# Chapter 6 – Triangles

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You might have come across an enclosed shape with three pointed tips; it is known as a triangle. A triangle is a polygon shape with three vertices and three edges. Being an enclosed shape with three sides, a triangle also has three angles whose sum is always 180 degrees. Triangle is one of the basic shapes in geometry. There are two ways to categorize triangles: the length of their sides or by their angle. Classifying triangles based on length are derived: isosceles triangle, equilateral triangle, and scalene triangle.

On the other hand, the three sorts of triangles derived based on their angles are acute angle triangle, right-angle triangle, and obtuse angle triangle. The perimeter for all sorts of triangles is the sum of all three sides of the same. For more information on a triangle, check video lectures on MSVgo. There, you can also learn ways to solve mathematical questions related to triangles.

#### Scalene Triangle

A scalene triangle is the type of triangle whose all three sides tend to have different lengths and different angles. Some of the right-angled triangles are scalene if the other two angles and sides are not congruent. Due to this reason, no line of the scalene triangle is in symmetry. Additionally, the angle opposite the longest side is generally the largest angle, while the small side’s angle is the smallest. Lack of symmetry is the key feature of this sort of triangle. The formula for calculating a scalene triangle area is half times the product of its height and base length. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Isosceles Triangle

The triangle with two equal sides and two equal angles is known as an isosceles triangle. The name ‘isosceles’ is derived from two Greek words: Iso, meaning same, and Skelos means legs. In an isosceles triangle, there are two same base angles with one other angle. The area of an isosceles triangle is calculated with the formula (b/4) * √(4a2 – b2), and its altitude is calculated with the formula (b/2a) * √(4a2 – b2). Key examples of isosceles triangles seen in the modern world are the faces of bipyramids and most of the Catalan solids. Since ancient times, the isosceles triangle was used in architecture and design to structure the pediments and gables of the constructed buildings. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Equilateral Triangle

The equilateral triangle’s basic nature is that it has three equal sides and three congruent angles of F degrees. If a perpendicular is drawn from its vertex, the opposite sides are bisected into equal halves. The ortho-center and centroid of the equilateral triangle are always at the same point. The area of an equilateral triangle is derived with formula √3a2/4, where a is the side. Additionally, the median, angle bisector, and altitude of the sides of the equilateral triangle are always the same. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Acute Angle Triangle

A triangle whose all three angles are less than 90 degrees is known as an acute angle triangle. The formula for calculating an acute angle triangle area is half the product of base and height, while its perimeter is the addition of the length of all three sides. Equilateral triangles are always acute angle triangles as all its angles are 60 degrees. Additionally, if a line is drawn from the acute angle triangle base to the opposite vertex, it is always perpendicular to the base. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Right Angle Triangle

The right-angle triangle is the triangle whose one angle is 90 degrees. This sort of triangle is the most used shape in mathematics due to its implications in Pythagoras theorem and trigonometry. Concerning the Pythagoras theorem, the right angle triangle depicts that hypotenuse is always the root of the sum of the squares of the base side and perpendicular side. On the other hand, the right-angle triangle is used in trigonometry as it always reflects the presence of three angles in the first quadrant due to the 90 degrees angle; thus, the values of sine, cos, and tan are derived easily using it. The first quadrant also reflects positive values, and the only sin, cos, and tan are positive in the first quadrant, while they change the value in the other three quadrants. Right angle triangle can be scalene or isosceles but never equilateral triangle as one of its angles is 90 degrees. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Obtuse Angle Triangle

An obtuse angle triangle is a triangle with one obtuse angle and two acute angles. There can be only one obtuse in a triangle because the sum of all the angles for a triangle is 180, and as per the definition of the obtuse angle, it is higher than 90 degrees. Thus, having two angles greater than 90 degrees will take the sum of the three angles to more than 180 degrees. For more information on this sort of triangle, go through the resource library on MSVgo.

#### Conclusion

Overall, the triangle is an enclosed geometrical shape with three sides, three angles, and three vertices. There are key basic types of triangles: the scalene triangle, isosceles triangle, and the equilateral triangle. There are three other sorts of triangles: acute angle triangle, right-angle triangle, and obtuse angle triangle.

#### FAQs

What are the six types of triangles?

The six types of triangles are scalene triangle, isosceles triangle, equilateral triangle, acute angle, triangle, right-angle triangle, and obtuse angle triangle.

What are the three main types of triangles?

The three main types of triangles are scalene triangle, isosceles triangle, and equilateral triangle.

What are the five properties of a triangle?

The five properties of a triangle are:

• It has three sides
• It has three vertices
• It has three angles
• The sum of the internal angles of a triangle is always 180°.
• The area of a triangle equals half the product of its height and base

What are congruent triangles in geometry?

If two angles and the included side of one triangle are similar to the corresponding constraints of another triangle, then both the triangles are said to be congruent.

For more fun and interactive lessons on Triangles, visit the MSVgo application.

### High School Physics

• Alternating Current
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• Dual nature of Radiation and Matter
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### High School Chemistry

• Acids, Bases and Salts
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• Aldehydes, Ketones and Carboxylic Acids
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### High School Biology

• Absorption and Movement of Water in Plants
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• Neural Control And Coordination
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• Plant Growth and Development
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• Pollution; Sources and its effects
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• The Fundamental Unit Of Life
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### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
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• Algebra – Principle of Mathematical Induction
• Binomial Theorem
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• Linear Programming
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• Mensuration – Areas
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• Number Systems
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• Permutations and Combinations
• Probability
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### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
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• Elements and Compounds
• Fibre To Fabric
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• Force And Pressure
• Forests: Our Lifeline
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• Garbage In, Garbage Out
• Getting To Know Plants
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• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
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• Organization in Living Things
• Our Environment
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• Reaching The Age Of Adolescence
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• The Living Organisms And Their Surroundings
• Transfer of Heat
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• Transportation In Animals And Plants
• Universe
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• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
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• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
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• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time