Did You Study the Most Important Math Theorems as per NCERT Class 10 Syllabus?

For students, theorems are the building blocks of basic mathematics. They also help develop deductive reasoning when students fully grasp the statements and their proofs. Learn more about these theorems, check out the information below.

What is a Theorem in Math?

A theorem is a type of statement which had been proven earlier based on other statements or axioms. You can say that theorems are already proven facts that are applied to various mathematical concepts. The theorems are created to break complex problems into simpler forms. Students can solve many difficult problems in Maths by applying the right theorems for specific questions.

Pythagoras Theorem in NCERT Class 10 Syllabus

According to the Pythagoras theorem the square of the hypotenuse length is equal to the sum of the lengths of the other two sides in the right-angled triangle.

The formula for Pythagoras Theorem

 H² = P² + B² where

·        H stands for Hypotenuse

·        P stands for Perpendicular

·        B stands for Base

Remainder Theorem

This Math theorem called Remainder Theorem is a useful concept in algebra of NCERT class 10 syllabus. It states that when a polynomial f(x) is divided by a linear divisor of the form (x - c), the remainder of this division is simply f(c). You can use this theorem in solving the large expressions.

Midpoint Theorem

The midpoint theorem states that the line segment drawn from the midpoint of any side to the midpoint of any other side of a triangle is parallel to the third side and is half of the length of the third side of the triangle.

Angle Bisector Theorem

This theorem says that the angle bisector of an angle in a triangle divides the opposite side into two segments which are proportional to the lengths of the other two sides. This theorem is beneficial when working with triangles and helps in finding unknown lengths.

Bayes' Theorem

The Bayes’ theorem says that the probability of an event A given that event B has occurred can be calculated on the basis of this formula:
 P(A|B) = [P(B|A) * P(A)] / P(B).

Ceva's Theorem

Ceva's Theorem deals with the concurrency of lines drawn from the vertices of a triangle to the opposite sides. It states that for points D, E, and F on sides BC, CA, and AB of triangle ABC, the lines AD, BE, and CF are concurrent if and only if:
 (AB/AC) * (CD/AE) * (EF/BD) = 1.
 This theorem is helpful in advanced geometry problems involving triangles.

Inscribed Angle Theorem

The Inscribed Angle Theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc. This theorem is essential for solving problems related to circles.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic says that every integer which is greater than 1 can be expressed uniquely as a product of prime numbers, irrespective of the order of the factors.

Conclusion

Students are advised to understand all the above-described theorems. They are an important component of Mathematics in the NCERT class 10 syllabus. We recommend that you explore these theorems, practise their applications, and watch your confidence in Math grow.

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