##
**Triangle | What is Triangle?**

A closed plane figure formed by three line segments is
called a

**triangle**. It is denoted by the symbol**Δ**.
In the figure alongside, PQR is a closed plane figure formed
by three line segments PQ, QR and RP. So it is a triangle. It is represented by
ΔPQR. The points P, Q and R are called the vertices of the triangle PQR.

###
**Types of triangles on the basis of
sides**

On the basis of sides there are three types of triangles:

####
**i. **__Scalene
Triangle__:

__Scalene Triangle__:

A triangle having non of the sides equal is called a scalene triangle. In
the given triangle, MN ≠ NP ≠ PM. So ΔMNP is a scalene triangle.

####
**ii. **__Isosceles
Triangle__:

__Isosceles Triangle__:

A triangle with having two sides equal is called an isosceles triangle. In the
given triangle, PQ = PR = 5 cm. So, ΔPQR is an isosceles triangle.

**:**

__Note__
Base angles are always equal of an isosceles triangle. In the given figure ∠PQR = ∠PRQ.

####
**iii. **__Equilateral Triangle__**: **

__Equilateral Triangle__

A
triangle with having all three sides equal is called an equilateral triangle. In the given
triangle, AB = BC = AC = 4.5 cm. So, ΔABC is an equilateral triangle.

**:**

__Note__
All
angles of an equilateral triangle are 60°. An equilateral triangle holds all
the properties of an isosceles triangle.

###
**Types of triangles on the basis of angles**

On
the basis of angles, there are three types of triangles:

####
**i. **__Acute Angled Triangle__**: **

__Acute Angled Triangle__

If all
the angles of a triangle are less than 90° or acute angles, then it is called
an acute angled triangle. In the given triangle, each angle of the triangle is
less than 90°. So, ΔABC is an acute angled triangle.

####
**ii. **__Obtuse Angled Triangle__**: **

__Obtuse Angled Triangle__

The
triangle with one angle is obtuse angle or more than 90° is called an obtuse
angled triangle. In the given figure, ∠RMN is an obtuse
angle. So, ΔMNR is an obtuse angled triangle.

####
**iii. **__Right Angled ____Triangle__:

__Right Angled__

The
triangle with one angle a right angle or equal to 90° is called a right angled
triangle.

In the
given figure, ∠PQR is 90°. So, ΔPQR
is a right angled triangle.

**:**

__Note__
If a right angled
triangle has two sides equal, then it is called a right angled isosceles
triangle.

###
**Properties of triangle:**

1. Sum of three angles of a triangle is always 180°.

2. Base angles of an isosceles triangle are always equal.

3. All angles of an equilateral triangle are equal to 60° each.

4. Base angles of a right angled isosceles triangle are equal to
45° each.

5. If any two angles of a triangle are equal, then the sides opposite to
them are also equal.

6. The exterior angle of a triangle is equal to the sum of two
opposite interior angles.

7. The sum of two sides of a triangle is greater than the third
side.

8. In any triangle, the side opposite to greater angle is longer
than the side opposite to the smaller angle.

9. The line drawn from the vertex of an isosceles triangle to the
mid point of its base is perpendicular to the base.

10.The bisector of the vertical angle of an isosceles triangle is always perpendicular
to the base.

11. The line joining mid-points of any two sides of a triangle is parallel to third side and is half the length of third side.

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