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Revision Notes

Pythagoras Theorem

Maharashtra Board · Class 10 · Mathematics

Quick revision notes for Pythagoras Theorem — Maharashtra Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

43 questions28 flashcards5 concepts

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Key Topics to Revise

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1. Core statement and notation

  • In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides.
  • For triangle PQR with angle PQR = 90 degrees, PR is the hypotenuse.
  • Using side letters p, q, r, Pythagoras theorem can also be written as q^2 = p^2 + r^2.
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2. Pythagorean triplets

  • In a triplet of natural numbers, if the square of the largest number is equal to the sum of the squares of the remaining two numbers, then the triplet is called a Pythagorean triplet.
  • The numbers in a Pythagorean triplet can be written in any order.
  • The triplets (11,60,61), (3,4,5), (5,12,13), (8,15,17), and (24,25,7) are Pythagorean triplets.
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3. Special right angled triangles

  • A 30 degrees - 60 degrees - 90 degrees triangle has fixed side ratios.
  • If acute angles of a right angled triangle are 30 degrees and 60 degrees, then the side opposite 30 degrees is half of the hypotenuse and the side opposite 60 degrees is (sqrt(3))/2 times the hypotenu
  • In triangle LMN with angle L = 30 degrees, angle N = 60 degrees, and angle M = 90 degrees, MN = (1/2) x LN and LM = (sqrt(3)/2) x LN.
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4. Similarity, geometric mean, and the main proof

  • If the altitude is drawn from the right angle vertex to the hypotenuse, the two triangles formed are similar to the original triangle and to each other.
  • In triangle ABC, if BD is drawn perpendicular to AC with A-D-C, then triangle ADB is similar to triangle ABC by the AA test.
  • In triangle BDC and triangle ABC, the triangles are similar by the AA test.

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Full Notes

Key Concepts

In a right angled triangleA triplet of natural numbersIf a and b are naturalIf the acute angles are 30°If the acute angles are 45°

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.

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