The Difference Between a Line, a Ray and a Segment
Learn to name points, lines, rays and planes, tell simple closed curves from open ones, and measure and classify every type of angle with a protractor.
What is the difference between a line, a ray and a line segment?
All three are straight, and they differ only in how far they extend. A line goes on for ever in both directions, a ray starts at one point and goes on for ever in one direction, and a line segment has two endpoints and therefore a measurable length.
This page covers everything in the ICSE Class 6 Mathematics chapter on fundamental geometrical concepts and angles: naming the basic figures, the relationships between lines, curves and their interiors, and measuring and classifying angles.
This page covers everything in the ICSE Class 6 Mathematics chapter on fundamental geometrical concepts and angles: naming the basic figures, the relationships between lines, curves and their interiors, and measuring and classifying angles.
How do you name points, lines, rays and planes?
A point marks a position and has no length, width or thickness. It is named with a capital letter, such as P.
A line through two points A and B is written , with arrows at both ends showing it never stops. A ray beginning at A and passing through B is — and the starting point must be named first, because is a different ray pointing the opposite way. A line segment is written , and only a segment has a length you can measure.
A plane is a flat surface extending for ever in all directions; the page you are reading is part of a plane.
Of the three straight figures, only the segment can be measured. Asking for "the length of a line" is a contradiction, since a line has no ends — which is exactly why examination questions say line segment when they want a measurement.
A line through two points A and B is written , with arrows at both ends showing it never stops. A ray beginning at A and passing through B is — and the starting point must be named first, because is a different ray pointing the opposite way. A line segment is written , and only a segment has a length you can measure.
A plane is a flat surface extending for ever in all directions; the page you are reading is part of a plane.
Of the three straight figures, only the segment can be measured. Asking for "the length of a line" is a contradiction, since a line has no ends — which is exactly why examination questions say line segment when they want a measurement.
What are collinear points, concurrent lines and perpendicular lines?
These words describe how figures sit in relation to one another.
Collinear points all lie on one straight line. Any two points are always collinear, because a line can be drawn through any two; three or more being collinear is the interesting case.
Concurrent lines are three or more lines passing through a single common point.
Intersecting lines cross at exactly one point. Parallel lines lie in the same plane and never meet, no matter how far extended, keeping a constant distance apart. Perpendicular lines intersect at a right angle, written .
For example, the two long rails of a railway track are parallel, the sleepers are perpendicular to them, and the spokes of a bicycle wheel are concurrent at the hub.
Parallel lines must be in the same plane. Two lines in different planes that never meet are called skew, not parallel — a distinction that matters later on.
Collinear points all lie on one straight line. Any two points are always collinear, because a line can be drawn through any two; three or more being collinear is the interesting case.
Concurrent lines are three or more lines passing through a single common point.
Intersecting lines cross at exactly one point. Parallel lines lie in the same plane and never meet, no matter how far extended, keeping a constant distance apart. Perpendicular lines intersect at a right angle, written .
For example, the two long rails of a railway track are parallel, the sleepers are perpendicular to them, and the spokes of a bicycle wheel are concurrent at the hub.
Parallel lines must be in the same plane. Two lines in different planes that never meet are called skew, not parallel — a distinction that matters later on.
What makes a curve simple, closed or open?
A curve is any figure drawn without lifting the pencil, and it can be straight, bent or both.
A curve is closed if it ends where it started, and open if its two ends are apart. A letter O is closed; a letter S is open.
A curve is simple if it does not cross itself, and non-simple if it does. A circle is a simple closed curve, while a figure of eight is closed but non-simple, because it crosses at the middle.
Every simple closed curve divides the plane into three distinct parts: the interior (the region inside), the boundary (the curve itself), and the exterior (everything outside).
For example, a boundary wall around a field is a simple closed curve — the field is the interior, the wall is the boundary, and the road outside is the exterior.
The interior and exterior are only well defined for simple closed curves. Once a curve crosses itself, "inside" stops having a single clear meaning.
A curve is closed if it ends where it started, and open if its two ends are apart. A letter O is closed; a letter S is open.
A curve is simple if it does not cross itself, and non-simple if it does. A circle is a simple closed curve, while a figure of eight is closed but non-simple, because it crosses at the middle.
Every simple closed curve divides the plane into three distinct parts: the interior (the region inside), the boundary (the curve itself), and the exterior (everything outside).
For example, a boundary wall around a field is a simple closed curve — the field is the interior, the wall is the boundary, and the road outside is the exterior.
The interior and exterior are only well defined for simple closed curves. Once a curve crosses itself, "inside" stops having a single clear meaning.
How do you measure and classify an angle?
An angle is formed when two rays share a starting point. That shared point is the vertex and the two rays are the arms. An angle is named with three letters, the vertex always in the middle: has its vertex at B.
To measure with a protractor, place its centre exactly on the vertex, line the baseline up along one arm, and read the scale where the second arm crosses. Use whichever of the two scales starts at zero on your chosen arm.
Angles are classified by size:
- acute: less than
- right: exactly
- obtuse: between and
- straight: exactly
- reflex: between and
- complete: exactly
A reflex angle is the one students forget. Every pair of arms actually makes two angles that together total — so an angle drawn as has a reflex partner of on the other side.
To measure with a protractor, place its centre exactly on the vertex, line the baseline up along one arm, and read the scale where the second arm crosses. Use whichever of the two scales starts at zero on your chosen arm.
Angles are classified by size:
- acute: less than
- right: exactly
- obtuse: between and
- straight: exactly
- reflex: between and
- complete: exactly
A reflex angle is the one students forget. Every pair of arms actually makes two angles that together total — so an angle drawn as has a reflex partner of on the other side.
Exam tip
The mistake most students make with a protractor
A protractor carries two scales running in opposite directions, and reading the wrong one turns into . Both numbers sit at the same mark, so the error is invisible unless you check.
Use the shape of the angle as your guard. Before reading, decide by eye whether the angle is acute or obtuse. If it looks clearly less than a right angle, the answer must be below — so if the scale offers 40 and 140, take 40.
The other half of the habit is placement: the centre hole must sit exactly on the vertex, and the baseline exactly along one arm. A protractor that has slipped by a millimetre gives a wrong reading no amount of careful scale-reading will fix.
Use the shape of the angle as your guard. Before reading, decide by eye whether the angle is acute or obtuse. If it looks clearly less than a right angle, the answer must be below — so if the scale offers 40 and 140, take 40.
The other half of the habit is placement: the centre hole must sit exactly on the vertex, and the baseline exactly along one arm. A protractor that has slipped by a millimetre gives a wrong reading no amount of careful scale-reading will fix.
Did you know
Why is the vertex always the middle letter in an angle's name?
Because several angles can share the same vertex, the name has to say which two arms you mean — and the only unambiguous way is to list an arm, the vertex, then the other arm.
So and both have their vertex at B but are different angles. Naming an angle by its vertex alone, as , is only safe when exactly one angle exists at that point.
So and both have their vertex at B but are different angles. Naming an angle by its vertex alone, as , is only safe when exactly one angle exists at that point.
Key takeaways
Lines and angles in 30 seconds
- A line extends for ever both ways, a ray one way from a fixed start, and a line segment has two endpoints — only the segment has a length.
- Collinear points share a line, concurrent lines share a point, parallel lines never meet in a plane, and perpendicular lines meet at a right angle.
- Curves are open or closed and simple or non-simple; a simple closed curve creates an interior, a boundary and an exterior.
- An angle is two rays from a common vertex, named with the vertex as the middle letter, and measured with the protractor centred on the vertex.
- Angles are acute, right, obtuse, straight, reflex or complete, and every drawn angle has a reflex partner making with it.
You will remember all of this far better after answering five questions on it than after reading it twice.
- Collinear points share a line, concurrent lines share a point, parallel lines never meet in a plane, and perpendicular lines meet at a right angle.
- Curves are open or closed and simple or non-simple; a simple closed curve creates an interior, a boundary and an exterior.
- An angle is two rays from a common vertex, named with the vertex as the middle letter, and measured with the protractor centred on the vertex.
- Angles are acute, right, obtuse, straight, reflex or complete, and every drawn angle has a reflex partner making with it.
You will remember all of this far better after answering five questions on it than after reading it twice.