A triangle is a closed shape that has three angles, three sides, and three vertices. PQR is the abbreviation for a triangle with three vertices that say P, Q, and R. It is also known as a trigon or three-sided polygon. In this mini-lesson, we’ll go over everything there is to know about triangles, which are all around us. If you look at the shape of signboards and your favourite sandwiches, you will notice that they form the shape of a triangle. In this article, we are going to discuss the types of triangles, properties of triangles.
Types of Triangles
Triangles are classified into three types based on their side length: scalene, isosceles, and equilateral.
- If the lengths of all three sides differ, the triangle is a scalene triangle.
- A triangle that has two sides that are the same length is known as an isosceles triangle.
- A triangle that has three sides that are all the same length is known as an equilateral triangle.
What are the Properties of a Triangle?
Every geometry shape has fixed properties that can be used to identify the relationship between different sides and angles. In this section, we will look at some of the most important triangle properties, which are listed below.
- Triangles have 3 sides, 3 vertices, and 3 angles.
- The angle sum property of a triangle states that the sum of a triangle’s three interior angles is always 180°.
- Triangle inequality states that the sum of the lengths of the triangle’s two sides is greater than the length of the triangle’s third side.
- The square of the hypotenuse in a right triangle equals the sum of the squares of the other two sides, according to the Pythagorean theorem.
- The longest side is the one opposite the greater angle.
- The triangle’s exterior angle property states that the triangle’s exterior angle is always equal to the sum of its interior opposite angles.
Have You Heard of the Term Pascals Triangle?
Pascals triangle, also known as Pascal’s triangle, is a triangular arrangement of binomial coefficients. It bears the name of the French mathematician named Blaise Pascal. The numbers in Pascal’s triangle are arranged so that each number is the sum of two numbers just above it. The triangle of Pascal is widely used in probability theory, combinatorics, and algebra.
In general, we can use Pascal’s triangle to find the coefficients of binomial expansion, the probability of heads and tails in a coin toss, the probability of certain combinations of things, and so on.
Pascal’s Triangle in Binomial Expression
Pascal’s triangle can also be used to calculate the coefficients of terms in a binomial expansion. Pascals triangle is a useful tool for quickly determining whether or not the binomial expansion of a given polynomial is correct.
Triangles in Real Life
Triangles are known to have several key advantages that make them ideal for both architects as well as curious students: they are extremely common, structurally sound, and simple to apply and use in daily life. A triangle’s strength stems from its shape, which distributes forces evenly between its three sides. Let’s go through them:
- Roofs -The roofs of the houses are not all triangular in shape. In any case, if you live in a snowy area, you will notice that the majority of the roofs on houses are triangular in shape. The obtuse triangle is best represented by these roofs. The reason for this is that one of the angles is greater than 90 degrees. The main goal of developing these types of roofs is to prevent water or snow from remaining on the roofs for an extended period of time.
- Pizzas and Sandwiches – The majority of students begin their days with sandwiches or pizza. These sandwiches and pizzas have triangular shapes as well. When you show your students this practical example of a triangular shape, they will never forget it. When the mothers of your students serve these sandwiches for breakfast, they will recall the triangular shape concept. These sandwiches come in a variety of shapes.
To know more about triangles in a fun and easy manner, you can visit the Cuemath website.