Chapter 7 · Class 9 CBSE · Free Worksheet PDF

Triangle Sums for Class 9 — Free CBSE Worksheet PDF with Answers

Download a free printable triangles worksheet for Class 9 CBSE with 30 practice questions covering types of triangles, properties, congruence, similarity, Pythagoras theorem, and area of triangles. Includes complete answer key. CBSE-aligned for the 2025-26 syllabus.

Last updated: 5 May 2026

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30 questions (Easy + Medium + Hard) with answer key. Fresh set generated daily.

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Sample Triangles Sums for Class 9 — Practice Questions

Here are 8 sample triangles sums from this Class 9 CBSE worksheet. Download the full PDF for all 30 questions with answers.

Q1.Which of the following statements correctly defines congruent figures?
A.A) Figures that have the same shape but different sizes.
B.B) Figures that have the same size but different shapes.
C.C) Figures that have exactly the same shape and the same size.
D.D) Figures that are reflections of each other.

Difficulty: Easy

Q2.If ΔPQR ≅ ΔXYZ, which of the following statements is NOT necessarily true?
A.A) PQ = XY
B.B) QR = YZ
C.C) ∠P = ∠X
D.D) PR = YZ

Difficulty: Easy

Q3.To prove ΔABC ≅ ΔDEF using the SSS (Side-Side-Side) congruence criterion, if we are given AB = DE and BC = EF, what additional information is required?
A.A) ∠B = ∠E
B.B) AC = DF
C.C) ∠C = ∠F
D.D) AB = EF

Difficulty: Easy

Q4.Rohan is trying to prove that ΔPQR ≅ ΔSTU using the SAS (Side-Angle-Side) congruence criterion. He states that PQ = ST, PR = SU, and ∠Q = ∠T. What is the mistake in Rohan's reasoning?
A.A) He should have used SSS criterion instead.
B.B) The angle must be the included angle between the two sides. ∠Q is not included between PQ and PR.
C.C) The sides chosen (PQ and PR) are incorrect for SAS.
D.D) The triangles cannot be proven congruent with the given information.

Difficulty: Easy

Q5.Consider two triangles, ΔABC and ΔXYZ. If it is given that ∠A = ∠X, AB = XY, and ∠B = ∠Y, which congruence criterion can be used to prove ΔABC ≅ ΔXYZ?
A.A) SSS
B.B) SAS
C.C) ASA
D.D) RHS

Difficulty: Easy

Q6.For two right-angled triangles to be congruent by the RHS (Right angle - Hypotenuse - Side) congruence criterion, which of the following is a mandatory condition?
A.A) All three sides must be equal.
B.B) They must have one pair of corresponding acute angles equal.
C.C) Their hypotenuses must be equal, and one pair of corresponding sides (other than the hypotenuse) must be equal.
D.D) The included angle between two sides must be 90°.

Difficulty: Easy

Q7.In an isosceles triangle ΔABC, if AB = AC and ∠B = 65°, what is the measure of ∠C?
A.A) 50°
B.B) 65°
C.C) 75°
D.D) 130°

Difficulty: Easy

Q8.In ΔDEF, if ∠D = ∠F, which of the following statements must be true?
A.A) DE = DF
B.B) EF = DF
C.C) DE = EF
D.D) ∠E = 90°

Difficulty: Easy

Answer Key — Sample Questions+
Q1:C) Figures that have exactly the same shape and the same size.
Q2:D) PR = YZ
Q3:B) AC = DF
Q4:B) The angle must be the included angle between the two sides. ∠Q is not included between PQ and PR.
Q5:C) ASA
Q6:C) Their hypotenuses must be equal, and one pair of corresponding sides (other than the hypotenuse) must be equal.
Q7:B) 65°
Q8:C) DE = EF

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicTriangles
BoardCBSE
Class9
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download free triangles sums for Class 9?+
You can download a free Triangles PDF worksheet for Class 9 CBSE right here on SparkEd. The worksheet includes 30 practice questions (types of triangles, properties, congruence, similarity, Pythagoras theorem, and area of triangles) at easy, medium, and hard levels with a complete answer key.
How many triangles questions are in this Class 9 worksheet?+
This SparkEd worksheet for Triangles Class 9 contains 30 questions — 10 easy, 10 medium, and 10 hard. The questions cover types of triangles, properties, congruence, similarity, Pythagoras theorem, and area of triangles. A fresh set is generated daily so students never repeat the same sheet.
Does the Triangles worksheet for Class 9 include answers?+
Yes! Every SparkEd worksheet comes with a complete answer key. Students can self-check their work after completing the sheet. The PDF is free to download and print.
Is this triangles worksheet aligned to CBSE syllabus?+
Yes. This worksheet is specifically designed for Class 9 CBSE students and aligned to the 2025-26 CBSE syllabus. All questions follow the CBSE exam pattern and difficulty level.
Can I print this Triangles worksheet?+
Absolutely! The worksheet downloads as an A4-size PDF that is ready to print. It includes the questions, space for working, and a separate answer key — perfect for classroom use or home practice.
How is this worksheet different from NCERT textbook exercises?+
SparkEd worksheets go beyond NCERT exercises by providing 30 questions at 3 progressive difficulty levels. Level 1 (Easy) builds confidence, Level 2 (Medium) tests application, and Level 3 (Hard) prepares for exams. Each worksheet includes word problems and conceptual questions, not just computation.

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