TYPES OF TRIANGLES

About "Types of Triangles"

Types of Triangles :

In geometry, triangles can be classified using various properties related to their angles and sides.

There are six different types of triangles. 

Here we are going to see, how triangles in geometry can be classified.

Equilateral Triangle

An equilateral triangle is a triangle in which all the three sides will be equal.

Each angle will be 60°.

Isosceles triangle

A triangle with two equal sides is called as isosceles triangle.

The angles corresponding to the equal sides will always be equal.

Scalene triangle

In a scalene triangle the length of all the three sides will be different.

And also all the three angles will be different. 

Right triangle

A right triangle is the triangle in which one of the angles is 90°.

Acute triangle

An acute triangle is a triangle with all three angles are less than 90 degree.

Obtuse triangle

An obtuse triangle is a triangle in which one of the angles is obtuse (greater than 90 degree).

Types of Triangles - Practice Problems

Problem 1 :

Identify the type of triangle whose angles are 35°, 40°, 105°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  All the given three angles are different.

(ii)  One of the angles is greater than 90°

From the above two points, 

The given triangle is a scalene and obtuse triangle. 

Problem 2 :

Identify the type of triangle whose angles are 55°, 65°, 60°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  All the given three angles are different.

(ii)  All the three angles are less than 90°

From the above two points, we have

The given triangle is a scalene and acute triangle. 

Problem 3 :

Identify the type of triangle whose angles are 50°, 40°, 90°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  All the given three angles are different.

(ii)  One of the angles is 90°

From the above two points, we have

The given triangle is a scalene and right triangle. 

Problem 4 :

Identify the type of triangle whose angles are 45°, 45°, 90°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  Two of the given angles are equal

(ii)  One of the angles is 90°

From the above two points, we have

The given triangle is an isosceles and right triangle. 

Problem 5 :

Identify the type of triangle whose angles are 70°, 70°, 40°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  Two of the given angles are equal

(ii)  All the three angles are less than 90°

From the above two points, we have

The given triangle is an isosceles and acute triangle. 

Problem 6 :

Identify the type of triangle whose angles are 30°, 30°, 120°.

Solution :

Let us consider the following two important points related to the given information. 

(i)  Two of the given angles are equal

(ii)  One of the angles is greater than 90°

From the above two points, we have

The given triangle is an isosceles and obtuse triangle. 

Problem 7 :

Identify the type of triangle whose sides are 5 cm, 6 cm and 7 cm. 

Solution :

The length of all the three sides are different. 

From the above point, we have

The given triangle is a scalene triangle.

Problem 8 :

Identify the type of triangle whose sides are 6 cm, 6 cm and 8 cm. 

Solution :

The lengths of two of the sides are equal.

From the above point, we have

The given triangle is an isosceles triangle.

Problem 9 :

If (3x + 3) is one of the angles of an acute triangle, then find the value of "x". 

Solution :

Since the given triangle is acute triangle, all the three angles will be less than 90°. 

So, (3x + 3) will also be less than 90°.

Then, 

3x + 3  < 90°

3x < 87°

x < 29°

Hence, the value of "x" is less than 29°.

Problem 10:

If 50°, 40° and (2x + 4)°are the angles of a right triangle, then find the value of "x". 

Solution:

Since the given triangle is a right triangle, one of the angles must be 90°

In the given three angles 50°, 40° and (2x+4)°, the first two angles are not right angles. 

So the third angle (2x+4)° must be right angle. 

Then,

2x + 4  =  90°

2x  =  86°

x  =  43°

Hence, the value of "x" is  43°.

Problem 11 :

If 2x, y and 3z are the angles of a acute triangle, find the value of "z". 

Solution:

Since the given triangle is acute triangle, all the three angles will be less than 90°. 

So, 3z will also be less than 90°.

Then, 

3z  <  90°

z  <  30°

Hence, the value of "z" is less than 30°.

Problem 12 :

If 2x+15, 3x and 6x are the angles of a triangle, identify type of the triangle. 

Solution :

Since 2x+15, 3x and 6x are the angles of a triangle, by property

(2x + 15) + 3x + 6x  =  180°

11x + 15  =  180°

11x  =  165°

x  =  15°

Plugging x = 15°, we get

First angle  =  2x + 15  =  2(15) + 15  =  45°

Second angle  =  3x  =  3(15)  =  45°

Third angle  =  6x  =  6(15)  =  90°

Let us consider the following two important points from the above calculation. 

(i)  Two of the angles are equal

(ii)  One of the angles is 90°

From the above two points, we have

The given triangle is an isosceles and right triangle. 

After having gone through the stuff given above, we hope that the students would have understood "Types of triangles". 

Apart from the stuff given above, if you want to know more about "Types of triangles",please click here.

Apart from the stuff given on "Types of Triangles", if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6