Class 5 Exam  >  Class 5 Notes  >  Mathematics for Class 5  >  Chapter Notes: Lines and Angles

Lines, Angles and Triangles / Geometry Class 5 Notes Maths

Point, Line, Line Segment and Plane

The three building blocks of geometry are points, lines and planes.

1. Point

A point is an exact location in plane or space.

A point has zero length, zero width and zero height. It represents a position only. We represent a point by a dot (.) and name it with a capital letter, as point P.
Some representations of a point in everyday life are:
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

2. Line

A line is a straight path of points that extends on and on in both the directions without ever ending.

The length of a line cannot be measured.
To show that a line extends endlessly in both the directions, you use arrowheads at both the ends.
A line is named by using any two points on a line.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThus, the line given alongside is named as Lines, Angles and Triangles / Geometry Class 5 Notes Maths (line PQ) or Lines, Angles and Triangles / Geometry Class 5 Notes Maths (line QP).

  • A horizontal line goes straight across. (Sleeping Line)
    Lines, Angles and Triangles / Geometry Class 5 Notes Maths
  • A vertical line goes straight up and down. (Standing Line)
  • A line can also be curved. A curved line is called a curve.
    Lines, Angles and Triangles / Geometry Class 5 Notes Maths

2. Line Segment

A part of a line is called a line segment.

A line segment has a fixed length that can be measured. The points at which the line segment begins and ends are called its endpoints. Every line segment has two endpoints. A line segment is named by using endpoints
The given line segment has C and D as endpoints. The line segment given here is named as Lines, Angles and Triangles / Geometry Class 5 Notes Maths
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

Thus, a line segment is also the shortest path between two points.
Some representations of a line segment from your everyday life are:
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

3. Ray

A ray is a straight path that has one endpoint and goes on and on in one direction.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThis ray begins at point P and goes through point Q. It does not stop at point Q. We name the given ray as Lines, Angles and Triangles / Geometry Class 5 Notes Mathswhere the first letter is always the endpoint.
The symbol ‘ → ’ shows that a ray has a fixed endpoint and extends endlessly in the other direction.
Some representations of rays from your everyday life are:
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

4. Plane

A plane is a flat surface that extends infinitely in all directions. It has no thickness.

In mathematics, a plane goes on and on in all directions without end. We usually work with just a part of a plane. Points and lines lie on a plane. A plane can be named by using any three points on it. The given figure shows plane ABC. The order of the points does not matter.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsSome representations of a plane surface from your everyday life are:
Lines, Angles and Triangles / Geometry Class 5 Notes Maths


Angle

An angle is a figure formed by two rays meeting at a common endpoint.

The common endpoint is called the vertex of the angle and the two rays are called the arms of the angle.
Looking at these pictures, you can form some idea of an angle:
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

The symbol for angle is ∠.

1. Naming an Angle
You can name an angle in three ways:

  • Using a three-letter name in the order: a point on oneray, vertex and a point on the other ray. ∠PQR or ∠RQP
  • Using only one-letter name, i.e., the vertex ∠Q. (This can be used when there is only one angle with this vertex.)
  • Using a number to name the angle, i.e., ∠1.

Lines, Angles and Triangles / Geometry Class 5 Notes Maths

2. Interior and Exterior of an Angle
The region between the rays, that is, the inside of an angle, is called the interior of the angle and the region outside the arms of angle is called the exterior of the angle.
The point P is in the interior of the angle, whereas points S and U are in the exterior of the angle. Points Q and R lie on the arms of the angle.
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

Measure the Angles

By measure of the angle, we mean the amount of rotation or turning.

Lines, Angles and Triangles / Geometry Class 5 Notes MathsJust as there are standard units of length, area, weight, etc., there are also standard units for the measurement of angles. The standard unit of measure for angles is the degree. The symbol for degree is °.
The angle formed by one complete rotation measures 360 degrees or 360°.
Look at the following example. The drawings below show angles of 40°, 150° and 270°.
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

Edurev Tips: One complete rotation is divided into 360 equal parts.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThe measure of one part is called one degree or 1°.

Look at the following clocks:
Lines, Angles and Triangles / Geometry Class 5 Notes MathsA hand of a clock turns from one position to another as it changes its direction. This change of direction or turning can be represented by drawing two arrows from one point.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThe picture alongside shows one complete rotation.

The least amount of turning that brings the hand back to its starting position is called one complete rotation.


Example 1: If a circle is divided into 20 equal parts, what will be the measure of an angle of each part?

Angle formed by one complete rotation = 360°.
∴ Measure of angle of each of the 20 equal parts = 360° / 20 = 18°.


Example 2: Calculate the angle between neighbouring spokes on each wheel.
(a)
Lines, Angles and Triangles / Geometry Class 5 Notes Maths
(b)
Lines, Angles and Triangles / Geometry Class 5 Notes Maths
(c)
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

(a) As the wheel (circle) is divided into 4 equal parts, the angle between the neighbouring spokes = 360° / 4 = 90°. 
(b) The wheel is divided into 3 equal parts, so the angle between the neighbouring spokes = 360° / 3 = 120°. 
(c) The wheel is divided into 8 equal parts, so the angle between the neighbouring spokes = 360° / 8 = 45°.


Measuring an Angle

The instrument used for measuring angles is called a protractor.

Lines, Angles and Triangles / Geometry Class 5 Notes MathsThe diagram on the right shows a protractor. It has the shape of a semi-circle and the angle at the centre is divided into 180°.


Edurev Tips: The inner scale of the protractor is marked from 0° to 180° anticlockwise. The outer scale of the protractor is marked from 0° to 180° clockwise. Each small division is 1°.

1. To Measure an Angle less than 180°
Step 1: Place the centre of the protractor at the vertex of the angle.
Step 2: Make sure that 0° line of the protractor is placed along one arm (AC) of the angle.
Step 3: Read the value on the protractor as indicated by the other arm (AB) of the angle. Thus, ∠ BAC = 60°.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsLines, Angles and Triangles / Geometry Class 5 Notes Maths

2. To Measure an Angle greater than 180°
Suppose, you are required to measure ∠x.
Step 1: Measure ∠a.
Step 2: Then, reflex ∠BOC = 360° – a°.
Lines, Angles and Triangles / Geometry Class 5 Notes Maths


Drawing Angles using Protractor

To draw an angle that measures 80°.
Step 1: Draw any ray OA.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsStep 2: Place the protractor such that its centre mark may fall on O, the endpoint of the ray. Align the ray with the 0° mark of one of the protractor scales. The endpoint O of the ray will be the vertex of the angle.
Step 3: Using the scale on which the ray OA aligns with 0°, mark the point at 80°. Label the point as B.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsStep 4: Remove the protractor and join B to O.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThus, ∠AOB is the required angle.

As you can see, we have drawn this angle using the inner scale on the protractor. What will be the angle like, if we use the outer scale on the protractor?
Lines, Angles and Triangles / Geometry Class 5 Notes MathsObserve the following angles.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsIrrespective of the length of the arms, each angle = 90°.


Types of Angles

Angles are named according to their measure between 90° and 180° and 180° and 360°. Look at the following illustrations. Sita sat on a roller coaster. Let her position be A. The roller coaster starts moving in an anticlockwise direction and this movement brings a change in Sita’s position.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsLines, Angles and Triangles / Geometry Class 5 Notes Maths


Equal Angles or Congruent Angles

When two angles have the same angle measure, we say that they are equal or congruent and write ∠ABC = ∠DEF.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThis means either angle can fit exactly over the other angle.


Parallel Lines

Parallel Lines are lines that lie on  the same plane and never meet, even if they are extended endlessly in both directions.

Parallel lines are always the same distance apart. The symbol || is used to show ‘‘is parallel to’’.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsHere, Line AB is parallel to line XY and line PQ || line RS. The following are some of the representations of parallel lines in our everyday life.
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

1. Intersecting Lines

Intersecting Lines are lines that cross each other at a point.

The following are some of the representations of intersecting lines in our everyday life.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsThe letter X is also an example of intersecting line segments.

2. Perpendicular Lines

When two intersecting lines meet to form right angles, they are called perpendicular lines.

They are indicated by the symbol Lines, Angles and Triangles / Geometry Class 5 Notes Maths (a square corner) in the diagrams.
Lines, Angles and Triangles / Geometry Class 5 Notes MathsLine AB is perpendicular to line CD and is written in short as Lines, Angles and Triangles / Geometry Class 5 Notes Maths
Lines, Angles and Triangles / Geometry Class 5 Notes Maths

⊥ is the symbol for ‘‘is perpendicular to’’.

Lines, Angles and Triangles / Geometry Class 5 Notes Maths

The document Lines, Angles and Triangles / Geometry Class 5 Notes Maths is a part of the Class 5 Course Mathematics for Class 5.
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FAQs on Lines, Angles and Triangles / Geometry Class 5 Notes Maths

1. What is the difference between a point, a line, a line segment, and a plane?
Ans. A point is a specific location in space, a line is a straight path that extends indefinitely in both directions, a line segment is a part of a line with two endpoints, and a plane is a flat surface that extends infinitely in all directions.
2. How do you define an angle in geometry?
Ans. An angle is formed when two rays share a common endpoint, called the vertex. The rays are known as the sides of the angle.
3. What are parallel lines and how are they related to each other?
Ans. Parallel lines are two or more lines that are always the same distance apart and never meet. They are always equidistant from each other.
4. Can two lines intersect at more than one point?
Ans. No, two lines can only intersect at one point. If two lines intersect at more than one point, they are considered the same line.
5. How can you determine if two lines are parallel or perpendicular?
Ans. Two lines are parallel if they have the same slope and will never intersect. Two lines are perpendicular if the product of their slopes is -1, resulting in a 90-degree angle between them.
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