types of triangles

This geometry video lesson is designed for 3-6-year-old children to help them learn the types of triangles and classify them using Montessori geometric stick boxes. 

Triangles are an important geometric shape in mathematics, with many applications in science, engineering, and design. A triangle is formed by connecting three non-collinear points. Triangles can vary in size, shape, and orientation, and can be classified based on their sides and angles. The sum of the interior angles of a triangle is always 180 degrees and is known as the triangle angle sum property. Moreover, triangles have many properties. 

This video lesson aims to educate the child to classify triangles by sides. A triangle can be classified as an equilateral triangle, isosceles triangle, and scalene triangle.

Types of Triangles

A. Classification of Triangles Based on Sides

Triangles can be classified based on the lengths of their sides. The three types of triangles based on their sides are:

  1. Equilateral triangle: An equilateral triangle has all three sides of equal length. The angles in an equilateral triangle are also equal, measuring 60 degrees each. Equilateral triangles are often used in architecture and engineering to create stable and symmetrical structures. The symmetry of equilateral triangles is also found in nature, such as in the arrangement of atoms in certain molecules.
  2. Isosceles triangle: An isosceles triangle has two sides of equal length and one side of a different length. The two angles opposite to the equal sides are also equal in measure. Isosceles triangles are commonly used in geometry proofs and constructing shapes, such as creating a kite or a rhombus. In addition, isosceles triangles also appear in nature, such as in the shape of certain leaves or the wings of some birds.
  3. Scalene triangle: A scalene triangle has all three sides of different lengths. The angles in a scalene triangle are also different in measure. While scalene triangles may not have the same symmetrical properties as equilateral and isosceles triangles, they are still important in various fields of study. For example, scalene triangles appear in astronomy as they are used to calculate the distances between stars. They are also used in trigonometry to solve real-world problems, such as finding the height of a building or the distance between two points on a map.

B. Classification of Triangles Based on Angles

Triangles can also be classified based on the measure of their angles. The three types of triangles based on their angles are:

  1. Acute triangle: An acute triangle has all three angles less than 90 degrees. In an acute triangle, all sides are less than the diameter of the circumcircle.
  2. Right triangle: A right triangle has one angle equal to 90 degrees. The side opposite to the right angle is called the hypotenuse. The hypotenuse is the longest side in a right triangle and is always opposite to the right angle.
  3. Obtuse triangle: An obtuse triangle has one angle greater than 90 degrees. In an obtuse triangle, the longest side is opposite to the obtuse angle, and the other two sides are less than the diameter of the circumcircle.

It is also possible for a triangle to have both equal sides and an angle greater than 90 degrees. Such triangles are called obtuse isosceles triangles. Similarly, a triangle with all sides of different lengths and a right angle is called a right scalene triangle.

Classification of triangles is important in geometry as it helps in identifying and solving various types of problems related to triangles, such as finding the area, perimeter, and height of a triangle. Triangles are also used in trigonometry, where they play a key role in studying angles and their relationships with sides. Triangles are also used in engineering and design, where they are used to model and analyze structures, such as bridges and buildings.

Here are Some Activities that can be Used to Introduce the Different Types of Triangles:

  1. Triangle identification game: In this game, students are given different types of triangles and have to identify them based on their properties. This can be done by either showing pictures of triangles or giving descriptions of their properties. This game helps students to understand the differences between the different types of triangles and how to identify them.
  2. Triangle construction: In this activity, students are given different measurements for the sides and angles of a triangle and have to construct them using a compass and ruler. This activity helps students to understand the properties of different types of triangles and how they can be constructed.
  3. Triangle sorting: In this activity, students are given a set of triangles and have to sort them based on their properties, such as the length of their sides or the measure of their angles. This activity helps students to develop their classification skills and understand the different properties of triangles.

These activities can be used in the classroom to introduce the different types of triangles and help students to understand their properties and applications.

Watch the video along with the child to understand how Montessori geometric stick boxes can help identify different types of triangles.

Related Video Resources

To watch more geometry video lessons, click here.

Video Created by: Justine McNeilly

FAQs

  • What are the 3 main types of triangles?

The three types of triangles based on their sides are:

    1. Equilateral triangle: All three sides are of equal length.
    2. Isosceles triangle: Two sides are of equal length, and the third side is of a different length.
    3. Scalene triangle: All three sides are of different lengths.
  • What is an equilateral triangle?

An equilateral triangle is a triangle with all three sides of equal length. The angles in an equilateral triangle are also equal, measuring 60 degrees each.

  • What is an isosceles triangle?

An isosceles triangle is a triangle with two sides of equal length, and one side of a different length. The two angles opposite to the equal sides are also equal in measure.

  • What is a scalene triangle?

A scalene triangle is a triangle with all three sides of different lengths. The angles in a scalene triangle are also different in measure.

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