NCERT Class 10 Maths – Exercise 6.1 Solutions

NCERT Class 10 Maths

Chapter 6 – Triangles | Exercise 6.1

(Rationalized Syllabus 2025-26)

Fill in the blanks using the correct word given in brackets:

(i) All circles are ________. (congruent, similar)

Explanation: Circles have the same shape but can have different radii.

✔️ similar

(ii) All squares are ________. (similar, congruent)

Explanation: All squares have the same shape (equal angles and proportional sides), but sizes may vary.

✔️ similar

(iii) All ________ triangles are similar. (isosceles, equilateral)

Explanation: Equilateral triangles always have all angles as 60°, maintaining the same shape. Isosceles triangles can have varying angles.

✔️ 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)

Explanation: These are the two necessary conditions for similarity of polygons.

✔️ (a) equal, (b) proportional

Give two different examples of pair of:

(i) Similar figures

1. Two equilateral triangles with sides 1 cm and 2 cm.

2. Two circles with radii 3 cm and 5 cm.

Both pairs have the same shape but different sizes.

(ii) Non-similar figures

1. A square and a rectangle (corresponding sides are not proportional in relation to angles).

2. An equilateral triangle and a right-angled triangle (corresponding angles are not equal).

These pairs have different shapes.

State whether the following quadrilaterals are similar or not:

Analysis:

We are comparing Quadrilateral PQRS (a Rhombus with side 1.5 cm) and Quadrilateral ABCD (a Square with side 3 cm).

Condition 1 (Sides): Ratio of corresponding sides:

$$\frac{1.5}{3} = \frac{1}{2}$$

The sides are proportional.

Condition 2 (Angles):

In square ABCD, all angles are $90^\circ$. In rhombus PQRS, the angles are not $90^\circ$.

Since the corresponding angles are not equal, the polygons are not similar.

✖️ Not Similar

🎉 Exercise 6.1 Completed