$ and $Y$, written as $\overleftrightarrow{XY}$)
13. $\overleftrightarrow{AC}$ (or $\overleftrightarrow{AB}$, $\overleftrightarrow{AD}$ since all are on the same line)
14. Plane $M$
15. (Draw a flat plane with three lines all intersecting at a single common point)
16. (Draw two parallel lines on a plane, or two skew lines on separate planes)
17. $B, A, C$ (or $E, A, C$)
18. $B, A, C, D$ (any four points on the labeled plane)
19. Plane $L$ (the labeled plane containing point $L$)