Class 10 Mathematics

# Triangle

## Exercise 6.1 (NCERT)

Question 1: Fill in the blanks using the correct word given in brackets:

(a) All circles are ………… (congruent, similar).

**Answer:** similar

**Explanation:** All circles are similar irrespective of difference in their radii. A smaller circle can be enlarged to the size of a larger circle and vice-versa is also true.

(b) All squares are ……………(similar, congruent).

**Answer:** similar

**Explanation:** All squares are similar because all the angles in a square are right angles and all the sides are equal. Hence, a smaller square can be enlarged to the size of a larger square and vice-versa is also true.

(c) All …………..triangles are similar. (isosceles, equilateral).

**Answer:** equilateral

**Explanation:** All equilateral triangles are similar because all the angles in an equilateral triangle are 60°. Moreover, all the sides of an equilateral triangle are equal. Hence, a smaller equilateral triangle can be enlarged to the size of a larger equilateral triangle and vice-versa is also true.

(d) Two polygons of the same number of sides are similar, if their corresponding angles are …………and their corresponding sides are ……………(equal, proportional).

**Answer:** equal, proportional

**Explanation:** This is similar to AAA criterion in case of triangles. If corresponding angles are same and the number of sides are similar in two polygons then the polygons are similar.

Question 2: Give two different examples of pair of

(a) Similar figures

**Answer:** Two equilateral triangles of different sides.

**Explanation:** Two equilateral triangles of different sides would be similar because all the angles are 60°. Hence, AAA criterion applies in this case.

(b) Non-similar figures

**Answer:** A rhombus and a rectangle

**Explanation:** In case of a rhombus, all the sides are equal and the angles can either be right angles or a combination of acute and obtuse angles. In case of rectangle; opposite sides are equal and all the angles are right angles. Hence, a rhombus and a rectangle are non-similar figures. There can be some exceptions; like in case of two squares of same sides. A square is a rhombus and a rectangle too.

Question 3: State whether the following quadrilaterals are similar or not.

**Answer:** These quadrilaterals are not similar.

**Explanation:** In the given quadrilaterals, the sides are in the same ration, i.e. all the sides are same in respective quadrilaterals. But angles in the smaller quadrilateral are not right angles but all the angles in the larger quadrilateral are right angle. Hence, these quadrilaterals are not similar.

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Theorem (Part 1)

Theorem (Part 2)

Exercise 6.2 (Part 1)

Exercise 6.2 (Part 2)

Exercise 6.3 (Part 1)

Exercise 6.3 (Part 2)

Exercise 6.3 (Part 3)

Exercise 6.4

Exercise 6.5 (Part 1)

Exercise 6.5 (Part 2)

Exercise 6.6 (Part 1)

Exercise 6.6 (Part 2)