Triangles – Exercise 6.1

Basics of Similarity

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

(i) All equilateral triangles are __________. (congruent, similar)

(ii) All rectangles having equal lengths and breadths are __________. (similar, congruent)

(iii) All __________ triangles are similar. (right-angled, equilateral)

(iv) Two polygons having the same number of sides are similar if their corresponding angles are __________ and their corresponding sides are __________. (equal, proportional)

2. Give two different examples each of:

(i) A pair of similar figures

(ii) A pair of figures which are not similar

Question 1
(i) similar
(ii) congruent
(iii) equilateral
(iv) equal, proportional

Question 2
(i) Two circles of different radii; two squares of different side lengths.
(ii) A square and a rectangle; a triangle and a pentagon.

Reasoning Questions

3. Two pentagons have their corresponding angles equal, but the ratios of their corresponding sides are not the same. State whether these two pentagons are similar. Give reasons for your answer.

4. Two quadrilaterals have their corresponding sides in the same ratio, but their corresponding angles are not equal. Are the two quadrilaterals similar? Justify your answer.

5. Three photographs of the same building are taken from the same position but printed in different sizes. State whether these photographs are similar or congruent. Give reasons.

3. For similarity of polygons, both conditions must be satisfied (corresponding angles equal AND corresponding sides proportional). Here, angles are equal but sides are not proportional. Therefore, the pentagons are NOT similar.

4. Similarity requires equal corresponding angles. The given condition states angles are not equal. Therefore, the quadrilaterals are NOT similar.

5. All photographs have the same shape (same building, same angle) but different sizes. Thus, they are similar but not congruent.

Triangles – Exercise 6.1

Overview

Basics of Similarity

Reasoning Questions