﻿ Points, Lines, and Planes Worksheet | Problems & Solutions

# Points, Lines, and Planes Worksheet

Points, Lines, and Planes Worksheet
• Page 1
1.
What are UC and UT in the figure?

 a. Parallel lines b. Intersecting lines c. Opposite rays d. None of the above

#### Solution:

The rays that have a common starting point and which travel in opposite directions are called opposite rays.

UT and UC have U as the common starting point and are traveling in opposite directions.

The rays UC and UT are called opposite rays.

2.
How many lines can be drawn passing through a point?
 a. One b. Zero c. Infinite d. Two

#### Solution:

Infinite number of lines can be drawn passing through a point.

3.
If a line can be drawn through a set of points, then the points are called ______ points.
 a. congruent b. noncollinear c. collinear d. None of the above

#### Solution:

If a line can be drawn through a set of points, the points are collinear.

The points are called collinear points.

4.
How many rays are there in the figure?

 a. 1 b. 5 c. 2 d. 3

#### Solution:

A ray is a part of a line. It has one end point and any number of points on one side of the end point.

A ray is named by the end point and any other point on the ray.

The rays in the figure, with C as the end point are CB, CD, CA.

The ray in the figure, with B as the end point is BD and with D as the end point is DB.

So, the total number of rays in the figure is 5.

5.
Identify the number of planes and the number of line segments in the figure.

 a. 3, 5 b. 5, 8 c. 4, 6 d. 6, 8

#### Solution:

There are 8 line segments in the figure.

6.
Where do the two planes intersect?

 a. point B b. plane ABP c. $\begin{array}{c}\stackrel{↔}{\text{AB}}\end{array}$ d. point A

#### Solution:

If two planes intersect, then they intersect in a line.
[Postulate.]

The two planes in the figure intersect in AB.

7.
Identify which of the following can be best represented as a point.
 a. A rope b. A book c. A peanut in the play ground d. A bed sheet

#### Solution:

A point has no dimension. It is represented by a small dot.

A peanut in the play ground represents a point.

8.
Identify which of these can be best represented by a line.
 a. The corner of a room b. A piece of thread c. A small hole in a big wall d. The peak of a pyramid

#### Solution:

A line has one dimension. It extends without end in two directions.

A piece of thread represents a line.

9.
Identify which of the following can be best represented by a plane.
 a. A droplet of water on the ground b. Rules on a notebook paper c. A piece of paper d. A star in the sky

#### Solution:

A plane has two dimensions. It is represented by a shape that looks like a floor or wall.

So, a piece of paper represents a plane.

10.
In how many ways can the line be represented?

 a. 5 b. 3 c. 2 d. 6

#### Solution:

The points P, Q ad R lie on the same line.

Choose two letters from the figure to name this line.

PQ, QP, QR, RQ, PR, RP

Therefore, the line can be represented in 6 possible ways.