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Pythagoras Theorem — Chapter Summary

Maharashtra Board · Class 10 · Mathematics

Summary of Pythagoras Theorem for Maharashtra Board Class 10 Mathematics. Part of the Maharashtra Board Class 10 Mathematics syllabus.

43 questions28 flashcards17 formulas & key relations5 concepts

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Overview

Count the square on the hypotenuse and compare it with the squares on the other two sides. In a right angled triangle, that check gives the central idea of Pythagoras theorem: the square of the hypotenuse equals the sum of the squares of the remaining two sides.

Key Concepts

In a right angled triangle

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. For triangle PQR with angle PQR =

A triplet of natural numbers

A triplet of natural numbers is a Pythagorean triplet if the square of the largest number equals the sum of the squares of the other two numbers. Exam

If a and b are natural

If a and b are natural numbers with a > b, then [(a^2 + b^2), (a^2 - b^2), (2ab)] is a Pythagorean triplet. For a = 5 and b = 3, the triplet is (34,16

If the acute angles are 30°

If the acute angles are 30° and 60°, then the side opposite 30° is half the hypotenuse and the side opposite 60° is (√3/2) times the hypotenuse. In tr

If the acute angles are 45°

If the acute angles are 45° and 45°, then each perpendicular side is (1/√2) times the hypotenuse. In triangle XYZ, XY = XZ = (1/√2) × ZY. If ZY = 3√2

Learning Objectives

  • State Pythagoras theorem in a right angled triangle.
  • Use the theorem in the forms PR^2 = PQ^2 + QR^2 and q^2 = p^2 + r^2.
  • Identify and verify Pythagorean triplets.
  • Use the formula [(a^2 + b^2), (a^2 - b^2), (2ab)] for Pythagorean triplets when a > b.
  • Apply side ratios of 30-60-90 and 45-45-90 triangles.

Frequently Asked Questions

What are the important topics in Pythagoras Theorem for Maharashtra Board Class 10 Mathematics?
Key topics in Pythagoras Theorem include Core statement and notation, Pythagorean triplets, Special right angled triangles, Similarity, geometric mean, and the main proof. Study these first, then practise questions on each for the Maharashtra Board Class 10 board exam.
How should I revise Pythagoras Theorem for the Maharashtra Board Class 10 board exam?
Learn the core ideas first, then work through the 43 practice questions on Pythagoras Theorem. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Pythagoras Theorem

All Maharashtra Board Class 10 Mathematics Chapter Summary

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