Geometrical Figures

**Category : **5th Class

**Geometrical Figures**

**Introduction**

We observe different types of figures around us. They are in different shapes. In this chapter we will discuss about different types of geometrical figures such as line, angles etc.

**Point**

To show a particular location, a dot (.) is placed over it, that dot is known as point.

**Example:**

In the above figure point A represents\[\frac{1}{3}\], point B represents\[\frac{2}{3}\], and point C represents 1.

**Line Segment **

Line segment is defined as the shortest distance between two fixed points. For example

It is denoted as \[\overline{AB}\].

**Example: **How many line segments are there in the figure?

(a) 2 (b) 4

(c) 8 (d) 16

(e) None of these

Answer (c)

**Ray **

It is defined as the extension of a line segment in one infinitive direction. For example:

It is denoted as \[\overrightarrow{AB}\].

**Example:** How many rays are there in the given figure?

(a) 2 (b) 4

(c) 12 (d) 16

(e) None of these

Answer (c)

**Line**

Line is defined as the extension of a line segment infinitive in either direction.

**Example:** How many lines are there in the following figure?

It is denoted as

** **

(a) 2 (b) 4

(c) 8 (d) 16

(e) None of these

Answer (a)

**Angle**

Inclination between two rays having common end point is called angle.

Angle is measured in degree. Symbol of the degree is "\[{}^\circ\]" and written as \[a{}^\circ ,\]

Where a is the measurement of the angle.

**Types of Angle**

There are different types of angles.

**Right Angle**

An angle whose measure is exactly \[90{}^\circ \] is a right angle.

**Acute Angle**

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

**Obtuse Angle**

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

**Straight Angle**

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

**Reflex Angle**

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

**Example:**

Name the angle which measures exactly\[90{}^\circ \]**.**

**Answer:** Right angle

**Example:**

Name the angle which measures between \[0{}^\circ \] and \[90{}^\circ \].

**Answer:** Acute angle

**Triangle**

The geometrical shapes having three sides are called triangle.

Triangle has been classified:

(a) On the basis of sides

(b) On the basis of angles

**Sides Based Classification**

On the basis of sides, triangle is of three types:

**Equilateral Triangle**

It is the triangle in which all the three sides are equal.

**Isosceles Triangle**

In this type of triangle two of the three sides are equal.

**Scalene Triangle**

In this triangle all the sides are unequal.

**Angle Based Classification**

On the basis of angles, triangles are of three types.

**Acute Angled Triangle**

A triangle whose all the angles are acute is called acute angled triangle.

**Obtuse Angled Triangle**

A triangle in which one angle is an obtuse angle is called an obtuse angled triangle.

**Right Angled Triangle**

A triangle in which one angle is \[90{}^\circ \] is called a right angled triangle.

PQR is a right-angled triangle as it contains a right angle

(\[\angle ~PQR\])

**Example:**

Name the triangle which has two equal sides.

**Answer:** Isosceles triangle

**Example:**

If the sum of two angles of a triangle is \[80{}^\circ \] the triangle is:

(a) Acute angled triangle

(b) Obtuse angled triangle

(c) Right angled triangle

(d) All of these

(e) None of these

Answer: (b)

Sum of two angles of a triangle is \[80{}^\circ \]

Therefore, third angle \[180{}^\circ -80{}^\circ =100{}^\circ \] which is an obtuse angle.

**Quadrilateral**

The geometrical figure having four sides is called quadrilateral.

**Types of Quadrilateral**

In this chapter we will study about two types of quadrilateral

(i) Rectangle (ij) Square

**Rectangle **

Rectangle is a quadrilateral in which:

(i) All angles are of\[90{}^\circ \];

(ii) Opposite sides are equal.

**Square**

Square is a quadrilateral in which:

(i) All angles are of \[90{}^\circ \]; (ii) All sides are equal.

**Example:**

How many angles of a rectangle are right angles?

(a) 1 (b) 2

(c) 3 (d) 4

(e) None of these

Answer (d)

**Example:**

How many sides a quadrilateral has?

(a) 1 (b) 2

(c) 3 (d) 4

(e) None of these

Answer (d)

**Circle**

Circle is a simple closed shape, whose all points are at the same distance from a given point in a plane.

**Chord**

It is the line segment joining two distinct points of the circle.

**Diameter**

The diameter is the length of the line through the center that touches two point on the edge of the circle.

**Radius**

Radius of a circle is half of the diameter.

In the above circle, 0 is the centre, OA, OB, and OC are radius, and DE is the chord of the circle.

**Example:**

If diameter of a circle is 25 cm, find the radius of the circle

**Answer:** \[Radius=\frac{25}{2}=12.5\text{ }cm\]

**Example:**

0 is the centre of a circle and P is the point on the line of the circle. Op is ........... of the circle.

(a) Radius (b) Diameter

(c) Chord (d) All of these

(e) None of these

Answer (a)

** **

**Cuboid**

Cuboid is a box shaped solid object. It has six flat faces, which are rectangular in shape.

**Cube**

Cube is also a box shaped solid object with six faces, which are square in shape.

*play_arrow*Introduction*play_arrow*Point and Line Segment*play_arrow*Angle*play_arrow*Quadrilateral*play_arrow*Geometrical Figures*play_arrow*Geometrical Figures

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