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Important Questions: CBSE Class 10 Mathematics Chapter 6 Triangles

Triangles is the most scoring chapter in CBSE Class 10 Mathematics geometry, yet students often stumble on similarity criteria and proportionality statements under exam pressure. This page presents 18 board-pattern questions grouped by marks — 1-mark MCQs, 2-mark VSAs, 3-mark applications, and 5-mark case-based — each with model answers drawn from CBSE marking schemes (2023-2025). Whether you are revising Basic Proportionality Theorem or preparing for areas of similar triangles, these questions mirror actual board paper difficulty and phrasing.

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Key takeaways

✓Chapter 6 Triangles accounts for 12-14 marks in the CBSE Class 10 Mathematics board paper, making it one of the highest-weightage geometry chapters.
✓Basic Proportionality Theorem (BPT) and its converse appear in 70 percent of CBSE question papers, often as 2-mark or 3-mark proofs.
✓Criteria for similarity (AAA, SAS, SSS) form the backbone of 3-mark and 5-mark numerical problems involving triangles and construction.
✓The relationship between areas of similar triangles (ratio equals square of corresponding sides) is tested in 90 percent of case-based questions since 2022.
✓Common mistakes include confusing similarity with congruence, incorrect application of Pythagoras theorem in non-right triangles, and wrong side-pairing in similarity proofs.
✓Practising 15-18 questions across all mark categories — 1-mark MCQs, 2-mark VSAs, 3-mark proofs, and 5-mark case studies — builds board-exam readiness within two weeks.
✓CBSETUTOR.ai offers unlimited doubt-solving for Triangles by uploading a photo of your NCERT exercise or sample paper at a flat ₹999/month for Classes 6-12, with a 3-day free trial.

Chapter overview and marks weightage in CBSE Class 10 board exam

Chapter 6 Triangles sits in Unit II: Geometry, which collectively carries 15 marks in the CBSE Class 10 Mathematics board paper. Triangles alone contributes 12-14 marks through three question types: a 1-mark MCQ or assertion-reason, one or two 2-mark VSAs on theorem statements or direct applications, a 3-mark numerical or proof (often BPT or similarity criteria), and a 5-mark case-based or integrated problem linking Pythagoras theorem with areas of similar triangles. The 2024 and 2025 board papers included a case study on architectural trusses requiring ratio calculations using SSS similarity, demonstrating CBSE's shift toward application-based assessment. Mastering this chapter efficiently unlocks nearly 10 percent of your total theory paper score.

Unit II (Geometry) = 15 marks; Triangles = 12-14 marks, the highest single-chapter weight in geometry.
Typical distribution: 1 MCQ (1 mark), 1-2 VSAs (2 marks each), 1 short answer (3 marks), 1 case-based (4-5 marks).
Questions span four core topics: similar triangles, Basic Proportionality Theorem (BPT), criteria for similarity (AAA, SAS, SSS), and areas of similar triangles.
2023 board paper included a 5-mark problem on a ladder, wall and ground forming a right triangle; 2024 had a truss case study; 2025 sample papers feature shadow-based similar triangles.
NCERT exercises 6.2 (BPT), 6.3 (criteria for similarity) and 6.4 (Pythagoras + areas) supply 80 percent of board-question stems.

1-mark questions: MCQ and assertion-reason

One-mark questions test quick recall of definitions, theorem names, and direct formula substitution. Recent CBSE papers (2023-2025) favour assertion-reason pairs where Statement A and Reason R must both be evaluated and their linkage assessed. Topics include identifying similarity criteria from given data, recognising BPT application, or choosing the correct ratio of areas. These questions reward clarity and speed; guessing without eliminating wrong options costs marks under negative marking (if applied). Below are four representative 1-mark MCQs with answers.

2-mark questions: VSA and direct applications

Two-mark questions demand a theorem statement plus one-step application, or a direct numerical with brief working. CBSE marking schemes award 1 mark for the correct theorem citation and 1 mark for accurate substitution. Omitting the theorem name costs half marks even if the calculation is correct. Common 2-mark topics include finding an unknown side using BPT, verifying similarity by checking side ratios, or computing perimeter ratios of similar triangles. Always write the theorem name explicitly and show unit consistency. Below are three exam-style 2-mark questions with model answers.

3-mark questions: proofs and numerical reasoning

Three-mark questions are the heart of Triangles: they test your ability to prove similarity using criteria (AAA, SAS, SSS), apply BPT in multi-step problems, or combine Pythagoras theorem with similarity. CBSE marking schemes split marks as: 1 mark for identifying the correct criterion or theorem, 1 mark for logical steps, 1 mark for final answer with units. Always draw and label a diagram neatly; examiners award method marks even if arithmetic slips occur. Below are four representative 3-mark questions with step-by-step model answers.

5-mark questions: case-based and integrated problems

Five-mark questions integrate multiple concepts — similarity criteria, BPT, Pythagoras theorem, area ratios — within a real-world scenario such as map scales, architectural plans, or shadows. CBSE introduced case-based questions in 2020; by 2024 they accounted for one compulsory 5-mark problem in every board paper. A typical case presents a 50-70 word context, a diagram, and four sub-questions (1+1+2+1 or 1+1+1+2 marks). Success depends on reading carefully, labelling the diagram, and answering each sub-question in sequence. Below are three full 5-mark case-based questions with detailed model answers.

How CBSE frames questions from Chapter 6 Triangles

CBSE question-paper setters draw heavily from NCERT exercises 6.2, 6.3 and 6.4, rephrasing numbers and contexts but preserving theorem structure. Between 2020 and 2025, four patterns emerged: (1) direct BPT application with one unknown (2-mark or 3-mark); (2) proving similarity using AA, SAS or SSS, often embedded in a construction or coordinate-geometry diagram (3-mark); (3) area-ratio problems where students must square the side ratio (3-mark or part of 5-mark); (4) case-based scenarios linking similar triangles to real objects — shadows, ladders, maps, architectural plans (5-mark). Recent papers avoid pure recall; every question requires at least one reasoning step. Assertion-reason MCQs test conceptual links, such as 'Is the converse of BPT applicable here?' Understanding these patterns lets you practise strategically rather than memorising hundreds of problems.

70 percent of 2-mark and 3-mark questions are lifted or adapted from NCERT exercises 6.2 (BPT), 6.3 (similarity criteria) and 6.4 (areas and Pythagoras).
Case-based 5-mark questions always provide a diagram; read the context first, label all given data on the figure, then tackle sub-questions in order.
Proof-type questions (3-mark) award 1 mark for diagram, 1 mark for theorem statement, 1 mark for logical steps; omitting the diagram or theorem name costs marks.
MCQs on similarity often use 'which of the following is not a valid similarity criterion' to test AAA vs. SSA confusion.
Pythagorean triplet recognition (e.g. 3-4-5, 5-12-13, 7-24-25) speeds up verification questions; memorise common triplets.
Integration with coordinate geometry: a 5-mark problem may give vertices, ask you to compute side lengths (distance formula), then verify similarity (SSS).

Common mistakes students make in Triangles chapter

Markers report recurring errors in Triangles answers: confusing similarity with congruence (writing ≅ instead of ~), applying Pythagoras theorem in acute or obtuse triangles, mis-pairing corresponding sides when checking similarity, omitting theorem names in proofs, and squaring the side ratio instead of taking the square root when finding area ratio. Another frequent slip is writing DE/AB = DF/BC when the correct correspondence is DE/AB = EF/BC; always draw both triangles with matching vertex order. In case-based questions, students skip sub-question (i) and jump to (iii), losing easy marks. Unit errors — mixing metres and centimetres within one calculation — also cost marks. Fixing these mistakes through repeated practice of past-year papers raises scores by 3-4 marks on average.

**Similarity ≠ Congruence:** Writing 'triangle ABC ≅ triangle DEF' when only angles match; use '~' for similarity and '≅' only when all sides and angles are equal.
**Wrong side pairing:** In SSS similarity, always list sides in corresponding order (smallest to smallest, etc.); random pairing fails the test.
**Pythagorean misuse:** Applying a² + b² = c² in a triangle that is not right-angled; always verify the 90° angle first.
**Forgetting to square or root:** If ratio of sides is 3:4, ratio of areas is 9:16, not 3:4; conversely if area ratio is 25:36, side ratio is 5:6.
**No theorem citation:** Writing 'by BPT' without the full statement costs 1 mark in 2-mark and 3-mark proofs.
**Unit inconsistency:** Mixing cm and m in the same equation; convert all lengths to one unit before substitution.
**Skipping sub-questions:** In a 1+1+2+1 case study, answering only the 2-mark part; each sub-question is independent and carries separate marks.

Strategic revision plan for Triangles using these questions

A focused two-week revision cycle ensures mastery. Week 1: solve all NCERT exercises 6.2, 6.3, 6.4 and match each with the corresponding important question from this page; re-write theorem statements in your own words and draw diagrams without looking at the book. Week 2: attempt these 18 questions under timed conditions (1 mark = 1 minute, 5 marks = 5-6 minutes), check model answers, list mistakes in a notebook, and redo errors the next day. Dedicate day 13 to case-based questions only, since their 5-mark weightage is disproportionate. Day 14: take a full 15-mark geometry mock (combining Triangles + Chapter 7) using CBSE sample papers. Supplement with CBSETUTOR.ai's photo-upload doubt solver for steps you cannot self-correct; the AI tutor explains theorem application in under 30 seconds, saving hours of forum searching. This structured loop converts Chapter 6 from a fear zone into a scoring stronghold.

**Days 1-3:** NCERT Ex 6.2 + Q5, Q6, Q7 (BPT and converse) — write full solutions, not just final answers.
**Days 4-6:** NCERT Ex 6.3 + Q1, Q2, Q8, Q10 (similarity criteria AAA, SAS, SSS) — practise diagram labelling.
**Days 7-9:** NCERT Ex 6.4 + Q3, Q9, Q11 (Pythagoras + area ratios) — memorise triplets 3-4-5, 5-12-13, 8-15-17.
**Days 10-12:** Case studies Q12, Q13, Q14 + CBSE sample paper case-based questions — time yourself strictly.
**Day 13:** Error notebook — redo every mistake from days 1-12; clarify doubts via CBSETUTOR.ai photo upload.
**Day 14:** Full 15-mark geometry mock (Triangles + Circles) — simulate exam pressure, then review marking scheme.

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Triangles rewards precision — one skipped theorem name or wrong side ratio costs marks. CBSETUTOR.ai's 24×7 AI tutor delivers instant, step-by-step solutions when you upload a photo of any NCERT exercise, sample paper, or past-year question. Stuck on proving triangle ABD ~ triangle CAB? Snap the problem; the AI identifies the similarity criterion, draws the labelled diagram, and explains each angle match in simple language. Unlike generic video lectures that you must watch start-to-finish, CBSETUTOR.ai answers your specific doubt in under 60 seconds. At ₹999 per month for all subjects across Classes 6-12 — one flat price, no hidden fees — it costs less than two hours with a local tutor yet is available every evening and weekend. Start your 3-day free trial today, upload your toughest Triangles proof, and experience how personalised AI tutoring transforms geometry from guesswork into confidence.

Photo-upload doubt solving: snap any Triangles question (NCERT, sample paper, PYQ) and receive a worked solution with diagram in under 60 seconds.
Step-by-step explanations: the AI tutor breaks every similarity proof into theorem statement → angle identification → criterion application → conclusion, mirroring CBSE marking schemes.
24×7 availability: practise late at night or early morning; no appointment needed, no waiting for tutor callbacks.
All subjects, all classes: ₹999/month covers Mathematics, Science, Social Science, English for Classes 6-12 — one subscription for your entire schooling.
3-day free trial: test the platform with five Triangles questions before committing; no credit card required for trial activation.
Performance insights: track which similarity criteria you solve fastest and which theorem statements you forget, so you revise strategically.

Quick reference: theorem names you must cite in answers

CBSE marking schemes explicitly allocate marks for naming the theorem before applying it. Omitting or misnaming a theorem — writing 'thales theorem' instead of 'Basic Proportionality Theorem', or 'congruence rule' instead of 'similarity criterion' — results in zero method marks even if your arithmetic is perfect. Below is a ready-reference list of exact theorem names and their symbolic short forms acceptable to CBSE evaluators. Copy these into your formula sheet and memorise the wording; in 3-mark proofs, writing the theorem name and statement together earns the first mark automatically.

**Basic Proportionality Theorem (BPT / Thales theorem):** If a line parallel to one side of a triangle intersects the other two sides, then it divides them in the same ratio. Symbol: DE || BC ⇒ AD/DB = AE/EC.
**Converse of BPT:** If a line divides two sides of a triangle in the same ratio, then it is parallel to the third side. Symbol: AD/DB = AE/EC ⇒ DE || BC.
**AAA (Angle-Angle-Angle) similarity criterion:** Two triangles are similar if their corresponding angles are equal.
**AA (Angle-Angle) similarity criterion:** Two triangles are similar if two pairs of corresponding angles are equal (third angle is automatically equal).
**SSS (Side-Side-Side) similarity criterion:** Two triangles are similar if their corresponding sides are proportional.
**SAS (Side-Angle-Side) similarity criterion:** Two triangles are similar if one angle is equal and the sides including that angle are proportional.
**Pythagoras theorem:** In a right triangle, (perpendicular)² + (base)² = (hypotenuse)².
**Theorem on areas of similar triangles:** The ratio of areas of two similar triangles equals the square of the ratio of their corresponding sides. Symbol: Area(ABC)/Area(DEF) = (AB/DE)².

Frequently asked questions

How many marks does Chapter 6 Triangles carry in the CBSE Class 10 board exam?+

Triangles contributes 12-14 marks out of 80 in the theory paper, making it the highest-weightage geometry chapter. Expect one 1-mark MCQ, one or two 2-mark questions, one 3-mark proof or numerical, and one 5-mark case-based problem combining similarity, BPT and area ratios.

Which is more important for boards: Basic Proportionality Theorem or similarity criteria?+

Both are equally critical. BPT appears in 70 percent of papers as 2-mark or 3-mark direct applications, while similarity criteria (AAA, SAS, SSS) form the backbone of 3-mark proofs and 5-mark case studies. Practise NCERT Ex 6.2 for BPT and Ex 6.3 for criteria; together they cover 90 percent of board questions.

How do I remember which similarity criterion to apply in a proof?+

Check what is given: if all three side ratios are provided or can be computed, use SSS; if one angle and two including sides are known, use SAS; if two or three angles are stated or derived (for example, common angle + right angle), use AA or AAA. Draw a small table of criteria in your rough work to decide quickly.

What is the most common mistake in area-ratio questions?+

Forgetting to square the side ratio. If the ratio of corresponding sides is 3:4, the ratio of areas is 9:16, not 3:4. Conversely, if area ratio is given as 25:49, take the square root to find side ratio 5:7. Write the formula 'Area ratio = (side ratio)²' at the top of every such answer.

Are Pythagorean triplets tested in the board exam?+

Yes. Questions like Q9 give three sides and ask you to verify if a triangle is right-angled. Recognising triplets (3-4-5, 5-12-13, 7-24-25, 8-15-17) saves calculation time. If sides are multiples of a triplet (for example, 6-8-10), divide by the GCD (2) to identify the base triplet.

How should I tackle a 5-mark case-based question on Triangles?+

Read the context paragraph once, underline numerical data, and label everything on the given diagram. Answer sub-questions in order; each carries separate marks. Show all steps — theorem names, ratios, unit conversions. Even if you cannot solve part (iii), attempt parts (i), (ii) and (iv) to collect 3 out of 5 marks.

Can I use 'Thales theorem' instead of 'Basic Proportionality Theorem' in my answer?+

Yes, both names are acceptable to CBSE. However, most NCERT textbooks and recent marking schemes use 'Basic Proportionality Theorem' or 'BPT'. If you write 'Thales theorem', add '(Basic Proportionality Theorem)' in brackets the first time to avoid confusion.

How many questions should I practise to be board-ready in Triangles?+

Solve all NCERT exercises 6.2, 6.3, 6.4 (about 35 questions), the 18 important questions on this page, and past three years' board papers (roughly 12 Triangles questions). That totals around 65 problems. Quality matters more than quantity; redo every mistake until you score full marks on retry.

What is the difference between similarity and congruence?+

Congruent triangles have identical shape and size (all sides and angles equal); notation ≅. Similar triangles have identical shape but different size (corresponding angles equal, sides proportional); notation ~. Congruence is a special case of similarity where the proportionality constant is 1. Never use ≅ when triangles have different side lengths.

Does CBSETUTOR.ai cover all Triangles theorem proofs and numericals?+

Yes. Upload any NCERT exercise, sample paper or past-year Triangles question via photo, and the AI tutor provides a step-by-step solution with diagrams, theorem citations and marking-scheme alignment. The platform covers every topic in Chapter 6 — BPT, converse of BPT, AAA/SAS/SSS similarity, Pythagoras, and area ratios. Start your 3-day free trial at ₹999/month for Classes 6-12 all subjects.

Related resources

CBSE Class 10 Mathematics Chapter 6 Triangles Worksheet with Answers Class 10 Mathematics Chapter 6 Triangles — Formulas & Key Points CBSE Class 10 Mathematics Chapter 5 Arithmetic Progressions Worksheet with Answers Important Questions: CBSE Class 10 Mathematics Chapter 5 Arithmetic Progressions AI Tutor for Class 10: The Smart Alternative to Tuition AI Tutor for Class 10 Maths: Learn Faster with Instant Help Class 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting Points Important Questions: CBSE Class 9 Mathematics Chapter 2 Polynomials

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