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NCERT Solutions · Class 10 · Chapter 6: Triangles

NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1

Exercise 6.1: Similar figures. Two polygons with the same number of sides are similar when their corresponding angles are equal and their corresponding sides are in the same ratio. Both conditions are needed (except for triangles).

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Exercise 6.1 questions and solutions

Exercise 6.1, Question 1

Fill in the blanks.
(i) All circles are ____.
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  1. Any circle is an enlargement of any other (scale factor = ratio of radii).
Answer: similar
(ii) All squares are ____.
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  1. All angles are \(90^\circ\) and all sides of each square are equal, so side ratios match.
Answer: similar
(iii) All ____ triangles are similar.
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  1. Every equilateral triangle has angles \(60^\circ, 60^\circ, 60^\circ\).
Answer: equilateral
(iv) Two polygons with the same number of sides are similar if their corresponding angles are ____ and their corresponding sides are ____.
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  1. Similarity needs both the same shape (angles) and a single scale factor (sides).
Answer: equal; proportional (in the same ratio)

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Exercise 6.1, Question 2

Give two examples each of similar and of non-similar figures.
(i) Similar figures
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  1. Figures that are enlargements of each other.
Answer: Any two circles; any two squares (also any two equilateral triangles).
(ii) Non-similar figures
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  1. Same number of sides is not enough: angles or side ratios differ.
Answer: A square and a (non-square) rhombus; a square and a non-square rectangle.

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Exercise 6.1, Question 3

The textbook figure shows a square and a rhombus with sides in a common ratio. Are they similar?
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  1. The sides are proportional, but the square's angles are \(90^\circ\) while the rhombus's angles are not.
  2. Corresponding angles are not equal, so the quadrilaterals are not similar.
Answer: No: sides proportional but angles not equal.

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Done the NCERT exercises? The board paper asks more

Triangles has 40 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.

Triangles: notes and questionsCreate a free accountTeachers: set it as homework

Triangles in our sample papers: Sample paper 1 (questions 8, 23, 28, 33) · Sample paper 2 (questions 9, 23, 29, 33) · Sample paper 3 (questions 10, 12, 19, 28, 33) · Sample paper 4 (questions 9, 29, 33) · Sample paper 5 (questions 9, 10, 28, 33).

Also useful: free MCQs and case studies for Triangles · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan

Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.