Pythagoras Theorem
FAQs on Pythagoras Theorem
What is the Pythagoras Theorem in Math?
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle. These triangles are also known as Pythagoras theorem triangles.
What is the Converse of Pythagoras Theorem?
The converse of Pythagoras theorem is: If the sum of the squares of any two sides of a triangle is equal to the square to the third (largest) side, then it is said to be a right-angled triangle.
What is the Use of the Pythagorean Theorem Formula?
The Pythagoras theorem works only for right-angled triangles. When any two values are known, we can apply the Pythagoras theorem and calculate the unknown sides of the triangle. There are other real-life applications of the Pythagoras theorem like in the field of navigation, engineering and architecture.
What is the use of the Pythagoras Theorem?
The Pythagorean theorem is used in various fields. A few of its applications are given below.
- Architecture, c
Pythagoras' Theorem
PythagorasOver years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°)
and squares are made on each of the three sides,
geometry/images/
then the biggest square has the exact same area as the other two squares put together! (press Go).
It is called "Pythagoras' Theorem" and can be written in one short equation:
a2 + b2 = c2
Note:
- c is the longest side of the triangle
- a and b are the other two sides
Definition
The longest side of the triangle is called the "hypotenuse", so the formal definition is:
In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.Sure ?
Let's see if it really works using an example.
Example: A "3, 4, 5" triangle has a right angle in it.
Let's check if the areas are the same:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
It works like Magic!
Why Is This Useful?
When we know two side lengths of a right triangle we can find the third side length.
How Do I Use it?
Write it down as an equation:
a2 + b2 = c2
ThePythagorean Theorem Formula
Pythagorean Theorem is one of the most fundamental and basic theorems in mathematics. It defines the relationship between the three sides of a right-angled triangle. This article will explain the Pythagorean Theorem Formula with examples and derivation. Let us learn the concept!
What is Pythagorean Theorem?
We are already aware of the definition and properties of a right-angled triangle. In this triangle with one of its angles as a right angle, it means 90 degrees. The side which is opposite to the degree angle is termed as the hypotenuse. The other two sides which are adjacent to the right angle are called legs of the triangle.
The Pythagorean Theorem is a very useful formula for determining the length of a side of a right triangle. This formula has many direct and indirect applications in the geometrical derivations and applications. In the triangle, the hypotenuse is the longest side.
We may easily locate the longest side by looking across from the right angle. The other two legs will be base and perpendicular, which are making a degree angle. There is no specific rule to consider the side as base or perpendicular. It does not matter at all.
Pythagoras Theorem
Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples. The formula and proof of this theorem are explained here with examples.
Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas. Let us learn the mathematics of the Pythagorean theorem in detail here.
Pythagoras Theorem Statement
Pythagoras theorem states that &#;In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides&#;. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
History
The theorem is named after a Greek Mathematician called Pythagoras.
Pythagoras Theorem Fo
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