Triangles | Exercise 6.1

Question 1

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)

Solution

Understand the Question

Congruent figures: Figures that have the exact same shape and the exact same size.
Similar figures: Figures that have the same shape, but not necessarily the same size.
Two polygons with the same number of sides are similar if:
1. Their corresponding angles are equal.
2. Their corresponding sides are in the same ratio (proportional).

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

Answer

(i) similar

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

Answer

(ii) similar

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

Answer

(iii) 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)

Answer

(iv) (a) equal, (b) proportional

Common Mistakes

Congruent vs. Similar: Confusing congruence with similarity. All circles and squares share the same shape, but they can have different sizes (radii or side lengths), making them similar, not necessarily congruent.
Isosceles vs. Equilateral: Assuming all isosceles triangles are similar. Isosceles triangles can have different vertex angles, whereas all equilateral triangles have fixed angles of $60^\circ$ .
Swapping Conditions for Polygons: Inverting the requirements for similar polygons — corresponding angles must be equal, while corresponding sides must be proportional.

Question 1

More questions in Exercise 6.1