[Maths Class Notes] on Obtuse Angled Triangle Pdf for Exam

A closed two-dimensional figure having three sides of either same or different lengths and three angles of same or different angles are called Triangle. There are three types of triangles based on the lengths of their sides and the measure of their angles. If one of the angles of the triangle is greater than 90 degrees, it is called an obtuse-angled triangle. This is one of the interior angles of a triangle and the other two angles of that triangle will be acute angles.

There are two other types of triangles other than the Obtuse triangle and those are:

 

Three Types of Triangles

These triangles are major of three types.

1. Equilateral Triangle – The triangle has all three sides equal.

2. Scalene Triangle –  The triangle in which none of the three sides is equal.

3. Isosceles Triangle – The triangle where any two sides of a triangle are equal.

 

What is an Obtuse Angles Triangle?

As mentioned above, if one of the angles of a triangle is greater than the other two (>90 degrees) i.e one of the angles is obtuse, that triangle is known as the Obtuse angled triangle. The sum of all the angles of a triangle is always 180 degrees regardless of the type of triangle. This is the reason that the other two angles in an obtuse angle triangle are acute.

 

Difference Between Acute, Obtuse and Right-angled triangle

Acute Angle Triangle – If all the three angles of a triangle are less than 90 degrees, it is called the Acute angled Triangle. It Is formed when two line segments are joined in such a way that the angle formed by them is less than 90 degrees.

Obtuse Angle Triangle – If one of the angles in the triangle is more than 90 degrees, that triangle is an obtuse angle triangle. It is formed when two line segments are joined in such a way that they form an angle of more than 90 degrees.

Right Angle Triangle –  If one of the angles of a triangle is more than 90 degrees, it is called the Right Angle Triangle. It is formed when the two line segments make an angle of 90 degrees after joining.

 

The Formula of Obtuse Angle Triangle

Area of an obtuse angle triangle = ½ * b * h, where b is the base and h is the height of the triangle.

The area of a triangle can also be found by using Heron’s formula

, i.e A = √(S(S-a)(S-b)(S-c)), where s is the semi perimeter of the triangle and a,b,c are the three sides of the triangle.

s = (a+b+c)/2

The perimeter of a triangle is the sum of all three sides = a +b + c cm

 

Can You Find Out if a Triangle is an Obtuse-Angled Triangle?

Yes, it’s easy to find out whether the triangle is obtuse-angled or not. If one of the angles of a triangle is more than 90 degrees and the other two are less than that, it would be an obtuse-angled triangle. 

For example – If one of the angles of a triangle is 120 degrees, and the other two angles are 40 degrees and 20 degrees, this triangle would be obtuse-angled as one of the angles is more than 90 degrees, i.e 120 degrees.

There’s also one more way to find whether a triangle is obtuse-angled. If the sum of squares of the two sides of a triangle is lesser than the largest side, it would be an obtuse-angled triangle.

So, if a, b and c are the three sides of the obtuse-angled triangle, then a² > b²  + c²

Properties of Obtuse Angled Triangle

1. The longest side of the obtuse triangle is the one opposite to the obtuse angle in that triangle.

2. As one of the angles is greater than 90 degrees in an obtuse triangle, so the other two angles will be acute.

3. An obtuse-angled triangle will have only one obtuse angle.

4. In an obtuse triangle, the centroid and incentre will lie inside the triangle and the circumcentre and orthocentre will lie outside the triangle.

 

Equilateral Triangle

The triangle with all 3 sides and angles are also equal is called an Equilateral triangle is a. The value of each angle of an equilateral triangle is 60 degrees and is also called an equiangular triangle. The equilateral triangle is a regular polygon or a regular triangle with angles that are equal and sides that are also equal.

 

Properties of Equilateral Triangle

An equilateral triangle has some properties which define a triangle as an equilateral triangle. Some properties of the Equilateral triangle are as follows- 

• The equilateral triangle is a regular polygon because it has three sides.

• The sides of an equilateral triangle are always equal in measurements.

• The angles of an equilateral triangle are always congruent and 60 degrees.

• Due to the Angle sum property in triangles, the sum of all the angles of an equilateral triangle is always equal to 180 degrees

• In an equilateral triangle, the perpendicular constructed from any of the vertices of the triangle to the opposite side bisects the side in equal lengths. It also bisects the angle of the triangle’s vertex into equal halves of 30 degrees each from where the perpendicular is constructed.

• In an equilateral triangle, the Ortho-center and Centroid are situated at the same point.

• The Angle Bisector, Median, and the Altitude of an equilateral triangle for all sides are located at the same.

• The area of an equilateral triangle can be found out by the formula = √3a²/ 4, (where a = side of the given equilateral triangle)

• The perimeter of an equilateral triangle can be found out by the formula = 3a (where a = side of the given equilateral triangle).

 

Scalene Triangle

A Scalene triangle is a triangle with all unequal sides and since all the 3 sides are unequal in a triangle, it means all the 3 angles will also be of different measures. In other words, the triangle with no equal sides is called a scalene triangle A scalene triangle is one of the 3 types of triangles based on the length of its sides.

 

Properties of Scalene Triangle

Some properties of the scalene triangle are as follows- 

• In a Scalene Triangle, there is no point symmetry.

• The Scalene Triangle has 3 sides with none of them of equal length.

• It has 3 angles with none of them with equal measure.

• A scalene triangle has no parallel sides.

• The interior angles of a scalene triangle can be acute, obtuse, or right angles. 

• In an acute scalene triangle, the center of the circumscribing circle will always lie inside the triangle.

• In an obtuse scalene triangle, the circumcenter will always lie outside the triangle.