Understanding Elementary Shapes: Meaning, Examples

Understanding Elementary Shapes: The important forms for understanding elementary shape in Class 6 CBSE and Class 7 include lines, angles, and triangles. A line segment is a straight line that begins at one fixed point and ends at another. When two line segments are united at a point, an angle is produced, and the angle is measured with the use of a protractor. A triangle is a figure made up of three line segments that meet at three separate locations to form a closed shape. Read on to find more.

What is a Line?

A line is a set of points in a straight path that extends in opposite directions without an end.

In other words, a line is a type of geometrical shape that can extend in both directions. A line is made up of a countless number of points. It is infinite and has no ends on both sides. A line is one-dimensional and has length but no width.

A line through two points \(A\) and \(B\) is written as \(AB\) or \(BA.\) Also, it is denoted by the letter  \(l\). ’.

A line segment has two endpoints. If we extend the two endpoints in either direction endlessly, we get a line. 

NCERT Solutions on Understanding Elementary Shapes

Here, \(AB\) is the line segment.

A ray is a portion of a line starting at a point and going in one direction endlessly.

Here, \(\overrightarrow {AB} \) is a ray.

Measuring Line Segments

We’ve seen a lot of line segments. A triangle is made up of three line segments, while a quadrilateral is made up of four. 

A line segment is a segment of a line that is fixed in place that enables the measurement of a line segment. A unique value measures each line segment termed its length that we use to compare line segments. We detect a relationship between the lengths of any two line segments when comparing them.

This can be done in three ways.

1. Comparison by Observation

Can you determine which one is longer just by looking at it? As you can see, \(AB\) is the longest of the two. However, you can’t always rely on your instincts. Take a look at the adjacent segments, for example:

It is possible that the difference in lengths between these two isn’t immediately obvious. As a result, alternative comparison methods must be used. The lengths of \(AB\) and \(PQ\) are the same in this adjacent image. This does not appear to be the case at first appearance. As a result, better line segment comparison methods are required.

2. Comparison by Tracing

We use tracing paper to compare \(AB\) and \(CD\). We trace \(CD\) and place the traced piece on \(AB\). The procedure is dependent on the accuracy with which the line segment is traced. Furthermore, if you want to compare two lengths, you must trace a new line segment. This is tricky, and you won’t be able to compare the lengths every time.

3. Comparison Using Ruler and a Divider

Have you seen all of the instruments in your instrument box, or do you know what they are? You have a ruler and a divider, among other things. Take note of how one of the ruler’s edges is marked. It’s broken down into \(15\) parts. Each of these \(15\) parts measures \({\rm{1\,cm}}\) in length. Each centimeter is broken down into ten subparts. The division of a centimeter is divided into \({\rm{1\,mm}}\) subparts.

Place the ruler’s zero mark at \(A\). See the mark to \(B\). This determines \(AB\)’s length. If the length is \({\rm{5}}{\rm{.8\,cm}}\), we can write it as Length \(AB{\rm{ = 5}}{\rm{.8\,cm}}\) or just \(AB{\rm{ = 5}}{\rm{.8\,cm}}\). Even in this method, mistakes are possible. The thickness of the ruler may make reading the marks on it difficult.

The eye should be appropriately positioned, just vertically above the mark, to obtain accurate measurements. Otherwise, angular viewing can cause mistakes.

Is it possible to avoid this issue? Is there a better way to do things? To measure length, we’ll utilise the divider.

Open the divider. Place one of its arms’ endpoints at \(A\) and the other arm’s endpoint at \(B\). Lift the divider and position it on the ruler, making sure the opening is not obstructed. Make sure one of the ruler’s endpoints is at zero. Note the mark to the other endpoint now.

Angle and Its Types

An angle is formed when two rays originate from the same originating point. The rays making an angle are called the arms of an angle. The originating point is called the vertex of an angle.

Types of Angles

The various types of angles are given below:

1. Right Angle

An angle that is precisely \({90^ \circ }\) is known as a right angle.

2. Straight Angle

When the arms of the angles lie in the opposite direction, they form a straight angle.

3. Acute Angle

An angle smaller than a right angle is called an acute angle. These are acute angles.

4. Obtuse Angle

If an angle is larger than a right angle but less than a straight angle, it is called an obtuse angle.  These are obtuse angles.

5. Reflex Angle

A reflex angle is larger than a straight angle but less than a complete angle. It looks like this. (See the angle mark)

6. Complete Angle

An angle of \({360^ \circ }\) is known as a complete angle.

Measuring Angles 

The angles can be acute, obtuse, or reflexive. This, however, does not provide a precise comparison. It is unable to determine which of the two obtuse angles is bigger. As a result, we must measure the angles to be more accurate in our comparison. With a protractor, we can accomplish it. 

The angle’s measurement in our metric system is known as the degree measure. \(360\) equal segments make up one complete revolution. Each component represents a degree. To say three hundred sixty degrees, we write \({360^ \circ }\).

Perpendicular Lines

When two lines intersect, and the angle between them is a right angle, then the lines are said to be perpendicular. If a line \(AB\) is perpendicular to \(CD\), we write \(AB \bot CD.\) .

Assume that \(AB\) is a line segment. Make a \(M\) in the middle of it. Let \(MN\) be a line that passes through \(M\) and is perpendicular to \(AB\). Is \(AB\) divided into two halves by \(MN\)? \(MN\) is perpendicular to \(AB\) and bisects it (that is, divides it into two equal parts). As a result, we refer to \(MN\) as the perpendicular bisector of \(AB\).

Polygons

A polygon is a simple closed curve formed by three or more line segments such that

(i) no two-line segments intersect except at their endpoints.
(ii) no two line segments with a common endpoint are coincident.

In other words, a polygon is a simple closed two-dimensional shape formed by joining the straight line segments.

Examples: equilateral triangle, square, scalene triangle, rectangle, etc

Types of Polygons

Classification of Triangles

Naming triangles based on sides

(i) Scalene triangle: A triangle having all three unequal sides is called a scalene triangle.

(ii) Isosceles triangle: A triangle having two equal sides is called an isosceles triangle.

(iii) Equilateral triangle: A triangle having three equal sides is called an equilateral triangle.

Naming triangles based on angles 

(i) Acute-angled triangle: If each angle is less than \({90^ \circ }\), the triangle is called an acute-angled triangle. 

(ii) Right-angled triangle: If any one angle is a right angle, then the triangle is called a right-angled triangle. 

(iii) Obtuse-angled triangle: If any one angle is greater than \({90^ \circ }\), then the triangle is called an obtuse-angled triangle.

Quadrilaterals

A quadrilateral is a two-dimensional shape having four sides, four angles, and four corners or vertices. The sum of internal angles of a quadrilateral is \({360^ \circ }\).

There are many types of quadrilaterals, and some particular types of quadrilaterals are discussed below:

Square – A quadrilateral whose all the sides are equal and each angle measures \({90^ \circ }\) is called a square.

Rectangle – A quadrilateral in which opposite sides are of equal length, and each angle is a right angle is called a rectangle.

Rhombus – A quadrilateral whose all sides are equal is called a rhombus.

Parallelogram – A quadrilateral is called a parallelogram if both pairs of its opposite sides are parallel.

Trapezium – The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.

Kite – A quadrilateral is called a kite if it has two pairs of equal adjacent sides but unequal opposite sides.

Three Dimensional Shapes

Here are a few forms you may encounter in your daily life. Each of the shapes is solid. It isn’t a flat shape at all.

Faces, Edges and Vertices

Many three-dimensional shapes have distinct faces, edges, and vertices. For example, consider a cube.

Each side of the cube is a flat surface called a flat face (or simply a face). Two faces meet at a line segment called an edge. Three edges meet at a point called a vertex.

Solved Examples – Understanding Elementary Shapes

Q.1. Count the number of sides of the polygons given below and name them:

Ans: (i) In this figure, the number of sides of the polygon is five, so it is a pentagon.
(ii) In this figure, the number of sides of the polygon is eight, so it is an octagon.
(iii) In this figure, the number of sides of the polygon is six, so it is a hexagon.
(iv) In this figure, the number of sides of the polygon is three, so it is a triangle.

Q.2. A square pyramid has a square as its base.

Then write the number of faces, edges, and corners.
Ans: 

Number of faces: \(5\)
Number of edges: \(8\)
Number of corners: \(5\)

Q.3. How many angles and diagonals, a quadrilateral has?
Ans: A quadrilateral has \(4\) angles and \(2\) diagonals.

Q.4. Write two examples of a cone.
Ans: Cone is a solid \(3D\) shape. The two examples of the cone are birthday caps and cone ice creams.

Q.5. How many right angles make the angle \({360^ \circ }\)?
Ans: We know \({90^ \circ }\) is equivalent to \(1\) right angle.
Hence, \({360^ \circ }\) is equivalent to \(\frac{{{{360}^ \circ }}}{{{{90}^ \circ }}} = 4\) right angles.

Summary

The first things we notice about an object are its colour and form. In many cases, we may determine the purpose of an object just by looking at it. As a result, it’s critical to understand the fundamental forms. A line segment is a straight line that begins at one fixed point and ends at another. When two line segments are united at a point, an angle is produced, and the angle is measured with the use of a protractor. A triangle is a figure made up of three line segments that meet at three separate locations to form a closed shape.

Curves or lines are used to create all of the shapes we see around us. We can notice corners, edges, planes, open curves, and closed curves in our surroundings. We use line segments, angles, triangles, polygons, and circles to organize them. They are of various sizes and measurements, as we have discovered. In this article, we discussed what a line is, measuring line segments in three ways, types of angles, measuring angles, naming of triangles based on sides and angles, quadrilaterals, polygons, and three-dimensional shapes, along with the solved examples. Also, we explored measuring line segments in three methods, types of angles, measuring angles, naming triangles based on sides and angles, quadrilaterals, polygons, and three-dimensional objects, and solved cases in this article.

Learn All the Concepts on Geometry

Frequently Asked Questions (FAQ) – Understanding Elementary Shapes

Q.1. What do you understand by elementary shapes?
Ans: If we look around, we can see so many shapes made up of lines and curves like lines, rays, line segments, angles, curves, polygons, circles, etc. All these shapes are of different sizes and measures. These are called elementary shapes.

Q.2. What is a protractor?
Ans: A protractor is a device used to measure angles.

Q.3. How to measure an angle?
Ans: We measure angles in degrees or radians. We generally use a protractor to measure an angle in degrees.

Q.4. What is the measure of one complete revolution?
Ans: The measure of one complete revolution is \({360^ \circ }\).

Q.5. What is a degree?
Ans:  A degree is a unit to measure an angle.

Q.6. What is the disadvantage in comparing line segments?
Ans: When comparing by direct observation, there are chances of occurring error in the readings.

Q.7. What type of angle is formed between the hands of a clock at \(9\) o’clock?
Ans: A right angle is formed between the hands of a clock at \(9\) o’clock.

Q.8. Why is it better to use a divider than a ruler?
Ans: Divider gives the most accurate results, and hence it is better to use consistently.

We hope this detailed article on understanding elementary shapes helped you in your studies. If you have any doubts or queries regarding this topic, feel to ask us in the comment section.