Exercise 6.1 – Stepwise Solutions
1. Fill in the blanks
(i) All circles are
similar.Reason: All circles have the same shape; their radii may differ but corresponding sides are proportional.
(ii) All squares are
similar.Reason: All angles are 90° and sides are proportional.
(iii) All
equilateral triangles are similar.Reason: Each angle is 60°.
(iv) Two polygons of the same number of sides are similar if:(a) their corresponding angles are
equal(b) their corresponding sides are
proportional
2. Examples
(i) Similar figures:- Two circles of different radii
- Two squares of different side lengths
(ii) Non-similar figures:- A square and a rectangle
- An equilateral triangle and a scalene triangle
3. Are the quadrilaterals similar?
Left Figure:All sides = 1.5 cmIt is a rhombus (angles are not 90°).
Right Figure:All sides = 3 cmAll angles are 90°It is a square.
Comparison:- Side ratio = 1.5 : 3 = 1 : 2 (proportional)
- But corresponding angles are NOT equal
Conclusion: The quadrilaterals are
NOT similar.
Final Answers Summary
1. (i) similar (ii) similar (iii) equilateral (iv) equal, proportional2. Examples given above3. The given quadrilaterals are NOT similar