Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.1
Exercise 4.1
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 triangles are similar, if their corresponding angles are .......... (proportional, equal)
(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)
(vi) 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
(i) All circles are similar.
(ii) All squares are similar.
(iii) All equilateral triangles are similar.
(iv) Two triangles are similar, if their corresponding angles are equal.
(v) Two triangles are similar, if their corresponding sides are proportional.
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are proportional.
2. Write the truth value (T/F) of each of the following statements:
(i) Any two similar figures are congruent.
⏵False
(ii) Any two congruent figures are similar.
⏵True
(iii) Two polygons are similar, if their corresponding sides are proportional.
⏵False
(iv) Two polygons are similar, if their corresponding angles are proportional.
⏵False
⏵False
(v) Two triangles are similar if their corresponding sides are proportional.
⏵True
⏵True
(vi) Two triangles are similar if their corresponding angles are proportional.
⏵True
⏵True