NCERT Solutions for Class 6 Maths Chapter 5 (Ex 5.6)
Exercise 5.6
1. Name the type of following triangles.
(i). Triangles with lengths of sides 7 cm, 8 cm, and 9 cm.
Ans: The triangle with different side lengths is called a scalene triangle. For the given triangle, all sides' lengths are different. Thus, the given triangle is a scalene triangle.
(ii). $\Delta ABC$ with $AB = 8.7\,{\text{cm}}$, $AC = 7\,{\text{cm}}$, and $BC = 6\,{\text{cm}}$.
Ans: The triangle with different side lengths is called a scalene triangle. For the given triangle, all sides lengths are different.Thus, the given triangle is a scalene triangle.
(iii). $\Delta PQR$ such that $PQ = QR = PR = 5{\text{ cm}}$.
Ans: A triangle with equal side length is called an equilateral triangle. All sides of the triangle, $\Delta PQR$are equal to 5 cm. Thus, the given triangle, $\Delta PQR$ , has all sides of equal length, so the triangle is an equilateral triangle.
(iv). $\Delta DEF$ with $m\angle D = 90^\circ $.
Ans: A triangle with one angle as $90^\circ $ is called a right-angled triangle. One angle of the triangle, $\Delta DEF$ is equal to $90^\circ $. Hence, $\Delta DEF$is a right-angled triangle.
(v). $\Delta XYZ$ with $m\angle Y = 90^\circ $ and $XY = YZ$.
Ans: A triangle whose one angle as $90^\circ $ and the adjacent legs to that angle are equal, then that kind of triangle is called a right-angled triangle. Since one angle of $\Delta XYZ$ measures 90 degree and two sides are equal, then, $\Delta XYZ$ is an isosceles right-angled triangle.
(vi). $\Delta LMN$ with $m\angle L = 30^\circ $, $m\angle M = 70$, and $m\angle N = 80^\circ $.
Ans: A triangle whose all angles are acute, that is, they are less than $90^\circ $ is called an acute-angled triangle. Since all the angles of $\Delta LMN$ are acute angles, then, $\Delta LMN$ is an acute-angled triangle.
2. Match the following:
Measure of triangle | Types of triangles |
(i). 3 sides of equal length | a. Scalene |
(ii). 2 sides of equal length | b. Isosceles right angle |
(iii). All sides of different length | c. Obtuse angle |
(iv). 3 acute angles | d. Right angle |
(v). 1 right angle | e. Equilateral |
(vi). 1 obtuse angle | f. Acute angle |
(vii). 1 right angle with two sides of equal length | g. Isosceles |
Ans: The terms are matched as follows:
3 sides of equal length-
When the triangle has equal side lengths, it is an equilateral triangle. Therefore, option (i) matches with option (e).
2 sides of equal length-
When the measure of 2 sides is equal, then, the triangle is an isosceles triangle. Therefore, option (ii) matches with option (g).
All sides of different length-
The triangle with different side lengths is called a scalene triangle. Therefore, option (iii) matches with option (a).
3 acute angles
The triangle with all angles less than $90^\circ $ is called an acute angled triangle. Therefore, option (iv) matches with option (f).
1 right angle
The triangle with one angle as $90^\circ $ is called a right angle. Therefore, option (v) matches with option (d).
1 obtuse angle
The triangle with an obtuse angle is called an obtuse angled triangle. Therefore, option (vi) matches with option (c).
1 right angle with two sides of equal length.
A right angled triangle with two sides of equal length is called an isosceles right-angled triangle. Therefore, option (vii) matches with option (b).
The matched pair as follows,
(i)-(e),(ii)-(g), (iii)-(a),(iv)-(f),(v)-(d),(vi)-(c), and (vii)-(b)
3. Name each of the following triangles in two different ways.
The triangle is as follows.
Ans: The triangle with all angles less than $90^\circ $ is called an acute angled triangle and a triangle that has two equal sides that triangle is called an isosceles triangle.The given triangle has two equal angles and we can see that those angles are less than $90^\circ $. Also, the triangle has two equal sides. Thus, on the basis of angles, it can be classified as an acute angled triangle and on the basis of side lengths, it can be classified as an isosceles triangle.
The triangle is as follows.
Ans: A triangle with one angle as $90^\circ $ is called a right-angled triangle. The triangle with different side lengths is called a scalene triangle. The given triangle has one angle whose measure is 90 degrees and all the side lengths are of different lengths. Thus, on the basis of angles, it can be classified as a right-angled triangle and on the basis of side lengths, it can be classified as a scalene triangle.
The triangle is as follows.
Ans: A triangle whose one angle is more than $90^\circ $ and less than $180^\circ $ is called an obtuse angled triangle. A triangle that has two equal sides is called an isosceles triangle. We can observe that the triangle has one larger angle. Also, the triangle has two equal sides, measuring 7 cm. Thus, on the basis of angles, it can be classified as an obtuse angled triangle and on the basis of side lengths, it can be classified as an isosceles triangle.
The triangle is as follows.
Ans: A triangle with one angle as $90^\circ $ is called a right-angled triangle and a triangle that has two equal sides that triangle is called an isosceles triangle. We can see that the given triangle has one angle whose measure is $90$ degree and two side lengths are different. Thus, on the basis of angles, it can be classified as a right-angled triangle and on the basis of side lengths, it can be classified as an isosceles triangle.
The triangle is as follows.
Ans: We can see that all the sides of the triangle are equal. When all the sides are equal the angles of the triangle are equal, the triangle is an equilateral triangle. Also, all the internal angles of an equilateral triangle are equal to $60^\circ $ which is less than $90^\circ $. Thus, on the basis of angles, it can be classified as an acute angled triangle and on the basis of side lengths, it can be classified as an equilateral triangle.
The triangle is as follows.
Ans: A triangle whose one angle is more than $90^\circ $ and less than $180^\circ $ is called an obtuse angled triangle and a triangle with sides of different length is called a scalene triangle.We can observe that the triangle has one larger angle (greater than $90^\circ $. Also, the triangle has different side lengths. Thus, on the basis of angles, it can be classified as an obtuse angled triangle and on the basis of side lengths, it can be classified as an scalene triangle.
4. Try to construct the triangle using match sticks. Can you make a triangle with the following number of match sticks? Also, state the reason if a triangle cannot be constructed with the given number of match sticks.
3 match sticks
Ans: An acute angled triangle can be made using three matchsticks because the sum of the two sides of a triangle can never be less than the third side. So, here, an acute angle will be formed.
4 match sticks
Ans: Four matchsticks can be arranged in the following way.
We can see that the figure formed is a square. So, a triangle cannot be made using 4 match sticks.
5 match sticks
Ans: Five matchsticks can be arranged in two ways shown below.
An acute angled triangle can be made using five matchsticks because the sum of the two sides of a triangle can never be less than the third side. So, here, an acute angle will be formed.
6 matchsticks
Ans: Six matchsticks can be arranged in the following way.
An acute angled triangle can be made using six matchsticks because the sum of the two sides of a triangle can never be less than the third side. So, here, an acute angle will be formed.
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.6
Opting for the NCERT solutions for Ex 5.6 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.6 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 5 Exercise 5.6 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
Besides these NCERT solutions for Class 6 Maths Chapter 5 Exercise 5.6, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.
Do not delay any more. Download the NCERT solutions for Class 6 Maths Chapter 5 Exercise 5.6 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.
