![]() What is the Converse of Pythagoras Theorem? These triangles are also known as Pythagoras theorem triangles. This theorem can be expressed as, c 2 = a 2 + b 2 where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle. 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. ![]() Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.įAQs on Pythagoras Theorem What is the Pythagoras Theorem in Math? Our mission is to transform the way children learn math, to help them excel in school and competitive exams. ☛ Related ArticlesĬuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12. People traveling in the sea use this technique to find the shortest distance and route to proceed to their concerned places. The Pythagoras concept is applied in interior designing and the architecture of houses and buildings. The face recognition feature in security cameras uses the concept of the Pythagorean theorem, that is, the distance between the security camera and the location of the person is noted and well-projected through the lens using the concept. It is mainly used in two dimensions in engineering fields. When the length or breadth is known it is very easy to calculate the diameter of a particular sector. Most architects use the technique of the Pythagorean theorem to find the unknown dimensions. Here are some of the applications of the Pythagoras theorem. The applications of the Pythagoras theorem can be seen in our day-to-day life. ![]() We can also say that CD × AC = BC 2.Īdding these 2 equations, we get AB 2 + BC 2 = (AD × AC) + (CD × AC) Thus △ABD ∼ △ACB, Therefore, AD/AB = AB/AC. Thus, △ABD ∼ △ACB (by AA similarity criterion) Derivation of Pythagorean Theorem FormulaĬonsider a right-angled triangle ABC, right-angled at B. Hence, corresponding angles in similar triangles lead us to equal ratios of side lengths. Also, if the angles are of the same measure, then by using the sine law, we can say that the corresponding sides will also be in the same ratio. Two triangles are said to be similar if their corresponding angles are of equal measure and their corresponding sides are in the same ratio. ![]() Pythagorean Theorem Formula Proof using Similar Triangles Hence, the Pythagoras theorem formula is proved. This means (a + b) 2 = + c 2.This leads to a 2 + b 2 + 2ab = 2ab + c 2. Step 4: The area of the square PQRS with side (a + b) = Area of 4 triangles + Area of the square WXYZ with side 'c'.Step 3: The area of the square WXYZ by arranging the four triangles is c 2.Step 2: The 4 triangles form the inner square WXYZ as shown, with 'c' as the four sides.The four right triangles have 'b' as the base, 'a' as the height and, 'c' as the hypotenuse. It can be seen that in the square PQRS, the length of the sides is 'a + b'. Arrange them in such a way that the hypotenuses of all the triangles form a tilted square. Take 4 congruent right-angled triangles, with side lengths 'a' and 'b', and hypotenuse length 'c'. Step 1: This method is also known as the 'proof by rearrangement'.For example, let us use the values a, b, and c as shown in the following figure and follow the steps given below: The proof of the Pythagoras theorem can be derived using the algebraic method. Proof of Pythagorean Theorem Formula using the Algebraic Method Let us have a look at both these methods individually in order to understand the proof of this theorem. Some of the most common and widely used methods are the algebraic method and the similar triangles method. The Pythagoras theorem can be proved in many ways.
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