Types of Triangles

🏆Practice types of triangles

Properties of triangles

The triangle is a geometric figure with three sides that form three angles whose sum is always 180o 180^o degrees.

A - Properties of triangles

Its vertices are called A,B A,B and C C

The union between these vertices creates the edges AB,BC AB,BC and CA CA
There are several types of triangles that we will study in this article.

Start practice

Test yourself on types of triangles!

einstein

In a right triangle, the side opposite the right angle is called....?

Practice more now

In the following section we will present the different types of triangles, along with illustrations and examples.


Equilateral triangle

An Equilateral triangle is a triangle whose sides have the same length.

Examples of equilateral triangles

A3-Examples of equilateral triangles


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Scalene triangle

A scalene triangle is a triangle whose sides are of different lengths (no two edges are the same).

Examples of scalene triangles:

Examples of Scalene Triangles


Isosceles triangle

An isosceles triangle is a triangle in which two of its sides have the same length. One of its properties is that, just as it has two equal edges, also two of its angles are equal.

Examples of isosceles triangles:

Examples of isosceles triangles


Do you know what the answer is?

Right triangle

A Right triangle is a triangle in which two sides form an angle of 90o 90^o degrees.

Examples of right triangles:

3 Examples of right triangles


Acute triangle

An acute triangle is a triangle in which all its angles are less than 90o 90^o degrees.

Examples of acute triangles:

3 Examples of acute triangles


Check your understanding

Obtuse triangle

An obtuse triangle is a triangle that has an obtuse angle, that is, greater than 90o 90^o degrees, which implies that the remaining two angles are less than 45o 45^o degrees.
This is because, as we have already mentioned, the sum of the interior angles of a triangle always equals 180o 180^o degrees.

Examples of obtuse triangles:

3 - Obtuse triangle


Do you want to learn more about triangles? For example, how to calculate their area or perimeter? Watch the complete video with everything you need to know about triangles!


Exercises on types of triangles and their properties:

Exercise 1

image 4 - What is the area of the rectangle?

Task:

What is the area of the rectangle?

Solution:

To find the missing side, we will use the Pythagorean Theorem on the triangle above.

Since the triangle is isosceles, we know that the length of the two sides is 7 7.

Therefore substituting in the formula of the Pythagorean Theorem we get A2+B2=C2A^2+B^2=C^2:

72+72=49+49=98 7^2+7^2=49+49=98

Therefore, the measure of side AB is. 98 \sqrt{98}

Answer:

The area of the rectangle is the product of its base and height, therefore:

98×10=98.99≈99u2 \sqrt{98}\times 10=98.99\approx 99u²


Do you think you will be able to solve it?

Exercise 2

Given a right triangle:

Exercise 5 Given a right-angled triangle

Task:

What is the length of the third side?

Solution:

The picture shows a triangle of which we know the length of two of its sides, and we want to know the value of the third side.

We also know that the triangle shown is a right triangle because the small box indicates which is the right angle.

The Pythagorean theorem says that in a right triangle the following is true:

172=82+X2 17²=8²+X²

We use the values of our triangle in the Pythagorean Theorem, and get the following equation:

172=82+X2 17²=8²+X²

289=64+x2 289=64+ x²

289−64=x2 289-64=x²

225=x2 225=x² , \sqrt{}

Find the square root:

15=x 15=x

Answer: 15=x 15=x


Exercise 3

Given the right triangle △ABC \triangle ABC

The area of the triangle is equal to 38cm⁡2 38\operatorname{cm}^2 , AC=8 cm AC=8\text{ cm}

The area of the triangle is equal to 38 cm2

Task:

Find the measure of the leg BC BC

Solution:

We will find the length of BC BC using the formula for finding the area of right triangles:

cateto×cateto2 \frac{cateto\times cateto}{2}

AC⋅BC2= \frac{AC\cdot BC}{2}=

8cm⁡⋅BC2=38cm⁡2 \frac{8\operatorname{cm}\cdot BC}{2}=38\operatorname{cm}^2

We multiply the equation by the common denominator.

×2 \times2

We then divide the equation by the coefficient of BC BC

BC=76cm⁡28cm⁡ BC=\frac{76\operatorname{cm}^2}{8\operatorname{cm}}

BC=9.5 cm BC=9.5\text{ cm}

Answer:

The length of the leg BC BC is 9.5 9.5 centimeters.


Test your knowledge

Exercise 4

The triangle △ABC \triangle ABC is a right triangle

Triangle ABC is a right triangle

The area of the triangle is equal to 6cm⁡2 6\operatorname{cm}^2

Task:

Calculate X X and the length of side BC BC

Solution:

We will use the formula for calculating the area of the right triangle:

cateto×cateto2=AC⋅BC2= \frac{cateto\times cateto}{2}=\frac{AC\cdot BC}{2}=

And we will compare the expression with the area of the triangle. 6cm⁡2 6 \operatorname{cm}^2

4cm⋅(X−1)2=6cm⁡2 \frac{4 cm\cdot(X-1)}{2}=6 \operatorname{cm}^2

We multiply the equation by 2 2

4cm(X−1)=12cm⁡2 4 cm(X-1)= 12\operatorname{cm}^2

We will omit the units to perform the operations.

We open the parentheses using the distributive property:

4X−4+4=12+4 4X -4+4=12 +4

4X=16 4X=16

X=164 X=\frac{16}{4}

X=4 X=4

We replace X=4 X=4 in the expression of BC BC and find that:

BC=X−1=4−1=3  BC=X-1=4-1=3\text{ }

BC=3 BC=3

Answer: X=4cm⁡ X=4\operatorname{cm} , BC=3cm⁡ BC=3\operatorname{cm}


Exercise 5

Task:

Calculate which is larger?

Exercise 8 Calculating which is larger

Given the right triangle △ABC \triangle ABC .

Which angle is larger: ∢B ∢B or ∢A ∢A ?

Solution:

It is given to us that the triangle △ABC \triangle ABC is a right trignle with ∢A=90° ∢A=90° and therefore we know that the last 2 2 angles are acute angles.

We know this without needing to calculate the exact value of ∢B∢B

Answer: ∢A>∢B ∢A>∢B


Do you know what the answer is?

Exercise 6

Given the right triangle △ABC \triangle ABC .

Exercise 9 Given the right triangle ABC.

∢A=20° ∢A=20°

Task:

Is it possible to calculate ∢C ∢C ?

If possible, calculate it.

Solution:

Given that △ABC \triangle ABC is a right triangle.

∢B=90° ∢B=90°

∢A=20° ∢A=20°

The sum of the angles 20°+90°+∢C=180° 20°+90°+∢C=180°

∢C=70° ∢C=70°

Answer: Yes, ∢C=70° ∢C=70°


Exercise 7

Determine which of the following triangles is obtuse, which is acute and which is right triangle

Task:

Determine which of the following triangles is obtuse, which is acute, and which is right triangle:

Solution:

1) We will see if the Pythagorean theorem holds for this triangle:

52+82=92 5²+8²=9²

25+64=81 25+64=81

89>81 89>81

The sum of the added squares is greater than the third square, therefore it is an acute triangle.

2) Now we will see this triangle:

72+72=132 7²+7²=13²

49+49=169 49+49=169

169>98 169>98

The sum of the added squares is a less than the third square, therefore it is an obtuse triangle.

3) 10.6≈113 10.6≈\sqrt{113}

The largest side of the 3 will be treated as the remainder.

72+82=1132 7²+8²=\sqrt{113}²

49+64=113 49+64=113

113=113 113=113

The Pythagorean theorem works, and therefore triangle 3 is a right triangle.

Answer:

A-acute triangle B- obtuse triangle C-right triangle.


Check your understanding

Exercise 8

Let's look at 3 3 angles:

Angle A A is equal to 30° 30°

Angle B B is equal to 60° 60°

Angle C C is equal to 90° 90°

Task:

Do these angles form a triangle?

Solution:

30°+60°+90°=180° 30°+60°+90°=180°

The sum of the angles in the triangle is 180° 180°

therefore these angles form a triangle.

Answer:

Yes, since the sum of the interior angles of the triangle is 180° 180° .


Exercise 9

Angle A A is equal to 90o 90^o

Angle B B is equal to 115o 115 ^o

Angle C C equals 35o 35 ^o

Task:

Do these angles form a triangle?

Solution:

90o+115o+35o=240o 90^o+115^o+35^o=240^o

The sum of the angles is greater than 180o 180^o

therefore these angles do not form a triangle.

Answer:

No, since the sum of the interor angles must be 180o 180^o and in this case the angles equal 240o 240^o


Do you think you will be able to solve it?

Review questions

What are the 7 types of triangles?

There are a variety of triangles. According to their sides and angles, we can list the following types:

  • Equilateral triangle
  • Scalene triangle
  • Isosceles triangle
  • Rectangular triangle
  • Acute triangle
  • Obtuse triangle
  • Oblique triangle

How are triangles classified according to their sides?

The different types of angles can be classified according to their sides or angles, let's see the classification according to the sides:

  • Equilateral triangle: All of its sides are equal and therefore its angles are equal.
  • Isosceles triangle: It has only two equal sides and two equal angles.
  • Scalene triangle: All three sides and angles are different.
A11 - How triangles are classified according to their sides


Test your knowledge

What are the sides of a scalene triangle like?

In a scalene triangle, all the sides have different values, that is, no sides are equal.


What do isosceles triangles look like?

Isosceles triangles have two equal sides and one different side, which gives them two equal angles.

What isosceles triangles look like

The above triangle is an isosceles triangle, so we can observe that

AB=AC AB=AC

∢B=∢C \sphericalangle B=\sphericalangle C


Do you know what the answer is?

What is the sum of the interior angles of a triangle?

One of the properties of triangles is that the sum of its interior angles must be 180o 180^o

Example:

Calculate the value of the angle C C , if we have a triangle whose angles have the following values:

∢A=60o \sphericalangle A=60^o

∢B=70o \sphericalangle B=70^o

Solution:

We know that the sum of the interior angles of a triangle is 180o 180^o , therefore:

∢A+∢B+∢C=180o \sphericalangle A+\sphericalangle B+\sphericalangle C=180^o

60o+70o+∢C=180o 60^o+70^o+\sphericalangle C=180^o

130o+∢C=180o 130^o+\sphericalangle C=180^o

Therefore:

∢C=180o−130o \sphericalangle C=180^o-130^o

∢C=50o \sphericalangle C=50^o

Answer

∢C=50o \sphericalangle C=50^o


If you are interested in learning more about triangles, you can visit one of the following articles:

In Tutorela you will find a variety of articles about mathematics.


Check your understanding

examples with solutions for types of triangles

Exercise #1

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #2

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer

Equilateral triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer

Isosceles triangle

Exercise #5

What kind of triangle is given here?

111111555AAABBBCCC5.5

Video Solution

Step-by-Step Solution

Since none of the sides have the same length, it is a scalene triangle.

Answer

Scalene triangle

Start practice