**Category : **5th Class

** Geometry**

**Learning Objectives**

** **

- Points
- Line Segment
- Ray
- Line
- Angle
- Triangle
- Angle Based Classification
- Quadrilateral
- Circle
- Radius

**Point**

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

**Line Segment**

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

It is denoted as AB.

**Ray**

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

It is denoted as AB.

**Line**

A line is denned as the extension of a line segment Infinitive in either direction

It is denoted as AB

**Angle**

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

Angle is measured in degree. Symbol of the degree is "o" 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 an 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.

**Triangle**

A geometrical shape having three closed sides are called triangle.

Triangle can be 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:

**(i) Equilateral Triangle**

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

**(ii) Isosceles Triangle**

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

**(iii) Scalene Triangle**

In this triangle all the sides are unequal.

**B. Angle Based Classification**

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

**(i) Acute Angled Triangle**

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

**(ii) Obtuse Angled Triangle**

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

**(iii) 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 (\[\angle PQR\])

**Quadrilateral**

The geometrical figure having four closed sides is called a quadrilateral.

**Types of Quadrilateral**

There are two types of quadrilateral;

(i) Rectangle

(ii) Square

**Rectangle**

A rectangle is a quadrilateral in which:

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

(ii) Opposite sides are equal.

**Square**

A square is a quadrilateral in which:

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

(ii) All sides are equal.

**Circle**

A circle is a close curved line whose all points are at the same distance from a given point in a plane.

Here, O is the centre of the circle.

**Chord**

It is a line segment joining two distinct points of the circle. Here, DE is a chord of the circle.

**Radius**

Radius of a circle is half of the diameter.

OA, OB, and OC are radius of the circle.

**Cuboid**

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

**Cube**

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

**Commonly Asked Question**

**Find the size of the given angle marked with \[\mathbf{x}{}^\circ \].**

**2. Sum of 5 angles of a hexagon is \[\mathbf{570}{}^\circ \]. What is the remaining angle?**

(a) \[120{}^\circ \] (b) \[130{}^\circ \]

(c)\[150{}^\circ \] (d) \[170{}^\circ \]

(e) None of these

**Answer: (c)**

**Explanation:** A hexagon has 6 sides.

So, the sum of all interior angles = (Number of sides – 2)\[\times 180{}^\circ =\left( 62 \right)~180{}^\circ =4~\times 180{}^\circ =720{}^\circ \]

Hence, the remaining angles = Sum of all 6 angles – Given sum of 5 angles \[=720{}^\circ 570{}^\circ =150{}^\circ \]

3. **If \[\angle POQ\]is a right angle in the given figure, then find the value of \[\mathbf{x}{}^\circ **

** \]**

a)\[45{}^\circ \] (b) \[50{}^\circ \]

(c)\[40{}^\circ \] (d) \[55{}^\circ \]

(e) None of these

**Answer: (b)**

**Explanation:** Given that \[\angle POQ=90{}^\circ \], and \[\angle AOP=40{}^\circ \]

\[\angle AOP+\angle POQ+\angle BOQ=180{}^\circ \] (Linear pair)

Or, \[40{}^\circ +90{}^\circ +x{}^\circ =180{}^\circ \] or, \[x{}^\circ =180{}^\circ 130{}^\circ =50{}^\circ \].

4. **In the figure given below, find the value of \[\mathbf{x}{}^\circ \].**

(a) \[42{}^\circ \] (b) \[43{}^\circ \]

(c) \[57{}^\circ \] (d) \[39{}^\circ \]

(e) None of these

**Answer: (b)**

**Explanation:** \[\angle EOD=\angle COF=85{}^\circ \] (Vertically Opposite Angles)

Now, for the straight line \[AB,\angle AOE+\angle EOD+\angle BOD=180{}^\circ \]

(Linear pair or supplementary adjacent angles)

So, \[52{}^\circ +85{}^\circ +x{}^\circ =180{}^\circ ,\] or \[x{}^\circ =180{}^\circ 137{}^\circ =43{}^\circ \]

5. **If an angle is its own complementary angle, then its measure is:**

(a) \[30{}^\circ \] (b) \[45{}^\circ \]

(c) \[60{}^\circ \] (d) \[90{}^\circ \]

(e) None of these

**Answer: (b)**

**Explanation:** Since the angle is its own complementary angle, both angles must be equal. So \[x{}^\circ \] is complementary of \[x{}^\circ \].

So, \[x{}^\circ +x{}^\circ =90{}^\circ \] or, \[x{}^\circ +x{}^\circ =45{}^\circ +45{}^\circ \] or,\[x=45{}^\circ \].

*play_arrow*Geometrical Shapes*play_arrow*Geometry

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