NCERT Solutions for Class 10 Maths Chapter 6 – Triangles Exercise 6.1 are provided here to help students understand the important concepts of similarity of triangles and the Basic Proportionality Theorem (BPT) in a clear and simplified manner. These solutions are prepared by subject experts according to the latest CBSE syllabus to help students perform well in their board examinations.
Exercise 6.1 mainly focuses on the Basic Proportionality Theorem, which explains how a line drawn parallel to one side of a triangle divides the other two sides proportionally. This exercise strengthens the foundation of similarity concepts, which are essential for solving advanced problems in the chapter.
NCERT Solutions Class 10 Maths Chapter 6 Exercise 6.1 Triangles
Q.
Fill in the blanks using the correct word given in brackets:
(i) All circles are _______. (congruent, similar)
(ii) All squares are______. (similar, congruent)
(iii) All _______triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if
(a) their corresponding angles are _______and
(b) their corresponding sides are_______. (equal, proportional)
Q.
Give two different examples of pair of
(i) similar figures. (ii) non-similar figures.
Q.
State whether the following quadrilaterals are similar or not:
By practicing this exercise, students will gain a better understanding of:
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Basic Proportionality Theorem (BPT)
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Ratio and proportion in triangles
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Application of parallel lines in triangles
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Logical reasoning and theorem-based questions
The solutions are presented in a step-by-step format to ensure better conceptual clarity and easy understanding.
Q1. Fill in the blanks using the correct word given in brackets:
(i) All circles are ___________. (congruent, similar)
(ii) All squares are ___________. (similar, congruent)
(iii) All ___________ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if:
(a) their corresponding angles are ____________ and
(b) their corresponding sides are ___________. (equal, proportional)
Solution:
(i) All circles are similar.
Reason: Two similar figures have the same shape but not necessarily the same size. The radii of circles may be different, so they are not congruent, but they are similar.
(ii) All squares are similar.
Reason: Squares always have equal angles and proportional sides. However, their side lengths may not be equal, so they are not necessarily congruent.
(iii) All equilateral triangles are similar.
Reason: In an equilateral triangle, all sides are equal and all angles are equal (each angle is 60°).
(iv) Two polygons of the same number of sides are similar if:
(a) their corresponding angles are equal, and
(b) their corresponding sides are proportional.
Reason:
Two polygons are similar when:
Q2. Give two different examples of pairs of:
(i) Similar figures
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Two equilateral triangles with sides 2 cm and 6 cm.
ΔABC ~ ΔDEF
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Two squares with sides 3 cm and 5 cm.
PQRS ~ UVWX
(ii) Non-similar figures
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A quadrilateral and a rectangle.
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A triangle and a parallelogram.
Q3. State whether the following quadrilaterals are similar or not:
Reasoning:
Two polygons with the same number of sides are similar if:
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All corresponding angles are equal.
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All corresponding sides are in the same ratio (proportion).
Solution:
In quadrilaterals ABCD and PQRS:
AB / PQ = BC / QR = CD / RS = DA / SP
So, the corresponding sides are proportional.
But,
∠A ≠ ∠P
∠B ≠ ∠Q
So, the corresponding angles are not equal.
Therefore,
Quadrilateral ABCD is not similar to Quadrilateral PQRS.
FAQs: Class 10 Maths Chapter 6 – Triangles Exercise 6.1
Q1. What is the main concept covered in Exercise 6.1?
Answer:
Exercise 6.1 focuses on the Basic Proportionality Theorem (BPT) and its applications in solving problems related to similar triangles.
Q2. What does the Basic Proportionality Theorem state?
Answer:
The theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
Q3. Why is Exercise 6.1 important for board exams?
Answer:
Questions based on BPT and similarity are frequently asked in board exams. Understanding this exercise helps students solve proof-based and application-based questions confidently.
Q4. What prior knowledge is required to solve Exercise 6.1?
Answer:
Students should understand:
Q5. How do NCERT Solutions help in preparation?
Answer:
NCERT Solutions provide accurate, step-by-step explanations aligned with CBSE guidelines, helping students build strong fundamentals and improve problem-solving skills.