Class 10 - Chapter 6: Triangles

Exercise 6.1

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

(i) All circles are similar. (congruent, similar)
Explanation: All circles have the same shape but can have different sizes (radii).

(ii) All squares are similar. (similar, congruent)
Explanation: All squares have equal corresponding angles (90 degrees) and proportional sides.

(iii) All equilateral triangles are similar. (isosceles, equilateral)
Explanation: Every equilateral triangle has internal angles of exactly 60 degrees, making their shapes identical.

(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. (equal, proportional)

2. Give two different examples of pair of:

(i) similar figures

• A pair of equilateral triangles with different side lengths (e.g., one with side 2 cm and another with side 5 cm).
• A pair of circles with different radii (e.g., one with radius 3 cm and another with radius 7 cm).

(ii) non-similar figures

• A triangle and a square (different geometric shapes and number of sides).
• A rectangle and a rhombus (angles are not equal, even though sides of a rhombus are proportional).

3. State whether the following quadrilaterals are similar or not:

Answer: The given quadrilaterals are not similar.

Reasoning:

• Side Ratio Check: The ratio of their corresponding sides is equal:
  1.5 / 3 = 1 / 2.
• Angle Check: The corresponding angles are not equal. Quadrilateral ABCD is a square with all angles equal to 90°, while quadrilateral PQRS is a rhombus with oblique angles.

Since both conditions for similarity (proportional sides AND equal angles) are not met, they are not similar.