Class 10 NCERT Solutions- Chapter 6 Triangles - Exercise 6.1

The Triangles are fundamental geometric shapes studied in Class 10 Mathematics. They are crucial for understanding the properties and relationships between the angles, sides, and overall structure of the shapes in Euclidean geometry. Exercise 6.1 in Chapter 6 of the NCERT textbook delves into the properties of the triangles and their applications offering the foundation for the more advanced concepts in geometry.

Triangles

A triangle is a polygon with three edges and three vertices. The sum of the internal angles of the triangle is always 180 degrees. There are several types of triangles classified based on their sides and angles:

• Equilateral Triangle: All three sides and all three angles are equal.
• Isosceles Triangle: The Two sides are equal and angles opposite these sides are also equal.
• Scalene Triangle: All three sides and all three angles are different.
• Acute Triangle: All three angles are less than 90 degrees.
• Obtuse Triangle: The One angle is greater than 90 degrees.
• Right Triangle: The One angle is exactly 90 degrees.

Question 1. Fill in the blanks by using the correct word given in brackets.

(i) All circles are ……………. . (congruent/similar)

Solution:

All circles are similar because they have radius in fixed proportion.

(ii) All squares are …………… . (similar/congruent)

Solution:

All squares are similar because the ratio of corresponding sides are equal.

(iii) All …………….. triangles are similar. (isosceles/equilateral)

Solution:

All Equilateral triangles are similar because the ratio of corresponding sides are equal. 

(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:

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

Question 2. Give two different examples of pair of

(i) similar figures. (ii) non-similar figures.

Solution:

(i) Similar figures. 

1. All rectangular boards are similar
2. All circular rings are similar

(ii) Non-similar figures

1. A notebook and a pen are non-similar
2. A rectangle and a circle are non-similar.

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

Solution:

Both the figures are non-similar. For similarity, the corresponding angles should be equal and corresponding sides are in the same ratio. But in this figure ratio of corresponding sides (AB/PQ = AS/PS = DC/SR = CB/RQ = 3/1.5 = 2) but corresponding angles are not equal.  

Related Articles:

• Triangles in Geometry
• Properties of Triangle
• Types of Triangles, Classifications, Practice Questions