Category : 4th Class
Geometry
Learning Objectives
In our daily life, we come across different types of objects that have specific geometrical shapes or geometrical figures which make them appear unique in their own manner. A shape is the form of an object or its external surface. In this chapter, we will learn about different kinds and names of geometrical shapes along with their meaning and pictures.
Point, Line Segment, Line and Ray
Point: A point has no dimensions. It has only position. It is denoted by a dot (.), for example, point A is marked in the figure shown below.
Line Segment: A line segment is a straight path between 2 points. It has a fixed length. In the figure given below, a line segment BC or CB is shown which is denoted as \[\overline{BC}\]or\[\overline{CB}\].
Line: A line is a straight path that goes on forever in both directions. It does not have fixed length. In the figure given below, a line PQ or QP is shown which is denoted as \[\overleftrightarrow{PQ}\] or\[\overleftrightarrow{QP}\].
Ray: A ray is a straight path that goes on forever in one direction. It has only one end point. In the figure given below, a ray AB is shown which is denoted by \[\overrightarrow{AB}\]
Straight Line and Curved Line
Straight Line: A straight line on horizontal plane is the shortest distance between two points. Only one straight line is possible between two points. In the figure given below, a straight line AB is shown which is the shortest distance between the points A and B.
Curved Line: The line other than straight line between two points is called curved line. Two points can be joined in many ways, therefore, infinite curved lines are possible between two given points. In the figure given below, in between two point A and B, a straight line AB and a curved line ADB are shown, where AB is the shortest line.
Closed Figure and Open Figure
Closed Figure: A closed figure is a figure which can be traced using the same starting and stopping points and without crossing or retracing any section of the figure. Square, triangle, circle, etc. are examples of closed figures.
Open Figure: An open figure is a figure which can be traced using the different starting and stopping points. Figures given below are examples of open figures which have an opening.
Types of Angles
There are different types of angles which have been classified into following groups based on their measurement.
Acute Angle
An angle which is greater than \[0{}^\circ \] but smaller than \[90{}^\circ \] is called an acute angle.
Right Angle
An angle which is exactly \[90{}^\circ \] is called a right angle.
Obtuse Angle
An angle which is greater than \[90{}^\circ \] but smaller than \[180{}^\circ \] is called an obtuse angle.
Straight Angle
An angle which is exactly \[180{}^\circ \] is called a straight angle.
Re flex Angle
An angle which is greater than \[180{}^\circ \] but smaller than \[360{}^\circ \] is called a reflex angle.
Complementary Angles and Supplementary Angles
Two angles are complementary when they add up to \[90{}^\circ \] or add up to a right angle.
Two angles are supplementary when they add up to \[180{}^\circ \] or add up to a straight angle.
Triangle
A geometrical shape or a simple closed figure bounded by three line segments is called a triangle. The line segments are called sides of the triangle.
Classification according to the sides
Scalene Triangle
A triangle whose all sides are of different length is called a scalene triangle. No angles are equal in a scalene triangle. In the triangle ABC given below, sides AB, BC and AC are not equal and also, \[\angle ABC,\text{ }\angle BAC\] and \[\angle ACB\] are not equal.
Isosceles Triangle
A triangle whose any two sides are of equal length is called an isosceles triangle. Opposite angles of equal sides of an isosceles triangle are equal. In the triangle ABC given below, sides AB and AC are equal and their opposite angles, \[\angle ABC\] and \[\angle ACB\] are equal.
Equilateral Triangle
A triangle whose all three sides are of equal length is called an equilateral triangle. All three angles of an equilateral triangle are of\[60{}^\circ \] . In the triangle ABC given below, sides AB, BC and AC are equal and\[\angle ABC\], \[\angle ACB\]and \[\angle BAC\] are equal to\[60{}^\circ \]. An equilateral triangle is also known as an equiangular triangle.
Classification According to Angles
Acute-angled Triangle
A triangle whose all angles are acute or all angles are smaller than \[90{}^\circ \] is called an acute-angled triangle. In the Triangle ABC given below, all three angles\[\angle ABC\], \[\angle ACB\] and \[\angle BAC\] are smaller than \[90{}^\circ \].
Right-angled Triangle
A triangle whose one angle is a right angle or equal to \[90{}^\circ \] is called a right-angled triangle. In the triangle ABC given below, \[\angle ABC\]is equal to \[90{}^\circ \].
Obtuse-angled Triangle
A triangle whose one angle is an obtuse angle or greater than \[90{}^\circ \] is called an obtuse-angled triangle. In the triangle ABC given below, \[\angle ABC\]is greater than\[90{}^\circ \].
Example:
1. An angle with measure \[91{}^\circ \] is a/an:
(a) acute angle (b) obtuse angle
(c) right angle (d) reflex angle
(e) None of these
Answer (b) is correct.
Explanation: An angle which is greater than \[90{}^\circ \] but smaller than \[180{}^\circ \] is called an obtuse angle.
2. Which one of the following has definite length?
(a) A line (b) A ray
(c) A line segment (d) A point
(e) None of these
Answer (c) is correct.
Explanation: A line, a ray or a point does not have definite length. A line segment has definite length.
3. How many triangles are there in the figure given below?
(a) 15 (b) 8
(c) 12 (d) 16
(e) None of these
Answer (c) is correct
Explanation: There are 8 small triangles and 4 triangles formed with the diagonals of square.
Therefore, the number of triangles is 12.
4. How many squares are there in the figure given below?
(a) 8 (b) 10
(c) 12 (d) 14
(e) None of these
Answer (c) is correct.
Explanation:
Total number of squares = \[6+6=12\]
5. Which one of the following is not pictured in the diagram given below?
(a) Ray OB (b) Line AB
(c) Angle AOB (d) Line segment BQ
(e) None of these
Answer (d) is correct.
Explanation: Ray OB, line AB and angle AOB are pictured but the line segment BQ is not pictured in the given diagram.
Commonly Asked Question
1. Number of centimetres of measured radius of a circle is a prime number. Number of centimetres of its measured diameter must be a/an:
(a) even number (b) odd number
(c) prime number (d) unique number
(e) None of these
Answer (a) is correct.
Explanation: Diameter of a circle is twice its radius.
Therefore, diameter = \[2\times \text{radius}=2\times \text{prime number}=\text{even number}\]
For example, if radii are: 2 cm, 3 cm, 5 cm, 7 cm ......
Then, the diameters will be: 4 cm, 6 cm, 10 cm, 14 cm ......
2. Number of centimetres of measured diameter of a circle is 4 times of the smallest odd prime number. The radius of the circle is:
(a) 4 cm (b) 6 cm
(c) 8 cm (d) 16 cm
(e) None of these
Answer (b) is correct.
Explanation: The smallest odd prime number = 3
Four times of 3 is \[4\times 3=12\]
Therefore, diameter = 12 cm. Hence, radius of the circle = (\[12\div 2\]) cm = 6 cm
3. A triangle can have maximum acute angle/angles.
(a) one (b) two
(c) three (d) four
(e) None of these
Answer (c) is correct.
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