Class 10 Pythagoras Theorem Worksheet Maharashtra Board

Class 10 Pythagoras Theorem Worksheet

This Class 10 Pythagoras Theorem worksheet is designed for Maharashtra State Board students who need structured practice after learning Chapter 2. It begins with concept-based multiple-choice questions and progresses to numerical problems, geometrical applications and board-exam-style questions.

Students practise identifying the perpendicular side, base and hypotenuse; finding unknown lengths; checking whether a triangle is right-angled; and using Pythagorean triplets. Each longer question should be solved one mathematical step per line so that the method is clear and easy to verify.

Important Pythagoras Theorem Rules

The Pythagoras theorem applies only to a right-angled triangle. The hypotenuse is the side opposite the right angle and is always the longest side of the triangle.

• The hypotenuse is always opposite the right angle.
• The hypotenuse is the longest side of a right-angled triangle.
• Use the positive square root because the length of a side cannot be negative.
• For the converse theorem, identify and square the longest side separately.
• Compare the square of the longest side with the sum of the squares of the other two sides.
• Common Pythagorean triplets include 3, 4, 5; 5, 12, 13; 7, 24, 25; and 8, 15, 17.

Questions Included in the Worksheet

How to Solve the Pythagoras Theorem Worksheet

1. Draw or study the triangle and mark the right angle.
2. Identify the hypotenuse as the side opposite the right angle.
3. Write the Pythagoras theorem before substituting the values.
4. Substitute all measurements using the same unit.
5. Calculate every square correctly and show one step per line.
6. Transpose carefully when calculating one of the shorter sides.
7. Take the positive square root of the final squared value.
8. Write the final answer with the correct unit and conclusion.

Benefits of Practising This Worksheet

• Revises the complete Pythagoras Theorem chapter in a structured format.
• Improves understanding of the hypotenuse and right-angle position.
• Provides practice in calculating unknown side lengths.
• Strengthens the application of the converse theorem.
• Develops confidence in solving practical word problems.
• Improves the presentation of complete mathematical working.
• Supports school tests, prelims and Maharashtra SSC Board examination preparation.

Common Mistakes Students Should Avoid

• Do not select the longest-looking side without checking the position of the right angle.
• Do not write c = a² + b². The correct relation is c² = a² + b².
• Do not add all three squared sides when calculating a shorter side.
• Do not apply the converse theorem without first identifying the longest side.
• Do not take the square root before completing the calculation involving squares.
• Do not write a negative value as the length of a side.
• Do not omit the unit from the final answer.
• Check every square and square-root calculation before writing the conclusion.

Frequently Asked Questions

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