Question 2

We will define similar and non-similar figures with examples.

Step 1 — Similar Figures

Similar figures have the same shape. Their sizes can be different. All corresponding angles are equal. Corresponding sides are in proportion.

Let's look at two equilateral triangles.

Example 1: Two equilateral triangles. Triangle 1 has side length 1 cm. Triangle 2 has side length 2 cm. All angles in both triangles are 60°. The ratio of their sides is 1:2. They are similar figures.

Let's look at two squares.

Example 2: Two squares. Square 1 has side length 1 cm. Square 2 has side length 2 cm. All angles in both squares are 90°. The ratio of their sides is 1:2. They are similar figures.

Step 2 — Non-Similar Figures

Non-similar figures do not have the same shape. Their corresponding angles might not be equal. Their corresponding sides might not be in proportion.

Let's look at a trapezium and a square.

Example 1: A trapezium and a square. A trapezium has one pair of parallel sides. A square has four equal sides. Their shapes are very different. They are non-similar figures.

Let's look at a triangle and a parallelogram.

Example 2: A triangle and a parallelogram. A triangle has three sides. A parallelogram has four sides. Their shapes are very different. They are non-similar figures.

Answer

(i) Two different examples of similar figures are:

1. Two equilateral triangles with side lengths 1 cm and 2 cm.
2. Two squares with side lengths 1 cm and 2 cm. (ii) Two different examples of non-similar figures are:
3. A trapezium and a square.
4. A triangle and a parallelogram.