Triangles Class 10 Maths Exercise 6.1 NCERT Solutions

The NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.1 cover all 3 questions on similar figures and polygon similarity, according to the latest 2026-27 CBSE syllabus. Each answer is solved step by step the way the board expects, with an Expert Solution that adds exam strategy.

• Questions covered: 3 in total, on definitions of similarity, real-life examples of similar and non-similar figures, and identifying whether two quadrilaterals are similar.
• Core concept: two figures are similar when they have the same shape; two polygons are similar only when both corresponding angles are equal and corresponding sides are proportional.
• Board value: Exercise 6.1 introduces the similarity framework that CBSE questions on BPT and triangle criteria in Exercises 6.2 and 6.3 rely on.

What Exercise 6.1 of Triangles Covers for Class 10

Exercise 6.1 is the opening set of Chapter 6. It sets up the definition of similar figures and the exact conditions under which two polygons count as similar. You need both conditions to hold at the same time: equal corresponding angles and proportional corresponding sides. Get that definition right and the rest of Chapter 6 follows naturally.

• Q1: fill in blanks using the correct word (congruent vs similar) for circles, squares, triangles, and polygons.
• Q2: give two examples each of similar pairs and non-similar pairs from everyday life.
• Q3: decide whether the square ABCD (side 3 cm) and rhombus PQRS (side 1.5 cm) shown in Fig. 6.8 are similar.

How to Solve Exercise 6.1 Question by Question

All three questions test the same core idea: similarity needs both conditions, not just one. A square and a rhombus have sides in ratio 2:1, but their angles disagree, so they are not similar. Two circles have identical shape regardless of size, so they are always similar. Think "same shape?" before writing anything down.

Similar and Non-Similar Figures: Class 10 Maths Chapter 6 Exercise 6.1 Concepts

Two figures are similar when one is a scaled copy of the other. Same shape, possibly different size. Congruent figures go further: same shape AND same size. The NCERT definition of similar polygons states:

• Two polygons with the same number of sides are similar if all corresponding angles are equal, and
• All corresponding sides are in the same ratio (proportional).

Square versus Rhombus: The Classic Non-Similar Pair in Exercise 6.1 Q3

Question 3 is the most important in Exercise 6.1 because it shows why both conditions must hold at the same time. Many students rush to call these two quadrilaterals similar after checking the sides. The angle check stops that mistake.

Common Mistakes Students Make in Triangles Exercise 6.1

Exercise 6.1 is short, but the definition-based questions still catch students off guard in exams. These are the mistakes that appear most often.

• Writing "congruent" instead of "similar" in Q1: congruent means equal shape AND equal size. The question says circles and squares of possibly different sizes, so "similar" is correct.
• Vague examples in Q2: writing "two triangles" without qualification will not score because two general triangles may or may not be similar. Name a specific pair, such as "two equilateral triangles" or "two photographs of the same image at different sizes."
• No reason stated in Q2: the examiner rewards a one-line justification of which condition passes or fails, not just the example.
• Calling the square and rhombus similar in Q3: proportional sides alone do not make two polygons similar. Always check both conditions.

Exercise 6.1 Marks and CBSE Board Relevance for Class 10 Maths

Exercise 6.1 itself carries 2 to 3 marks in internal assessments. In the board paper, the definitions from this exercise appear as fill-in-the-blank or short-answer questions in the 1-mark and 2-mark slots.

These solutions follow the 2026-27 NCERT exactly. The working style used here, with a clear two-condition check for every polygon, is what the CBSE marking scheme expects.

Other Resources for Class 10 Maths Chapter 6 Triangles

Use the table below to jump to the other resources for this chapter and the other exercises of Triangles. Each link opens the matching Collegedunia page.

NCERT Solutions for Class 10 Maths Triangles: All Exercises

Chapter 6 Triangles has three exercises. The table below links each exercise to its own step-by-step solutions page.

NCERT Solutions for Class 10 Maths: All Chapters

Use the table below to jump to the NCERT Solutions for the other chapters of Class 10 Maths. Every chapter uses the same step-by-step answer style.

All NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.1 with Step-by-Step Solutions

Exercise 6.1

Q 6.3

State whether the following quadrilaterals are similar or not:

Check SolutionExpert Solution

Concept used. Two polygons are similar only when both tests pass at the same time: corresponding angles equal and corresponding sides in the same ratio. If either test fails, the polygons are not similar. From the figure ABCD is a square (all sides 3 cm, all angles 90^∘) and PQRS has all four sides 1.5 cm, which makes it a rhombus whose angles are not right angles.

1. Check the side ratio. Every side of ABCD is 3 cm and every side of PQRS is 1.5 cm, so ABPQ=31.5=2. All corresponding sides share the ratio 2:1, so the side test passes.
2. Check the angles. In the square each angle is 90^∘. In the rhombus PQRS the angles are not 90^∘ (a slanted rhombus has two acute and two obtuse angles).
3. Compare. The corresponding angles are not equal, so the angle test fails even though the side test passed.

The two quadrilaterals are not similar, because their corresponding sides are proportional but their corresponding angles are not equal.

KI

Karthik Iyer

M.Sc Mathematics, Anna University

Verified Expert

The square-versus-rhombus trap, stated cleanly. This is the classic counter-example showing why both similarity conditions are needed at the same time.

• Read the figure: PQRS has equal sides but tilted corners, which makes it a rhombus rather than a square. Note this before testing anything.
• Sides pass: all ratios reduce to 2:1, so the proportional-sides condition holds and might fool a quick reader into calling them similar.
• Angles fail: a square is locked at four 90^∘ corners while a non-square rhombus is not, so the corresponding angles disagree and similarity breaks.
• Why both matter: this single example is the reason the definition asks for equal angles and equal side ratios together, not either one on its own.

Writing the side ratio first and then pointing to the angle mismatch gives a complete, examiner-friendly justification. Many students stop at the equal sides and wrongly call the pair similar, so the angle line is the one that actually earns the mark here.

Not similar: sides are in ratio 2:1 but the square's 90^∘ angles do not match the rhombus angles.