Maharashtra Board Practice Worksheet
Class 10 Maths 2 Chapter 1
Similarity Worksheet
Strengthen your preparation with the Maharashtra Board Class 10
Maths 2 Chapter 1 Similarity Worksheet. Practise multiple-choice
questions, theorem-based questions, numerical problems, proofs
and board-exam-style applications with sufficient space for
complete working.
Worksheet objective: Revise the complete Similarity
chapter, identify areas that require improvement and practise writing
clear step-by-step geometry answers before the Maharashtra SSC Board
examination.
Class 10 Maths 2 Chapter 1 Similarity Worksheet
This Class 10 Similarity worksheet is designed for Maharashtra
State Board students who want structured practice beyond reading
textbook solutions. It includes questions based on similar
triangles, the Basic Proportionality Theorem, corresponding sides,
proportional segments, areas of similar triangles and applications
of similarity.
The worksheet begins with concept-based multiple-choice questions
and gradually moves towards calculations, theorem applications and
proof-based questions. This progression helps students check their
fundamental understanding before attempting longer board-exam
problems.
Concepts Covered in the Similarity Worksheet
△
Similar Triangles
Identify corresponding angles and sides, write similarity
statements in the correct order and use proportional sides
to calculate unknown lengths.
∥
Proportionality Theorems
Apply the Basic Proportionality Theorem, its converse and
the angle-bisector theorem to solve geometrical problems.
A
Areas of Similar Triangles
Use the relationship between corresponding sides and areas
of similar triangles to solve numerical and proof-based
questions.
Important Similarity Rules for This Worksheet
Two triangles are similar when their corresponding angles are
equal and their corresponding sides are proportional. The
triangles have the same shape, but they are not required to have
the same size.
If △ABC ∼ △PQR, then AB/PQ = BC/QR = AC/PR
Area of △ABC ÷ Area of △PQR = (AB ÷ PQ)²
If DE ∥ BC, then AD/DB = AE/EC
-
In the AAA similarity test, corresponding angles of the two
triangles are equal.
-
In the SAS similarity test, one corresponding angle is equal
and the including sides are proportional.
-
In the SSS similarity test, all three pairs of corresponding
sides are proportional.
-
The ratio of the areas of two similar triangles equals the
square of the ratio of their corresponding sides.
-
A line parallel to one side of a triangle divides the other
two sides proportionally.
Types of Questions Included
Multiple-Choice Questions
The MCQ section checks important definitions, similarity
criteria, corresponding sides, proportional ratios and theorem
applications. Students should solve each question before
checking the available options.
Find the Unknown Length
These questions require students to identify similar triangles,
write the correct proportion and calculate an unknown side or
segment. The correspondence between the vertices must be
maintained throughout the solution.
Theorem-Based Questions
Students practise the Basic Proportionality Theorem, its
converse and related results. Proofs should contain the given
information, construction when required, theorem statement,
logical steps and final conclusion.
Area and Ratio Questions
These questions connect the ratio of corresponding sides with
the ratio of areas. Students must remember that the area ratio
involves the square of the corresponding-side ratio.
Board-Exam-Style Problems
The final section includes mixed questions that require
students to select the appropriate similarity test or theorem.
These questions support Maharashtra SSC examination revision
and help students practise complete step-by-step presentation.
How to Solve the Similarity Worksheet
-
Read the complete question and mark all the given measurements
on the diagram.
-
Identify the two triangles that may be similar.
-
Write the equal corresponding angles or proportional sides.
-
State the correct AAA, SAS or SSS similarity test.
-
Write the similarity statement in the correct order.
-
Form a proportion using only corresponding sides.
-
Solve the resulting equation one mathematical step per line.
-
Write the final answer with its correct unit and geometrical
reason.
Benefits of Practising This Worksheet
-
Revises all important Similarity concepts in one structured
practice activity.
-
Improves understanding of corresponding sides and angles.
-
Develops confidence in theorem-based and proof-based questions.
-
Provides practice in writing complete mathematical steps.
-
Helps identify common calculation and diagram-reading mistakes.
-
Supports school tests, unit tests, prelims and SSC Board
examination preparation.
-
Encourages students to solve independently before checking the
answer key or chapter solutions.
Common Mistakes Students Should Avoid
-
Do not write the vertices of similar triangles in the wrong
corresponding order.
-
Do not compare a side from one triangle with a
non-corresponding side from the other triangle.
-
Do not use a similarity test without writing the required
equal angles or proportional sides.
-
Do not forget to square the side ratio when calculating the
ratio of areas.
-
Use the Basic Proportionality Theorem only when the required
line is parallel to one side of the triangle.
-
Do not write only the final answer in a theorem-based question.
Practise Before Checking the Solutions
Attempt every question independently and show complete working.
After completing the worksheet, compare your method with the
Chapter 1 Similarity solutions. Correct every mistake and attempt
the difficult questions again without looking at the answer. This
process is more effective than simply reading the solution.
Frequently Asked Questions
Select any question to view its answer.
What topics are covered in the Class 10 Similarity worksheet?
The worksheet covers similar triangles, similarity tests,
the Basic Proportionality Theorem, its converse,
corresponding sides, area ratios and board-exam-style
applications.
What are the three tests of similarity?
The three commonly used tests are AAA similarity, SAS
similarity and SSS similarity.
What is the Basic Proportionality Theorem?
If a line is drawn parallel to one side of a triangle and
intersects the other two sides, it divides those two sides
in the same ratio.
How do I identify corresponding sides of similar triangles?
First match the equal angles. The sides opposite equal
angles are corresponding sides. The order of vertices in
the similarity statement also shows the correspondence.
Are similar triangles always congruent?
No. Similar triangles have the same shape, but they may
have different sizes. Congruent triangles have the same
shape and the same size.
What is the relationship between the areas of similar triangles?
The ratio of the areas of two similar triangles is equal to
the square of the ratio of their corresponding sides.
Why is the order of vertices important in similarity?
The order indicates which angles and sides correspond.
Incorrect vertex order leads to incorrect proportions and
wrong answers.
Does this worksheet contain MCQs and numerical questions?
Yes. It includes concept-based multiple-choice questions,
numerical problems, theorem applications, proofs and mixed
board-exam-style questions.
Is this worksheet useful for Maharashtra SSC Board preparation?
Yes. It revises important Maharashtra Board Similarity
concepts and provides practice in the step-by-step format
required for school and SSC examinations.
Should I check the solutions while completing the worksheet?
Attempt the worksheet independently first. Check the
solutions only after completing a question or after making
a genuine attempt.
How many times should I practise the Similarity worksheet?
Complete it once for practice and attempt the incorrect or
difficult questions again during revision. Repeated
practice improves theorem selection and calculation speed.
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