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Chapter Summary

Pythagoras Theorem

Maharashtra Board · Class 10 · Mathematics

Summary of Pythagoras Theorem for Maharashtra Board Class 10 Mathematics. Key concepts, important points, and chapter overview.

43 questions28 flashcards5 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?
Pythagoras Theorem covers several key topics that are frequently asked in Maharashtra Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Pythagoras Theorem — Maharashtra Board Class 10 Mathematics?
Understand the core concepts first, then work through the 43 practice questions available for this chapter. Revise formulas and 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 13 chapters — Maharashtra Board Class 10 Mathematics Chapter Summary

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