The document explains the mathematical concepts of subsets of a line, including line segments, rays, and opposite rays. It provides exercises on identifying and calculating the number of line segments and rays formed with various points. It also defines congruent segments as those with the same length.

1. Grade 7 – Mathematics
Quarter III
SUBSETS OF A LINE

2. SUBSETS OF
A LINE
Prepared by:
Jo-Ann E. Rogon

3. SUBSETS OF A LINE
Line Segment Rays Opposite Rays

4. SUBSETS OF A LINE
Line Segment
- A subset of a line consisting of two
endpoints and all the points in between.

5. 1. Name the different line segments
given 3 points.
Answer: Line segments EF, EG and FG.
2. How many line
segments can be formed
given 4 points?
6 line segments

6. where n is the number of points in
a given line.
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒍𝒊𝒏𝒆 𝒔𝒆𝒈𝒎𝒆𝒏𝒕𝒔 =
𝒏 ( 𝒏 − 𝟏)
𝟐
𝒏 ( 𝒏 −𝟏)
𝟐
=
𝟒 ( 𝟒 −𝟏)
𝟐
=
𝟒 (𝟑)
𝟐
=
𝟏𝟐
𝟐
= 6 line segments

7. Find the number of line segments
formed in a given line with…
1. 6 points
2. 8 points
3. 9 points
4. 10 points
5. 15 points
15 line segments
28 line segments
36 line segments
45 line segments
105 line segments

8. Two line segments are said to be
congruent segments if they have the
same measure or length.

9. SUBSETS OF A LINE
Ray
- A subset of a line with only one endpoint
and extends infinitely in only one direction.

10. Name all the rays given 3 points?
- without listing the different rays, we can
find the number of rays formed in a given
line.

11. 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑹𝒂𝒚𝒔 𝒊𝒏 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒍𝒊𝒏𝒆
= 𝟐(𝒏 − 𝟏)
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑹𝒂𝒚𝒔 𝒊𝒏 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒓𝒂𝒚
= (𝒏 − 𝟏)

12. SUBSETS OF A LINE
Opposite Rays
- Are rays with a common endpoint but
extending infinitely in opposite directions.

13. Determine the number of line segments and
rays formed in a given line with…
1. 5 points
2. 7 points
3. 16 points
4. 19 points
5. 25 points