NCERT Solutions Class 10 Maths Chapter 6: Triangles

Q: Fill in the blanks using the correct word given in brackets: (iii) All __________ triangles are similar. (isosceles, equilateral)

All equilateral triangles are similar.

Q: State whether the following quadrilaterals are similar or not:

The quadrilaterals are not similar because their corresponding angles are not equal, even though their sides are proportional.

Detailed solutions for Exercise 6.1 (Introduction to Similarity).

Ex 6.1 Ex 6.2 Ex 6.3

#### **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)** #### **A1. Solution:** (i) All circles are **similar**. (Reason: They have the same shape but can have different radii). (ii) All squares are **similar**. (Reason: All angles are $90^\circ$ and sides are always proportional). (iii) All **equilateral** triangles are similar. (Reason: Each angle is always $60^\circ$). (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**. #### **Q2. Give two different examples of a pair of:** **(i) similar figures.** **(ii) non-similar figures.** #### **A2. Solution:** **(i) Similar figures:** 1. Any two circles (e.g., a circle of radius 2 cm and a circle of radius 5 cm). 2. Any two equilateral triangles (e.g., one with side 3 cm and another with side 6 cm). **(ii) Non-similar figures:** 1. A circle and a triangle. 2. A scalene triangle and an equilateral triangle. #### **Q3. State whether the following quadrilaterals are similar or not:** *(Refer to the image in the textbook: A rhombus PQRS with sides 1.5 cm and a square ABCD with sides 3 cm)* #### **A3. Solution:** The two quadrilaterals are **not similar**. **Reasoning:** 1. **Sides:** The ratio of the corresponding sides is constant: $\frac{1.5}{3} = \frac{1}{2}$. The sides are proportional. 2. **Angles:** In square ABCD, all angles are $90^\circ$. However, in rhombus PQRS, the angles are not $90^\circ$. Since the corresponding angles are not equal, the two quadrilaterals are not similar.