4th Class Mathematics Geometry Geometry

Geometry

Category : 4th Class

LEARNING OBJECTIVES

• 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 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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