# Equilateral, Isosceles and Scalene Triangles

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Equilateral, Isosceles and Scalene Triangles
CCSS.MATH.CONTENT.5.G.B.3

## Equilateral, Isosceles, and Scalene Triangles – Introduction

Triangles are fundamental geometric shapes that are classified based on the lengths of their sides and the measures of their angles. Every triangle has three sides, three angles, and the sum of the interior angles always adds up to 180 degrees. Understanding the different types of triangles is essential for geometry and applies to various real-life contexts—from engineering to art.

## Equilateral, Isosceles, and Scalene Triangles – Definition

A triangle is a polygon with three edges and three vertices. Its three angles always sum to 180 degrees, which is one of the fundamental rules governing triangles.

The properties of a triangle largely depend on its side lengths and angles. These aspects define the type of triangle and determine its classification. There are three primary types of triangles that we will explore: equilateral triangles, isosceles triangles, and scalene triangles.

How many sides does a triangle have?
What is the sum of the interior angles of any triangle?
If one angle of a triangle is 90 degrees and the second angle is 60 degrees, what is the measure of the third angle?

Here's a table summarizing the characteristics of Equilateral, Isosceles, and Scalene triangles, tailored for educational purposes:

Triangle Type Sides Angles Description
Equilateral All three sides are equal. All three angles are equal, each 60°. A triangle where all sides and angles are the same, providing perfect symmetry.
Isosceles At least two sides are equal. The angles opposite the equal sides are equal. A triangle with two equal sides and two equal angles, offering a base of symmetry.
Scalene All sides are of different lengths. All angles are different. A triangle with no equal sides or angles, showing no symmetry.

### Equilateral Triangles – Definition and Properties

Equilateral triangles are the simplest to identify. With their symmetrical appearance, they convey a sense of balance and equality.

Equilateral triangles have three sides of equal length and three angles that are each 60 degrees.

They are often used in signs and symbols because of their equal-sided properties, which can signify balance and harmony.

### Isosceles Triangles – Definition and Properties

Isosceles triangles can be thought of as the 'siblings' of equilateral triangles, sharing some similar traits but also having their own unique properties.

An isosceles triangle has at least two sides of equal length, and the angles opposite those sides are also equal.

Their distinctive shape is utilized in architecture to create structures that are both aesthetically pleasing and structurally sound.

### Scalene Triangles – Definition and Properties

Contrasting with equilateral and isosceles triangles, scalene triangles present a more diverse set of angles and side lengths.

A scalene triangle has three sides of different lengths and, consequently, three distinct angles.

This diversity makes them particularly useful in solving complex geometric problems where variability is needed.

## Equilateral, Isosceles, and Scalene Triangles – Practice

What type of triangle has all three sides the same length?
How many sides are equal in an isosceles triangle?
What makes a scalene triangle different from other triangles?
In which triangle are all the angles equal?
Which triangle has at least two equal angles?
What type of triangle would you have if each side and each angle were different?

## Equilateral, Isosceles, and Scalene Triangles – Summary

Key Learnings from this Text:

• Equilateral triangles have all sides and angles equal.
• Isosceles triangles have at least two equal sides and angles.
• Scalene triangles have no equal sides or angles.
• The special properties of these triangles are useful in solving a variety of geometric problems.
• Recognizing these different triangles in the real world can be both educational and practical.

Explore more about triangles by engaging with interactive practice problems and resources that can further enhance your understanding of geometry.

## Equilateral, Isosceles, and Scalene Triangles – Frequently Asked Questions

What distinguishes an equilateral triangle from an isosceles triangle?
Can an isosceles triangle also be an equilateral triangle?
How can you identify a scalene triangle?
Why are triangles important in geometry?
Can you find the area of a triangle if you only know one side length?
How do the properties of triangles apply in the real world?
What is the sum of the angles in any triangle?
Are all isosceles triangles also scalene triangles?
What additional information do you need to solve for a scalene triangle's area?
Why do equilateral triangles appear balanced?

### TranscriptEquilateral, Isosceles and Scalene Triangles

Equilateral, isosceles, and scalene triangles. Triangles are three-sided, two-dimensional polygons with three vertices. Based on the types of interior angles, triangles are classified as acute, right, or obtuse. Triangles are also classified based on the length of their sides. The term congruent refers to the sides of a shape that are the same length. A triangle can have three congruent sides, two congruent sides, or none at all. Triangles are sorted into three types based on their side congruency: equilateral, isosceles, and scalene. A triangle with three congruent sides is called an equilateral triangle. Equilateral is derived from two Latin words: aequus, which means equal, and latus, which means side. Therefore, equilateral literally means having all equal sides. To show that a triangle is equilateral, we draw a single line on each side, like this. Because all of the triangle's sides are congruent, all of the angles are also the same size. An equilateral triangle can be divided into three smaller triangles, that are also equilateral. They also have three symmetry lines. This means that they appear the same from a variety of perspectives. As a result, they can be used in architecture, art, and design. The next triangle is an isosceles triangle. This triangle has two congruent sides. Isosceles is a combination of two Greek words: isos meaning equal and skelos is leg or side. As a result, isosceles means equal legs or equal sides. The two equal-length sides of an isosceles triangle are called legs, and the third side is called the base. An isosceles triangle has two equal angles. There is only one line of symmetry in the isosceles triangle. This cuts the triangle in half. Because each part is a mirror image of the other, if you folded the triangle along the line of symmetry, the two parts would perfectly match. Isosceles triangles can be found in a variety of everyday objects and structures. Engineers use the isosceles triangle shape for landmarks. Slices are frequently cut into this shape for easy sharing, and even some musical instruments have an isosceles triangle design that helps create a unique sound. This triangle has a balance and stability that makes it very useful. A scalene triangle is the final classification. This triangle has zero congruent sides. All three sides are different lengths. Scalene is derived from the Greek word skalenos, which means uneven or crooked. Therefore, the term "scalene literally means "uneven-sided. A scalene triangle's three angles are all different, implying that the triangle lacks symmetry. We can see scalene triangles in things like sailboats, and bicycles. To summarize, triangle classifications are useful in geometry because they enable us to identify and differentiate between various types based on their properties. A triangle's unique properties can be used in both mathematical calculations and practical, everyday life applications.

1 comment
1 comment
1. that intro slayz

From Isabella, 4 months ago

## Equilateral, Isosceles and Scalene Triangles exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Equilateral, Isosceles and Scalene Triangles .
• ### Do you know the keywords for triangles?

Hints

Think about the word equilateral, what do you think the first part equi means?

An isosceles triangle has a base and two legs. What do we know about the two legs?

Solution

Triangle - A three-sided, two-dimensional polygon with three vertices.

Congruent - Sides of a shape that have the same length.

Equilateral Triangle - A triangle with three congruent sides and three equal angles.

Isosceles Triangle - A triangle with three congruent sides and three equal angles.

Scalene Triangle - A triangle with no congruent sides and no equal angles.

• ### Do you know the parts of a triangle?

Hints

We mark congruent sides (equal sides) with lines to indicate they are the same length.

There are two types of angle in this triangle, which one is the right-angle?

An equilateral triangle has all sides equal, an isosceles triangle has two sides equal and a scalene triangle has no equal sides.

Solution

The image shows the correct labels.

• ### What types of triangles are these?

Hints

Equilateral triangles have all sides equal and all angles equal.

Isosceles triangles have two sides equal and two angles equal.

Scalene triangles have no sides equal and no sides equal.

Solution

The image shows the correct label for each triangle.

• ### How many lines of symmetry?

Hints

You can identify lines of symmetry using a mirror. Each side is identical to the other.

If you line up your mirror on a line of symmetry you will see your original image.

The number of lines of symmetry is not always the same as the number of equal sides.

Solution

A line of symmetry cuts a shape into identical mirror image shapes.

A scalene triangle has no lines of symmetry.

An isosceles triangle has one line of symmetry.

An equilateral triangle has three lines of symmetry.

• ### What type of triangle is this?

Hints

A triangle is a polygon and a polygon is an enclosed shape (all the sides meet). Which one is not a triangle?

In an equilateral triangle, how many sides are equal?

An isosceles triangle has two equal sides.

A scalene triangle has no equal sides.

Solution

A scalene triangle has no equal sides.

An isosceles triangle has two equal sides.

An equilateral triangle has three equal sides.

The sides of a triangle must meet.

• ### What type of triangle is described?

Hints

You can use the same word more than once.

We can define triangles based on the number of equal sides or equal angles.

For example, an isosceles triangle has two equal sides and it has two equal angles. We can also say the opposite, a triangle with two equal sides or two equal angles is isosceles

Take care with your spelling, these words may help you:

Equilateral, Isosceles, Scalene.

Solution

A triangle has sides with lengths $5$ cm, $6$ cm and $6$ cm. This type of triangle is called isosceles.

A triangle has three angles of $60$°. This type of triangle is called equilateral.

A triangle has sides with lengths $8$ cm, $9$ cm and $12$ cm. This type of triangle is called scalene.

A triangle has angles of $40$°, $70$° and $70$°. This type of triangle is called isosceles.