Types of Triangles

Triangles are shapes that we see everywhere in our daily lives. They are one of the simplest yet most fascinating shapes in geometry. In this lesson, we will explore different types of triangles based on their sides and angles, and understand their properties. Triangles are shapes with three sides and three angles. Each triangle has its own specific characteristics that make it unique and classify it under specific types. Let's start by looking at the different ways to classify triangles.

Classification based on sides

The first way to classify triangles is to look at the length of their sides. There are three main types of triangles based on their sides: equilateral, isosceles, and scalene triangles. Let's look at each type in detail.

Equilateral triangle

An equilateral triangle has three sides that are the same length. This means that if you measure each side of the triangle, they will all be equal. Because of this, all the angles inside this triangle will also be equal, with each measuring 60°.

The properties of an equilateral triangle include:

• All sides are equal in length.
• All angles are equal which is 60°.
• It is a polygon with three similar sides.

For example, if you have a triangle with each side 5 cm, it becomes an equilateral triangle because each side is equal to 5 cm.

Isosceles triangle

An isosceles triangle has two sides of equal length. The angles opposite to these sides are also equal. This is a common type of triangle where either the base angles are equal or the two sides have the same length.

The properties of an isosceles triangle include:

• Two sides that are equal in length.
• Two angles that are equal.
• The angle between two equal sides is called the vertex angle.

For example, in an isosceles triangle with sides 6 cm, 6 cm, and 4 cm, the two sides measuring 6 cm are equal.

Scalene triangle

In a scalene triangle all the sides have different lengths. In this type of triangle, no sides or angles are the same. The measure of each side will be different, and the angles will also be different.

The properties of a scalene triangle include the following:

• None of the sides are equal.
• No angles are equal.
• The lengths of the three sides are different.

A good example of a scalene triangle is one whose sides measure 5 cm, 6 cm, and 7 cm. Each side has a different length.

Classification based on angles

Triangles can also be classified based on their angles. There are three main types of triangles based on the angles: acute, right, and obtuse triangles. We will learn about each of these below.

Acute triangle

An acute triangle is a triangle whose all three angles are less than 90°. This means that in an acute triangle, no angle will reach or exceed a right angle.

The properties of an acute-angled triangle include the following:

• All angles are less than 90°.
• It can be an equilateral, isosceles or scalene triangle.

For example, a triangle with angles 50°, 60° and 70° is an acute triangle because all angles are less than 90°.

Right triangle

A right triangle has one angle exactly 90°, which is called a right angle. This type of triangle is very important in geometry as it is used in various calculations and theorems.

The properties of a right-angled triangle include:

• One angle is exactly 90°.
• The side opposite the right angle is the longest and is called the hypotenuse.

For example, if the angles of a triangle are 90°, 30° and 60°, then it qualifies as a right triangle because one of its right angles is 90°.

Obtuse triangle

In an obtuse triangle, one angle is more than 90°. This type of angle is called an obtuse angle. An obtuse triangle will have only one such angle because the sum of all the angles of the triangle must be 180°.

The properties of an obtuse-angled triangle include the following:

• An angle greater than 90°.
• It can be an isosceles or scalene triangle, but cannot be an equilateral triangle.

For example, if a triangle has angles of 120°, 30° and 30°, this makes it an obtuse triangle because one of the angles is greater than 90°.

Conclusion

In summary, triangles are versatile and important shapes in the study of geometry. By understanding how triangles are classified, we can understand more about their properties and their interaction in different structures. Remember:

• Triangles classified based on the sides can be equilateral, isosceles or scalene.
• Triangles classified based on the angles can be acute-angled, right-angled, or obtuse-angled.

This exploration of triangles gives us a basic understanding of their types and properties. You can now identify and classify triangles you see – whether on paper, in structures, or in nature. Remember, the foundation of understanding triangles will help solve more complex geometric problems in the future!

Mathematic:
    - Side length: s1, s2, s3
    - Angles: a1, a2, a3

Criteria:
    - if s1 = s2 = s3 -> equilateral
    - If s1 = s2 ≠ s3 or s1 ≠ s2 = s3 or s1 = s3 ≠ s2 -> isosceles
    - if s1 ≠ s2 ≠ s3 -> scalene

    - If a1  90° or a2 > 90° or a3 > 90° -> obtuse angle

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