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 will be 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 are obtuse (greater than 90 degree).
Types of angles-practice problems with answer:
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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.
Let us look at the next problem on "Types of triangles"
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°
Let us look at the next problem on "Types of triangles"
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.
If you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
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 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
