# 3rd Class Mathematics Points, Lines and Rays Triangles

## Triangles

Category : 3rd Class

### Triangles

A plane figure bounded by three straight lines is called a triangle. The figure given below is a triangle ABC. The straight line AB, BC and CA are the line segments,

Therefore, the triangle ABC has: three sides, AB, BC and CA. Three anglesB and and three vertices A, B and C.

Remember the following about a triangle:

• A triangle has three sides.
• A triangle has three angles.
• A triangle has three vertices.
• The sum of all three angles of a triangle is
• The symbol for the representation of a triangle is.
• The perimeter of a triangle is the sum of its sides.

A figure has three sides and three vertices if one of the angle of a figure is given then which one of the following is the name of the figure?

(a) An angle

(b) A point

(c) A triangle

(d) All of these

(e) None of these

Explanation

A figure has three sides and three vertices. Hence, the name of the figure is triangle.

Equilateral Triangle A triangle whose all sides are equal is called an equilateral triangle. In the given, AB = BC = CA =4 cm. Therefore,   is an equilateral triangle. If the sides of a triangle are equal then its angles are also equal. Therefore, an equilateral triangle has equal sides and equal angles. In the given figure, the angles of the triangle are  Sum of the anglesof a triangle is always

Therefore,

Remember the following about the equilateral triangle:

• The sides of an equilateral triangle are always equal.
• Angles of an equilateral triangle are always equal.
• Sum of all three angles of an equilateral triangle is
• The measurement of every angle of an equilateral triangle is
• Perimetre of an equilateral triangle is the sum of length of its sides.

Two angles of a triangle are equal. If third angle is half of the sum of two angles then which one of the following is the name of the triangle?

(a) A right angle

(b) An equilateral triangle

(c) Isosceles triangle

(d) All of these

(e) None of these

Explanations: Let the angle of a triangle is

Then third angle  hence, the angles of the triangle are equal.

Thus, triangle is an equilateral triangle.

Isosceles Triangle

A triangle whose two sides are equal is called isosceles triangle. In an isosceles triangle, opposite angles of equal sides are also equal. In the figure given below two equal sides of a triangle ABC are AB and AC. The opposite angle of side AB is  and opposite angle of side AC is   ABC. Hence, an equilateral triangle has two equal sides of equal opposite angles.

In the above figure, AB = AC = 4cm and their opposite angles

Remember the Fallowing about an isosceles triangle:

• An isosceles triangle has two equal sides.
• An isosceles triangle has two equal angles of their equal opposite sides.
• The perimetre of an isosceles triangle is the sum of its side lengths.

Scalene Triangle

A triangle whose all sides are unequal is called a scalene triangle. In triangle ABC,

AB = 1 cm, BC = 4 cm and CA = 3 cm. The sides of the triangle are not equal and therefore, it is called a scalene triangle. The perimetre of a scalene triangle is the sum of its side length.

Right Angled Triangle

A triangle which has one of the angles equal to  is called a right angled triangle.

In the figure below the triangle ABC is a right angled triangle. The line segment AB is perpendicular to BC, therefore, BC is the base of the triangle and AC is called the hypotenuse of the triangle. The length of hypotenuse AC is the longest side of the triangle.

Remember the following about a right angled triangle:

• A right angled triangle has one angle of 90°.
• Hypotenuse is the longest side of a right angled triangle.
• The sum of other two angles of a right angled triangle is always equal to a right angle.
• The area of a right angled triangle  Base x Height.
• The length of hypotenuse of a right angled triangle

• The length of base of a right angled triangle

• The length of perpendicular of a right angled triangle

• Perimetre of a right angled triangle is the sum of its all sides.

Sum of two angles other than the right angle of a right angled triangle is always a:

(a) Straight angle

(b) Reflex angle

(c) Right angle

(d) acute angle

(e) None of these

Explanation

Sum of all angles of a triangle is, if one angle is  then the sum of other two angles is also a right angle.

How many triangles are there in the figure given below?

(a) 2

(b) 1

(c) 3

(d) 4

(e) None of these

The total length of sides of a triangle is 57 cm. If the sum of two equal sides is the twice of third side then the triangle is a/an?

(a) Right triangle

(b)Equilateral triangle

(c) Isosceles triangle

(d) All of these

(e) None of these

Explanations

Let the sum of two sides of the triangle is x. Hence, third side of the triangle

will be  According to the question ,

Thus, third side of the triangle will be

Hence, the triangle is an equilateral triangle.

Consider the following statements:

Statement 1: Sides of a right angled triangle are always equal.

Statement 2: Two sides of an isosceles triangle are equal.

Which one of the following options is correct about the above statements?

(a) Statement 1 is false and 2 is true

(b) Statement 1 is true and 2 is false

(c) Both statements 1 and 2 are false

(d) All of these

(e) None of these

Explanation

A triangle which has two equal sides is called an isosceles triangle.

In the following figure, two lines are intersecting to each other. Find the number of triangles formed in the given figure?

(a) 4

(b) 3

(c) 6

(d) 8

(e) None of these

A line AB is bisecting the figure into two equal triangles. If the length of opposite sides of the figure is equal then which one of the following types of triangle is formed?

.

(a) Isosceles triangles

(b) Equilateral triangles

(c) Scalene triangles

(d) All of these

(e) None of these

Explanations

Two scalene triangles will be formed on bisecting by a line AB.

How many edges are there in the figure given below?

(a) 8

(b) 12

(c) 13

(d) None of these

(e) All of these

Explanation A cube has 12 edges.

The measurement of an angle is 65°. What is the measurement of its complement?

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanation

Two angles are drawn by Peter on a horizontal line. If the measurement of one angle is  then find the measurement of another angle on the same horizontal?

(a)

(b)

(c)

(d) All of these

(e) None of these

Explication

Sum of the angles of a quadrilateral is 360°. If the figure has four equal angles then the measurement of each angle of the figure is?

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanations Measurement of each angle of the quadrilateral

A line is extended on both directions but its extended lines are not a straight line. The extended lines are?

(a) Line segments

(b) Curved lines

(c) Straight line

(d) All of these

(e) None of these

How many lines are possible between two given points?

(a) Two

(b) One

(c) Three

(d) All of these

(e) None of these

Explanation

Only one line is possible between two points.

Through a given point lines can be drawn, is it correct or not?

(a) False

(b) True

(c) Cannot say

(d) All of these

(e) None of these

Expiration

Infinite lines can be drawn through a given point.

Pintoo has drawn a length of line of 10 cm. The line drawn by Pintoo is?

(a) A ray

(b) A line segment

(c) A line

(d) All of these

(e) None of these

Explanation

A fixed length of line is called a line segment.

John draws a line from O and it ends at A, by mistake he marks a arrow at the end point on it. The figure drawn by John is?

(a) A ray

(b) A line segment

(c) A line

(d) All of these

(e) None of these

Explanations The figure drawn by John starts from 0 and an arrow mark is at end point.

• A line does not have end points.
• A ray has one end point.
• A line segment has two end points.
• One line can be drawn through two given points.
• Infinitive lines can be drawn through a point.
• A line is the collection of points.
• A ray can be extended on its arrow mark.
• A line can be extended on both directions.
• A line segment has a fixed length.
• The unit for the measurement of an angle is degree.
• An angle is included within two rays.
• A triangle has three sides, three vertices and three angles.
• Cube, cylinder and cone are solid figures.
• The sides of an equilateral triangle are equal.
• the sum of all three angles of a triangle is
• If two sides of a triangle are equal then it is called isosceles triangle.
• Perimeter of a plane figure is the sum of its side length and width.

• Relation among the base, height and hypotenuse of a right angled triangle was first described by great scientist Pythagoras.
• Distance between the sun and the earth was first calculated by Aritarchos.

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