📘 Chapter 2 – Lines and Angles
Textbook Page 11 Explanation (Part 1)
This part explains the meaning of a Line Segment and why the shortest distance between two points is always a line segment.
📏 Segment
"Draw line x on a paper. Take points P and Q on the line x. The part of the line from point P to point Q is a line segment (part of line or segment of line). Points P and Q are the endpoints of the line segment. This line segment is called line segment PQ or line segment QP and is read and written as seg PQ or seg QP."
A line segment is a part of a line.
A line goes on forever in both directions, but a line segment has a fixed beginning and a fixed ending.
In the textbook figure, the line has two points named P and Q. The part of the line between P and Q is called a line segment.
- P → One endpoint
- Q → Other endpoint
- PQ → Line Segment
Since the segment starts at P and ends at Q, we can call it Segment PQ.
We can also call it Segment QP because both names represent the same line segment.
- A line segment has two endpoints.
- A line segment has a fixed length.
- It does not continue forever.
📝 Do It Activity
"Take two points A and B on a paper. Connect them in different ways. There are many ways to get from A to B, the shortest of which (path 2) is the line segment AB."
The textbook shows four different routes from point A to point B.
Some routes are curved. Some are zig-zag. Some are longer.
Among all these routes, the straight route is the shortest.
That shortest straight path is called Line Segment AB.
- walk around many streets,
- take a curved road,
- take a zig-zag road,
- or walk in one straight line.
🔍 Difference Between a Line and a Line Segment
| Line | Line Segment |
|---|---|
| Continues forever in both directions. | Has a fixed beginning and fixed ending. |
| Has no endpoints. | Has two endpoints. |
| Length cannot be measured. | Length can be measured. |
🌟 Part 1 Summary
- A line segment is a part of a line.
- A line segment has two endpoints.
- Segment PQ and Segment QP are the same segment.
- The shortest distance between two points is always a straight line segment.
- A line continues forever, but a line segment has a fixed length.
☀️ Ray
"A ray is a part of a line that starts from a point and extends indefinitely in one direction. The point from which the ray starts is called the starting point of the ray."
A ray is a part of a line.
Unlike a line, a ray does not continue forever in both directions.
A ray has one fixed starting point, but it keeps going forever in one direction only.
- A line has no endpoints.
- A line segment has two endpoints.
- A ray has one starting point.
🌞 Real Life Examples of Rays
☀️ 1. Sun Rays
The rays of the sun start from the Sun and travel in one direction towards the Earth.
So they behave like rays in geometry.
🔦 2. Torch Light
Light comes out from one point inside the torch and travels forward.
Therefore torch light is another example of a ray.
🔫 3. Light Coming from a Laser Gun
The laser beam starts from one point and goes straight in one direction.
So it also represents a ray.
📐 Understanding Ray AB
"In the adjacent diagram, point A is the starting point of ray AB and B is a point on the ray other than point A. The ray is read and written from its starting point, as ray AB and not ray BA."
Look carefully at the figure.
The ray starts from point A.
It passes through point B.
After B, the ray keeps going forever in the same direction.
- Starting point = A
- Another point on the ray = B
- Correct name = Ray AB
- Wrong name = Ray BA
The name of a ray always begins with its starting point.
📝 Practice Set 2.1
In the figure, different points, rays, line segments and one complete line are shown.
Before answering the questions, carefully observe the diagram.
| Question | What you have to identify |
|---|---|
| (i) Points | Write the names of all marked points. |
| (ii) Line Segments | Find the parts having two endpoints. |
| (iii) Rays | Find the figures having one starting point and one arrow. |
| (iv) Collinear Points | Find the points lying on the same straight line. |
| (v) Line | Find the figure having arrows at both ends. |
| (vi) Non-collinear Points | Find points which are not on the same straight line. |
💡 Quick Revision
| Shape | Endpoints | Direction |
|---|---|---|
| Line | No Endpoints | Infinite in Both Directions |
| Line Segment | Two Endpoints | Fixed Length |
| Ray | One Starting Point | Infinite in One Direction |
🌟 Part 2 Summary
- A ray starts from one point and extends forever in one direction.
- Sun rays, torch light and laser light are good examples of rays.
- A ray is always named from its starting point.
- Ray AB is correct, but Ray BA is not correct.
- Always observe a figure carefully before identifying points, rays, lines and line segments.