Points, Rays, Lines and Intervals Worksheet for 12-Year-Olds

Instructions

1. Read the definitions and examples carefully.
2. Complete each section from left to right.
3. Use capital letters when naming points.
4. For drawings, use a ruler when possible. Remember:
   • A point is shown by a dot.
   • A line extends forever in both directions.
   • A ray starts at one endpoint and extends forever in one direction.
   • An interval is the part of a line between two endpoints. It is also commonly called a line segment.
5. Check your answers with the Answer Key when you finish.

1. Learn the Geometry Words

Example:

• In A •──────• B, the figure is an interval AB.
• In A •──────• B──────>, the figure is a ray AB because it starts at A and passes through B.
• In <────── A •──────• B ──────>, the figure is a line AB.

2. Match the Definition

Write the correct letter on each blank.

• A. Point
• B. Line
• C. Ray
• D. Interval

1. _____ A straight path that extends forever in both directions.
2. _____ A location represented by a dot and a capital letter.
3. _____ A straight path with one endpoint that extends forever in one direction.
4. _____ The part of a line between two endpoints.

3. Name the Figures

Write the correct name for each figure. Use the words point, line, ray, or interval and the correct capital letters.

A. M •

Answer: __

B. P •────────• Q

Answer: __

C. R •────────• S────────>

Answer: __

D. <──────── T •────────• U ────────>

Answer: __

Hint: For a ray, the first letter names the endpoint. A ray from R through S is named ray RS.

4. Identify the Parts

Look at each figure and answer the questions.

Figure 1

A •────────• B

1. What type of figure is shown? __
2. What are the endpoints? __
3. Name the figure in both possible orders. __

Figure 2

C •────────• D────────>

4. What type of figure is shown? __
5. Which point is the endpoint? __
6. Through which point does the ray pass? __
7. Name the ray. __

Figure 3

<──────── E •────────• F ────────>

8. What type of figure is shown? __
9. Name the figure in both possible orders. __

5. Sort the Names

Place each name in the correct column. Some names may be used more than once if they describe the same kind of figure.

Names to sort: point H, line JK, ray LM, interval NO, point P, ray QR

6. Label and Draw

Use a ruler and complete each task.

1. Draw a point. Label it X.

2. Draw an interval with endpoints Y and Z.

3. Draw a ray with endpoint G that passes through H.

4. Draw a line that passes through K and L.

5. Draw two different rays that have the same endpoint, N. Label another point on each ray O and P.

7. Correct the Mistake

Each student made one mistake. Rewrite the answer correctly.

1. A student names the ray shown below as ray BA.

   A •────────• B────────>

   Correct answer: __

2. A student says that the figure below is a line.

   C •────────• D

   Correct answer: __

3. A student names the point below as point q.

   q •

   Correct answer: __

4. A student says that a line has only one endpoint. Is this correct? Explain.

   ---

   ---

8. Real-World Geometry Mission

A hiking trail is shown in different ways on a park map.

• Map A shows a trail section that begins at the parking lot and ends at the picnic area.
• Map B shows a trail that begins at the ranger station and continues in one direction beyond the map.
• Map C shows a straight path that continues in both directions beyond the map.

Answer the questions.

1. Which map should use an interval? Explain why.

   ---

2. Which map should use a ray? Explain why.

   ---

3. Which map should use a line? Explain why.

   ---

4. Give two everyday objects or paths that could be modeled by an interval.

   ---

9. Optional Challenge

1. Points A, B, and C lie on the same straight path. B is between A and C.

   a. Name one interval with endpoints A and B: ____

   b. Name one interval with endpoints B and C: ____

   c. Name one interval with endpoints A and C: ____

   d. Name the line that passes through all three points: ___

2. Explain why ray AB and ray BA are usually different rays.

   ---

   ---

3. Can a point have an endpoint? Explain your answer.

   ---

Answer Key

2. Match the Definition

1. B — Line
2. A — Point
3. C — Ray
4. D — Interval

3. Name the Figures

A. Point M

B. Interval PQ or interval QP

C. Ray RS

D. Line TU or line UT

4. Identify the Parts

Figure 1

1. Interval
2. A and B
3. Interval AB and interval BA

Figure 2

4. Ray
5. C
6. D
7. Ray CD

Figure 3

8. Line
9. Line EF and line FE

5. Sort the Names

• Points: point H, point P
• Lines: line JK
• Rays: ray LM, ray QR
• Intervals: interval NO

6. Label and Draw

Answers may look different, but they should include the required labels and markings.

1. One dot labeled X.
2. A straight path with endpoints Y and Z, with no arrows.
3. A straight path beginning at G, passing through H, with an arrow beyond H. This is ray GH.
4. A straight path with arrows on both ends passing through K and L. This is line KL or line LK.
5. Two rays beginning at N, one passing through O and the other passing through P.

7. Correct the Mistake

1. Ray AB. The ray begins at A and passes through B.
2. Interval CD. It has two endpoints and no arrows.
3. Point Q. Point labels use capital letters.
4. No. A line has no endpoints because it extends forever in both directions.

8. Real-World Geometry Mission

1. Map A should use an interval because the trail section has two endpoints: the parking lot and the picnic area.
2. Map B should use a ray because it begins at the ranger station and continues forever in one direction.
3. Map C should use a line because it continues forever in both directions.
4. Answers may vary. Examples include a ruler, a table edge, a sidewalk between two buildings, or a road section between two intersections.

9. Optional Challenge

1. a. Interval AB or interval BA

   b. Interval BC or interval CB

   c. Interval AC or interval CA

   d. Line AB, line AC, or line BC

2. Ray AB begins at A and passes through B. Ray BA begins at B and passes through A, so they have different endpoints and point in different directions.

3. No. A point is only a location. It does not extend in any direction, so it cannot have an endpoint.