Maharashtra Board Practice Worksheet
Class 10 Maths 2 Chapter 2
Pythagoras Theorem Worksheet
Strengthen your preparation with the Maharashtra Board Class 10
Maths 2 Chapter 2 Pythagoras Theorem Worksheet. Practise MCQs,
missing-side calculations, Pythagorean triplets, theorem
applications and board-exam-style questions.
Worksheet objective: Learn to recognise right-angled
triangles, select the hypotenuse correctly and apply the Pythagoras
theorem or its converse with complete step-by-step working.
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.
∟
Right-Angled Triangles
Identify the right angle and the side opposite it before
selecting and applying the appropriate formula.
c²
Missing Side Lengths
Calculate an unknown side using squares, subtraction and
positive square roots.
✓
Converse Theorem
Compare the square of the longest side with the sum of the
squares of the other two sides.
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.
In right-angled △ABC, if ∠B = 90°, then AC² = AB² + BC²
Hypotenuse² = Perpendicular² + Base²
If c² = a² + b², the angle opposite side c is a right angle
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The hypotenuse is always opposite the right angle.
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The hypotenuse is the longest side of a right-angled triangle.
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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
Multiple-Choice Questions
The MCQ section checks important concepts such as identifying
the hypotenuse, selecting the correct theorem statement,
recognising Pythagorean triplets and choosing the correct
calculation.
Find the Unknown Side
Students use the Pythagoras theorem to calculate the hypotenuse
or one of the shorter sides. They must substitute the values
correctly, simplify the squares and take the positive square
root.
Converse of Pythagoras Theorem
These questions require students to determine whether three
given side lengths form a right-angled triangle. Students first
identify the longest side and then compare both sides of the
required relationship.
Pythagorean Triplets
Students identify familiar Pythagorean triplets and verify
whether the given numbers satisfy a² + b² = c². This improves
calculation speed during examinations.
Application Problems
Questions involving ladders, poles, diagonals, rectangular
fields and shortest distances connect the theorem with
practical measurements.
Board-Exam Practice
Mixed board-exam-style questions develop theorem selection,
logical presentation, accurate calculation and the correct
geometrical conclusion.
How to Solve the Pythagoras Theorem Worksheet
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Draw or study the triangle and mark the right angle.
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Identify the hypotenuse as the side opposite the right angle.
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Write the Pythagoras theorem before substituting the values.
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Substitute all measurements using the same unit.
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Calculate every square correctly and show one step per line.
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Transpose carefully when calculating one of the shorter sides.
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Take the positive square root of the final squared value.
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Write the final answer with the correct unit and conclusion.
Benefits of Practising This Worksheet
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Revises the complete Pythagoras Theorem chapter in a structured
format.
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Improves understanding of the hypotenuse and right-angle
position.
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Provides practice in calculating unknown side lengths.
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Strengthens the application of the converse theorem.
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Develops confidence in solving practical word problems.
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Improves the presentation of complete mathematical working.
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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.
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Do not write a negative value as the length of a side.
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Do not omit the unit from the final answer.
-
Check every square and square-root calculation before writing
the conclusion.
Check Your Work with Chapter 2 Solutions
Attempt every worksheet question independently and show complete
working. After completing the worksheet, compare your method,
mathematical steps and final answers with the complete Chapter 2
Pythagoras Theorem solutions.
View Chapter 2 Solutions →
Frequently Asked Questions
Select any question to view its answer.
What does the Chapter 2 worksheet cover?
It covers the Pythagoras theorem, its converse,
Pythagorean triplets, missing-side calculations and
practical applications.
How do I identify the hypotenuse?
The hypotenuse is the side opposite the right angle. It is
also the longest side of a right-angled triangle.
What is the Pythagoras theorem formula?
If c is the hypotenuse and a and b are the other two sides,
then c² = a² + b².
What is the converse of the Pythagoras theorem?
If the square of the longest side equals the sum of the
squares of the other two sides, the triangle is
right-angled.
What is a Pythagorean triplet?
A Pythagorean triplet is a set of three positive integers
that satisfies a² + b² = c², such as 3, 4 and 5.
Does this worksheet contain MCQs?
Yes. It includes concept-based MCQs followed by numerical,
theorem-based and application questions.
Is this worksheet useful for Maharashtra SSC preparation?
Yes. It supports school tests, unit tests, prelims and
Maharashtra SSC Board examination revision.
How should I write a Pythagoras theorem solution?
Write the theorem first, substitute the measurements, show
one calculation per line, take the positive square root and
write the final answer with its unit.
When should I check the Chapter 2 solutions?
Check the solutions only after attempting each problem and
showing complete working independently.
How many times should I practise this worksheet?
Complete it once for practice and solve the incorrect or
difficult questions again during examination revision.
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