Mathematics · Triangles · NCERT Exercises
Exercise 6.1
Complete, independently verified solutions for NCERT Exercise 6.1.
Mathematics · Chapter 6 · NCERT Exercises
Question
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
Board-exam working:
(i) All circles have the same shape, though their radii may differ. Therefore, all circles are similar.
(ii) All squares have four right angles and their corresponding sides are proportional. Therefore, all squares are similar.
(iii) All equilateral triangles have three 60° angles and proportional corresponding sides. Therefore, all equilateral triangles are similar.
(iv) By the definition of similar polygons, corresponding angles must be equal and corresponding sides must be proportional.
Final answer
(i) similar; (ii) similar; (iii) equilateral; (iv) (a) equal, (b) proportional.
Question
Question 2
Give two different examples of pairs of (i) similar figures and (ii) non-similar figures.
Solution
Board-exam working:
(i) Any two circles are similar. Any two squares are also similar.
For circles, the shape is the same; for squares, all corresponding angles are equal and corresponding sides are proportional.
(ii) A circle and a square are not similar. A square and a non-square rectangle are not similar.
A circle and square have different shapes. For the square and non-square rectangle, corresponding side ratios are not all equal.
Final answer
(i) Two circles; two squares. (ii) A circle and a square; a square and a non-square rectangle.
Question
Question 3
State whether the quadrilaterals in Figure 6.8 are similar or not.
Solution
Board-exam working:
In PQRS, every side is 1.5 cm. In ABCD, every side is 3 cm.
Thus corresponding sides are proportional:
However, ABCD has four right angles, whereas the corresponding angles of PQRS are not all right angles.
For polygons to be similar, both corresponding angles must be equal and corresponding sides must be proportional.
Since the angle condition fails, the quadrilaterals are not similar.
Final answer
The quadrilaterals are not similar.