Geometry

In this chapter, students will gain knowledge about the different shapes they come across in their environment and get acquainted with their names. They will also develop the skill to distinguish between these shapes. To start, we will establish a strong foundation by going through the basics of geometry.

Geometry

Geometry is a branch of mathematics that deals with the study of lines, figures and solids.

Geometric shapes are fundamental components of geometry. They are used in our daily lives and the natural world around us. The following are real-world examples of certain geometric shapes:

Types of Geometrical Shapes

Theyare one-dimensional (1D) shapes, two-dimensional (2D) shapes and three-dimensional (3D) shapes. In this case, "D" stands for "dimensional".

One-Dimensional (1D) Shapes

One-dimensional (1D) shapes are defined as the length of a line. 1D shapes can be drawn with only a line and a few curves. 

Examples of 1D shapes include points, straight lines, rays, parallel lines and curves.

Types of Lines

→Straight Line: In geometry, a straight line is defined as a straight and infinite 1D figure that extends in both directions. It represents the shortest possible path between any two points. It is shown as:

For example, a car moves in a straight line.

There are three types of straight lines. They are:

→Slanting Line: A straight line that leans or slants in another direction while remaining straight. It is shown as:

→Vertical Line: A straight line that extends from top to bottom and bottom to top.

→Horizontal Line: A straight line that stretches from left to right and right to left.

→Curved Line: A curved line is not straight and consists of curves.

For example, a car moves along a curved line.

→ Parallel Lines: These lines exist in the same plane and maintain a constant distance from each other. They can be horizontal or vertical in orientation. 

The following figure shows that Line 1 is parallel to Line 2.

For example, a railway track runs parallel.

→ Intersecting Lines: Intersecting lines meet at a point, sharing exactly one point of intersection.

For example, the blades of a scissor intersect each other.

→ Perpendicular Lines: Perpendicular lines intersect at a right angle forming an L-shaped. When horizontal and vertical lines intersect, they are perpendicular to each other. Here m is perpendicular to l.

For example, the minute hand is perpendicular to the hour hand of a clock at 3 O’Clock.

→ Ray: A ray is a straight line with only one endpoint extending infinitely in one direction.

For example, a ray of light emits from the sun.

→ Angle:An angle is formed when two rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

For example, you can use a protractor to measure 30°, 45°, 60°, 90° and 180°.

Let's explore different types of angles:

Types of Angles

a. Acute Angle: It is an angle greater than 0° but less than 90°.

b. Right Angle: It is an angle exactly equal to 90°, resembling the shape of the letter 'L.'

c. Obtuse Angle: It is an angle greater than 90° but less than 180°.

d. Straight Angle: It is an angle exactly equal to 180°, resembling a straight line.

e. Reflex Angle: It is greater than 180° but less than 360°. It is larger than a straight angle but doesn't go all the way around in a circle.

f. Complete Angle: It is an angle exactly equal to 360°. It is also known as a full angle. When you travel all the way around in a circle, you've completed a full circle.

Two-Dimensional (2D) Shapes

Two-dimensional shapes are flat figures that can be represented on a surface like paper. They have two special dimensions: length and breadth. Some examples of 2D shapes are closed figures, shown as

Three-Dimensional (3D) or Solid Shapes

Three-dimensional (3D) shapes are solid objects with three dimensions: length, breadth and height. It includes cubes, cuboids, cones and cylinders which are found around us. Some examples of solid shapes are shown in

Example 1: What does the candle look like?

a) Cone
b) Cube
c) Cuboid
d) Cylinder

Answer: d) Cylinder

Explanation: The shape of the candle is a cylinder. 

Example 2: What is the reflex angle for the angle given below?

a) 421°
b) 299°
c) 199°
d) 99°

Answer: b) 299°

Explanation: The reflex of the angle 61° = 360° − 61°
                                                             = 299°