source: ncert_exercises
topic: geometry
class_level: class_10
chapter: ch6
exercise: ex6.1
difficulty: beginner
Class 10 | Ch6: Triangles | Exercise 6.1
Key Concepts:
- Similar figures: same shape, not necessarily same size.
- All congruent figures are similar, but not vice versa.
- Equilateral triangles are always similar. Squares with same side length are congruent.
Q1. Fill in the blanks using correct word: similar/congruent. (i) All circles are ___. (ii) All squares are ___. (iii) All equilateral triangles are ___. (iv) Two triangles are similar if their corresponding angles are ___ and corresponding sides are ___. Answer: (i) similar. ✅ (ii) similar. ✅ (iii) similar. ✅ (iv) equal; proportional. ✅
Q2. Give two different examples of pair of: (i) similar figures (ii) non-similar figures. Answer: (i) Similar: Two circles of different radii; Two squares of different sizes. ✅ (ii) Non-similar: A triangle and a quadrilateral; A circle and a square. ✅
Q3. State whether the following are true or false. Explain. (i) Two quadrilaterals of the same number of sides are similar. (ii) Two polygons of same number of sides are similar if their corresponding angles are equal and corresponding sides are equal. Answer: (i) FALSE. Quadrilateral shape matters — a square and a rectangle both have 4 sides but are not similar. ✅ (ii) TRUE. This is the definition of similar polygons. ✅