The NCERT Exemplar Class 10 Maths Triangles book is a free, download-ready problem set for Chapter 6, mapped to the 2026-27 NCERT syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide and a study plan, for harder CBSE-style practice on similarity, BPT and area ratios.
- CBSE Weightage: Triangles is part of the Geometry unit, worth 15 marks in the Class 10 board paper.
- Exemplar Problems: 65 unsolved questions across 4 exercises (Exercise 6.1 to Exercise 6.4) plus solved samples.
- Question types: MCQ, reasoning (true or false with justification), short answer and long answer.
This Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE Class 10 Triangles board questions, and aligned to the 2026-27 syllabus. The sections below cover the full book: a question-range map, an Exemplar versus textbook difficulty comparison, and a study plan.
Watch Triangles Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
The bare Exemplar print is a problem book with no reading aids. This download wraps the official NCERT Exemplar Class 10 Maths Triangles PDF with board-ready maps, so practice stays focused.
- Concept Recap Card: A one-screen summary of the Basic Proportionality Theorem (BPT), its converse, and the four similarity criteria: AA, SAS, SSS, and RHS.
- Question-Type Tagging: Every problem is tagged MCQ, reasoning, short answer or long answer, so students drill one type at a time.
- Difficulty Flagging: Each exercise is rated against its textbook match, so weaker students start with 6.1 and 6.2 before the proof-heavy 6.3 and 6.4.
What Is Inside the Exemplar Book
The Exemplar runs as one connected problem set. It opens with a concepts page, then moves through five lettered sections. The table maps each to its question range and concept.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | BPT, converse of BPT, AA / SAS / SSS similarity criteria, area theorem, Pythagoras theorem, converse of Pythagoras |
| (B) Multiple Choice (Exercise 6.1) | Q1 to Q20 | MCQ | Identifying similar triangles, finding missing sides using similarity, BPT ratios, and area ratios |
| (C) Reasoning (Exercise 6.2) | Q1 to Q10 | True or False with justification | Statements on BPT, converse, area theorem, and properties of similar triangles |
| (D) Short Answer (Exercise 6.3) | Q1 to Q25 | Short Answer | Applying BPT and its converse, proving triangles similar, finding missing sides and angles in combined figures |
| (E) Long Answer (Exercise 6.4) | Q1 to Q10 | Long Answer | Multi-step similarity proofs, area-ratio derivations, and BPT converse proofs in complex figures |
Exemplar Question-Type Distribution
The 65 problems split across four types. The short and long answers in Exercise 6.3 and 6.4 carry the most transfer value, while 6.1 and 6.2 sharpen MCQ recall and assertion-reason justification.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Exercise 6.1 | 20 | 1-mark board MCQ and quick recall of similarity criteria and BPT ratios |
| Reasoning (True or False) | Exercise 6.2 | 10 | Assertion-reason and justification items on triangle theorems |
| Short Answer (SA) | Exercise 6.3 | 25 | 2 and 3-mark board problems on BPT, converse, and similarity proofs |
| Long Answer (LA) | Exercise 6.4 | 10 | 5-mark multi-step proofs and area-ratio derivations |
Why the Exemplar Matters for Triangles Prep
The Exemplar uses the same ideas as the textbook but raises the bar. It chains two proof steps into one problem and asks you to justify true-or-false claims about BPT. It also uses general algebraic conditions where the textbook gives a number, so you apply two or three criteria in sequence.
- BPT and Its Converse: Boards often include one problem applying BPT or proving its converse in a combined figure. Exercise 6.3 Q1 to Q10 train this.
- Area Ratio Theorem: The area-ratio of similar triangles is a repeat 3-mark board topic. Exercise 6.3 Q11 to Q25 require similarity before the area theorem applies.
- Multi-Step Proof Problems: Exercise 6.4 Q1 to Q10 train the "prove two triangles similar, then derive a length or area relationship" style, reused on the board as case-based and HOTS questions.
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three cases.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Basic Proportionality Theorem | "In triangle ABC, DE is parallel to BC. If AD = 1.5 cm and DB = 3 cm, find AE." | "A line parallel to BC of triangle ABC intersects AB and AC at points D and E respectively. Prove that ADAB = AEAC and state which similarity result this follows from." |
| AA Similarity | "State whether triangles ABC and PQR are similar. Give reasons." | "Triangles ABC and DEF are such that angle A = angle D and AB/DE = AC/DF. Prove that angle B = angle E and hence that triangle ABC is similar to triangle DEF." |
| Area Ratio | "Two similar triangles have sides in ratio 3:4. Find the ratio of their areas." | "If areas of two similar triangles are in ratio 64:121, find the ratio of their perimeters and the ratio of corresponding medians." |
The Exemplar always adds a layer: a general proof, a justification step, or a follow-on derivation. Students who practise only the textbook often lose 1 to 2 marks per board proof.
Full worked solutions: Triangles Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar does not replace the textbook. Interleave them: read a topic, solve the textbook exercise, then attempt the Exemplar problems on it. A four-day plan spreads the load.
- Day 1 (BPT and its converse): Attempt Exemplar MCQs Exercise 6.1 Q1 to Q10 and reasoning items Exercise 6.2 Q1 to Q5.
- Day 2 (Similarity criteria): Revise AA, SAS, SSS. Attempt Exercise 6.1 Q11 to Q20 and Exercise 6.3 Q1 to Q12.
- Day 3 (Area ratios and combined figures): Attempt Exercise 6.3 Q13 to Q25 under a 60-minute timer.
- Day 4 (Long-answer proofs): Attempt Exercise 6.4 Q1 to Q10 under an 80-minute timer, writing each criterion, its justification, and every ratio step in full.
Triangles PDF Download Formats and Languages
The Triangles Class 10 Exemplar PDF comes in formats suited to different revision styles, as shown below.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The Triangles Exemplar PDF and its Hindi-medium edition follow the same notation and question numbering as the printed NCERT 2026-27 release:
- NCERT-faithful: Every problem matches the printed Exemplar line for line, including solved samples with full proof steps.
- Solutions separate: Step-by-step answers live on the linked Exemplar Solutions page, so the book PDF stays a clean practice set.
- State-board alignment: State-board students find the same BPT and similarity content; only the exercise numbers may differ.
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 10 Maths Triangles: free PDF above, aligned to 2026-27.
Student Feedback
In a March 2026 survey of 9,140 Class 10 students, 71% said the long-answer similarity proofs in Exercise 6.4 were the hardest part of Chapter 6. On average, students lost 1.8 marks on Triangles by not naming the similarity criterion (AA, SAS, SSS) in their proof steps.
Source: Collegedunia survey of 9,140 Class 10 students, March 2026.
| Resource | Link |
|---|---|
| Exemplar Book PDF | Triangles Exemplar Book PDF |
| NCERT Solutions | Triangles NCERT Solutions |
| Notes | Triangles Class 10 Notes |
| Formula Sheet | Triangles Formula Sheet |
| NCERT Book PDF | Triangles NCERT Book PDF |
| Exemplar Solutions | Triangles Exemplar Solutions |
| Handwritten Notes | Triangles Handwritten Notes |
NCERT Exemplar Class 10 Maths Triangles Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Triangles PDF for free?
Ans. You can download the Triangles Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Triangles Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers BPT, its converse, the AA / SAS / SSS similarity criteria, the area theorem for similar triangles, and the Pythagoras theorem with its converse.
Ques. How many problems are in the Class 10 Maths Triangles Exemplar PDF?
Ans. The Triangles Exemplar PDF contains 65 unsolved problems, split as 20 MCQ (Exercise 6.1), 10 reasoning items (Exercise 6.2), 25 short answer (Exercise 6.3) and 10 long answer (Exercise 6.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Triangles?
Ans. Yes. The Exemplar chains two proof steps into one problem, asks students to justify true-or-false claims about BPT and similarity, and uses general algebraic conditions where the textbook gives a specific numerical figure. This layered style matches the HOTS and case-based questions in recent CBSE Class 10 board papers.
Ques. Should I attempt the Triangles Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar first usually leaves students stuck on multi-step BPT and area-ratio proofs.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 6?
Ans. The ten long-answer problems in Exercise 6.4 are closest to the CBSE 5-mark style. They cover multi-step similarity proofs where students must establish that two triangles are similar using a named criterion, then derive a length or area relationship from that result.
Ques. What are the key theorems tested in the Triangles Exemplar?
Ans. The main results tested throughout the Exemplar are: (1) Basic Proportionality Theorem and its converse, (2) AA, SAS, and SSS similarity criteria, (3) the area theorem (ratio of areas of similar triangles equals the square of the ratio of their corresponding sides), and (4) the Pythagoras theorem with its converse. The Exemplar also tests the RHS similarity criterion for right triangles.
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