4th Class Mathematics Geometry Geometry

Geometry

Category : 4th Class

LEARNING OBJECTIVES

This lesson will help you to:—

  • understand two dimensional and three dimensional geometrical figures.
  • learn about line symmetry, symmetrical and asymmetrical shapes.
  • determine the number of line of symmetry.
  • identify the different types of triangles on the basis of sides and angles.
  • understand the different kinds of angles.
  • learn about the angle sum properties of triangle and quadrilateral.
  • Know about the terms related to the circle.

 

QUICK CONCEPT REVIEW

Circle

  • A circle is a closed figure formed by points equidistant from a fixed point.
  • Every circle has a fixed centre.
  • The perimeter of the circle is called its circumference
  • The distance between the centre and any point on the circle is called its radius.

A line segment passing through the centre of the circle, whose end points lie on the circle is called the diameter of the circle.

 

  • The diameter of a circle is twice the radius.
  • A line segment whose end points lie on the circle is called a chord.
  • The diameter is the longest chord of a circle.
  • Any part of a circle is called an arc.
  • If an arc represents half of the circle it is a semicircle.

 

ANGLE

Two rays with a common end point form an angle. It is denoted by\[\angle \].

  • The common end point is known as the vertex of the angle.
  • The rays forming an angle are called the arms or sides of the angle.
  • Angles measures in degrees.
  • An angle whose measure is between\[{{0}^{o}}\]and\[{{90}^{o}}\]is called an acute angle.
  • An angle whose measure is\[{{90}^{o}}\]is called a right angle.
  • An angle whose measure is more than\[{{90}^{o}}\]but less than\[{{180}^{o}}\]is called an obtuse angle.
  • An angle whose measure is\[{{180}^{o}}\]is called a straight angle and whose measure is\[{{360}^{o}}\]is called whole angle.
  • An angle whose measure is more than\[{{180}^{o}}\]but less than\[{{360}^{o}}\]is called a reflex angle.

 

A TRIANGLE

  • A triangle is a closed figure having three sides, three vertices and three angles. It is denoted by\[\Delta \].
  • Triangles can be classified on the basis of their sides and angles.
  • Triangle in which all sides are equal is called equilateral
  • Triangle in which two sides are equal is called isosceles
  • Triangle in which all the three sides are different is called scalene
  • Right angled Triangle:-

In this, only one angle is of \[{{90}^{o}}\]

  • A cute - angled triangle:-
  • All angles of this triangle are acute.
  • Obtuse - angled triangle:-
  • In this triangle, at least one angle is an obtuse angle.
  • The sum of 3 angles of a triangle is\[{{180}^{o}}\].


A QUADRILATERAL

  • A quadrilateral is a four - sided closed figure. It has four vertices, and four angles.
  • The sum of four angles of a quadrilateral is\[{{360}^{o}}\].
  • Square, Rectangle, parallelograms etc. are examples of quadrilateral.

 

SYMMETRY

  • Symmetrical shapes can be folded into two matching equal halves
  • The place from where symmetrical shapes are folded is called the line of symmetry.
  • A symmetrical shapes cannot be folded into two equal halves.
  • A symmetrical shapes do not have a line of symmetry.
  • The line of symmetry is also known as mirror line or line of reflection.
  • If a figure can be folded such that one part of it exactly matches with the other then the figure has a line of symmetry.
  • A square has four lines of symmetry, rectangle has two lines of symmetry and a triangle (whose 3 sides are equal) has 3 lines of symmetry
  • Some figures have only one line of symmetry. Eg.

             

  • Some figures have no line of symmetry for e.g.

                      

TESSELLATIONS

  • We can fit some shapes of tiles such that there are no gaps and they do not overlap. These tilings ore called tessellations.

Tessellating shape

Shape that does not tessellate

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