NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1 - Triangles
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A triangle is a polygon that has three sides and three corners. It is one of the basic geometrical shapes with a minimum number of lines polygon. For comparing and describing triangles congruence property is used. Two triangles are said to be congruent if they are identical in terms of their shape and size. But not all the figures or shape that has similar shape or size need to be congruent. In other words, triangles are said to be congruent if the corresponding sides or angles of one shape are equal to the corresponding sides or angles of the other triangle.
This Story also Contains
- Download Free Pdf of NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1
- Assess NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1
- Topics Covered in Chapter 6, Triangles: Exercise 6.1
- NCERT Solutions Subject Wise
- Subject-Wise NCERT Exemplar Solutions
NCERT solutions of Class 10 maths ex 6.1 concentrate on triangles and their similarity and congruence concept. Here we will discover the meaning of comparable triangles, and learn how comparable geometric forms differ and why they're grouped together. These distinctions between similar geometric shapes will aid your understanding of how these triangles differ. NCERT solutions for exercise 6.1 Class 10 Maths chapter 6 Triangles discuss the concept of geometry as per the NCERT Book, which helps us to grasp new ideas in advanced classes.
Assess NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1
Answer:
All circles are similar.
Since all the circles have a similar shape. They may have different radii, but the shape of all circles is the same.
Therefore, all circles are similar.
Answer:
All squares are similar.
Since all the squares have a similar shape. They may have a different side, but the shape of all squares is the same.
Therefore, all squares are similar.
Answer:
All equilateral triangles are similar.
Since all the equilateral triangles have a similar shape. They may have different sides but the shape of all equilateral triangles is the same.
Therefore, all equilateral triangles are similar.
Answer:
Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are proportional.
Thus, (a) equal
(b) proportional
Q2 (1) Give two different examples of a pair of similar figures.
Answer:
The two different examples of a pair of similar figures are :
1. Two circles with different radii.
2. Two rectangles with different breadth and length.
Q2 (2) Give two different examples of a pair of non-similar figures.
Answer:
The two different examples of a pair of non-similar figures are :
1. Rectangle and circle
2. A circle and a triangle.
Q3 State whether the following quadrilaterals are similar or not:
Answer:
Quadrilateral PQRS and ABCD are not similar as their corresponding sides are proportional, i.e. $1:2$, but their corresponding angles are not equal.
Also Read-
Topics Covered in Chapter 6, Triangles: Exercise 6.1
1. Definition of Triangle: A triangle is a polygon that has three edges and three vertices. It means the polygon with the minimum number of sides is called a triangle. To understand the terms related to triangles student must know the basic definition of a triangle.
2. Congruent Triangles: This is the basic concept that is used to compare triangles. Two triangles are said to be congruent if they same size and shape. Two criteria for triangle congruence are as follows -
Their corresponding angles are equal and
Their corresponding sides are in the same ratio.
3. Similar Figure: Two triangles or any other figure are said to be similar if they have the same shape, but not necessarily have the same size. For example, two equilateral triangles in which each side of the first triangle is 6cm and each side of the other triangle is 8cm are said to be similar because both are equilateral triangles.
Also see-
NCERT Solutions Subject Wise
Students must check the NCERT solutions for Class 10 Maths and Science given below:
Subject-Wise NCERT Exemplar Solutions
Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:
Frequently Asked Questions (FAQs)
Q: Can a triangle and square be similar to each other?
A:
No, because they have different number of sides. Triangle has three and square has 4
Q: What are similar figures?
A:
Two figures are similar to each other if they have the same shape but are of different size.
Q: What is the sum of all the angels of a triangle?
A:
Sum of the angels of a triangle is 180 degrees.
Q: What are the conditions for two figures to be similar according to NCERT Solutions for Class 10 Maths Exercise 6.1?
A:
Two figures with same number of sides are similar if
their corresponding angles are equal and
their corresponding sides are in the same ratio,
Q: Can two circles of any radius be similar to each other?
A:
Yes, any two given circles are always similar to each other.
Q: Why can’t a rectangle and a square be similar to each other?
A:
Because, the sides of rectangle are not equal to each other. Thus, the ratio of sides is not same for all the sides.
Q: Does similarity mean the figures are congruent?
A:
No, similarity means that the figures are just of same shape it doesn’t mean that they are equal.
Q: Can we proof that any two regular polygons of same side are similar to each other?
A:
Yes, if their number of sides are equal to each other then the two are similar.
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