Geometrical Shapes

Category : 3rd Class

Geometrical Shapes

 

Introduction

Lines, angles and rays are the basic concept of geometrical figures. Basic geometrical figure was first introduced in text by great mathematician Euclid.

 

Lines and Its Characteristics

Point

A precise location or place on a plane. Point is usually represented by dot.

A is a point

 

Line

Line is a geometrical figure formed by points moving along a fixed direction and the reverse direction. Line may be straight or curved.

                                

                        Straight line                                            Curved line

 

Line Segment

A straight line which links two points without extending beyond them.

 

AB is a line segment

 

Ray

A ray extends infinity in one direction, but ends at a single point in the other direction.

                       

OA is a ray

Intersecting Point

The point where two lines meet or cross.

                                                 

 

 

In the pictures above points J, K, L, M and O are intersecting points.

 

To Draw a Line Segment of a given Length

The following are the steps used to draw the line segment.

For example: Line segment of 6 cm.

Step 1: Place the ruler on the plane paper.

Step 2: Mark a point A on the paper against 0 mark of ruler.

Step 3: Mark another point B on the same paper at the length of 6 cm.

Step 4: Draw a line between A and B.

           

            AB is the required length of 6 cm.

 

Ø  Example

AO = 4 cm and OB = 5 cm. Find the length of AB.

            A.   .O   .B

            (a) 9 cm                                                            (b) 5 cm

            (c) 8 cm                                                             (d) 7 cm

            (e) None of these

Ans.     (a)

            Explanation: Length of AB = (4 + 5) cm = 9 cm.

 

Ø  Example

            Identify the line from the figures given below:

            (a)                               (b)

            (c)                               (d) All the above

            (e) None of these

Ans.     (c)

            Explanation: A line is extended from both the ends.

 

Angles

When two or more lines meet at a point then angle is formed. A complementary of an angle is obtained by subtracting the angle from a right angle. A supplementary angle is obtained by subtracting the angle from a straight angle.

 

A Right Angle

An angle whose measure is exactly 90° is a right angle.

\[\angle \] ABC is a right angle

 

An Acute Angle

An angle whose measure is less than \[90{}^\circ \] is an acute angle.

\[\angle \] DEF is an acute angle

 

An Obtuse Angle

An angle whose measure is greater than \[90{}^\circ \] but less than \[180{}^\circ \] is a obtuse angle.                               

\[\angle \]LMN is an obtuse angle

 

Straight Angle                                                         

An angle whose measure is \[180{}^\circ \]a straight angle.       

\[\angle \] ACB is straight angle

                 

A Reflex Angle

An angle whose measure is greater than \[180{}^\circ \] but less than \[360{}^\circ \] is a reflex angle

\[\angle \] JOP is a reflex angle

Triangles                                                               

A region bounded by three line segments is called triangular region and figures is called a triangle.

 

Equilateral Triangle

A triangle whose all sides are equal is called equilateral triangle.

Triangle ABC is an equilateral triangle.                                        

 

Isosceles Triangle

A triangle whose two sides are equal is called isosceles triangle.

In triangle ABC AB = AC = 4 cm hence, triangle ABC is an isosceles triangle.

 

Scalene Triangle

A triangle whose sides are unequal is called scalene triangle. In the figure below side lengths of triangle ABC are not equal hence, triangle ABC is a scalene triangle.

 

A Right Angle Triangle

A triangle whose one angle is a right angle is called right angled triangle. In the picture below triangle ABC is a right angle.

 

  •           Example

One side of a triangle is perpendicular to another side. What is the name of the triangle?

            (a) Straight angle                                                (b) Reflex angle

            (c) Right angle                                                    (d) All the above

            (e) None of these

Ans.     (c)

            Explanation: Because triangle has one right angle.

 

  •           Example

All three angles of a triangle are equal then the measurement of every angle will be?

            (a) \[60{}^\circ \]                                                          (b) \[90{}^\circ \]

            (c) \[30{}^\circ \]                                                           (d) \[20{}^\circ \]

            (e) None of these

Ans.     (a)

            Explanation: Sum of all angles of triangle is\[180{}^\circ \]. So, each angle\[=\,\,\frac{180}{3}\,\,=\,\,60{}^\circ \].

 

 

Other Topics

Notes - Geometrical Shapes
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