NCERT Solution for Class 7 Maths Chapter 6
NCERT Solution for Class 7 Maths Chapter 6 The Triangle and its Properties, In this chapter we discuss about Median, Altitude and Angle sum property etc.
The student learn the given solutions and they can download the solution in pdf format of all the exercise of this chapter. Student can access directly here from the given link.
Definitions:
Medians of a triangle: A median connects a vertex of a triangle to the mid-point of the opposite side of the vertex.
Altitude of the triangle: An altitude is the shortest distance from the vertex to the opposite side of the vertex.
You can direct access here Class 7 Maths Chapter 5
Solutions Exercise 6.1
The student can access the solution of class 7 maths chapter 6 from the given link. For direct access the solutions click Exercise 6.2, Exercise 6.3, Exercise 6.4 and Exercise 6.5 . They can download the pdf of the all exercise from the link, which is given above.
Triangle and its Properties class 7 Exercise 6.2
Student Can access the solution of class 7 maths chapter 6 from the given link. For direct access the solutions click Exercise 6.1, Exercise 6.3, Exercise 6.4 and Exercise 6.5 . They can download the pdf of the all exercise from the link, which is given above.
Class 7 maths chapter 6 Solutions Exercise 6.3
For direct access the solutions click Exercise 6.1, Exercise 6.2, Exercise 6.4 and Exercise 6.5 . They can download the pdf of the all exercise from the link, which is given above.
Solution Exercise 6.4
Free pdf and solution for class 7 chapter 6 from the given link. For direct access the solutions click Exercise 6.1, Exercise 6.2, Exercise 6.3 and Exercise 6.5 . They can download the pdf of the all exercise from the link, which is given above.
Solution Exercise 6.5
The student can access the solution of class 7 maths chapter 6 from the given link. For direct access the solutions click Exercise 6.1, Exercise 6.2, Exercise 6.3, and Exercise 6.4 . They can download the pdf of the all exercise from the link, which is given above.
Definitions:
Medians of a triangle: A median connects a vertex of a triangle to the mid-point of the opposite side of the vertex.
Altitude of the triangle: An altitude is the shortest distance from the vertex to the opposite side of the vertex.
Think, Discuss and Write:
1. How many medians can a triangle have?
In any triangle there are three medians exist.
2. Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).
The answer of this statement is YES! Because it is known that median, divide the any sides of the triangle in two equal parts. Therefore the median of the triangle lies wholly interior in triangle.
1. How many altitudes can a triangle have?
In any triangle can have three altitudes. Altitude may be exterior or interior.
2. Will an altitude always lie in the interior of a triangle? If you think that this need not be true, draw a rough sketch to show such a case.
NO! Because it is known that the altitude of any triangle is the shortest distance from vertex to the opposite side. Therefore, the altitude of any triangle will be exterior or interior. So the given statement is not true.
3. Can you think of a triangle in which two altitudes of the triangle are two of its sides?
In a right angle triangle, which has two altitudes of the triangle are two of its sides?
4. Can the altitude and median be same for a triangle?
Yes! In an equilateral triangle, altitude and median are same.
5. Are the exterior angles formed at each vertex of a triangle equal?
The answer of this question is NO! Because it is possible that the sides of the triangle may be different length. If the length of the triangle is different then the exterior angle will be different. This statement holds in an equilateral triangle, because there are all sides are equal. Therefore all the exterior angle of the equilateral triangle is same. But not in an isosceles triangle, scalene triangle and a right triangle. class 7 maths chapter 6.
6. What can you say about the sum of an exterior angle of a triangle and its adjacent interior angle?
The sum of an exterior angle of a triangle and interior angle are 180 degree. Therefore they make linear pair. And you also can say that, it is a supplementary angle, exterior, and interior angle are supplement to each other.
Question related to Definitions:
1. What can you say about each of the interior opposite angles, when the exterior angle is (i) a right angle? (ii) an obtuse angle? (iii) an acute angle?
Answer:
(i) If an exterior angle of any triangle is a right angle then interior opposite angle will be acute angles.
(ii) If an exterior angle of any triangle is an obtuse angle then interior opposite angle will acute angles and obtuse angle.
(iii) If an exterior angle of any triangle is an acute angle then interior opposite angle will be acute angles.
2. Can the exterior angle of a triangle be a straight angle?
NO! It is impossible, it is known that the sum of all angles in a triangle is 180 degree. If any exterior angle will 180 degree, then two sides of the triangle collapse to each other.Then triangle will not exist. Therefore any exterior angle of the triangle can not be 180 degree.
Questions related to Angles:
1. Can you have a triangle with two right angles?
We know that the sum of all angles of the triangle is 180 degree. But if the sum of any two angles will 180 degree (Two right angle). Then third angle should be zero, which is not possible. Therefore two right angles in a triangle can not be possible.
2. Can you have a triangle with two obtuse angles?
It is known that the sum of all angles of the triangle is 180 degree. And it is also known that obtuse angle is measured greater than 90 degree but less than 180 degree. Let we take two obtuse angles (100 degree and 120 degree) of a triangle, then the sum of both angles are (100 +120) = 220 degree. Which is greater than 180 degree. Then third angle should be – 30 degree for satisfy the angle sum property. Therefore two obtuse angles in a triangle can not be possible.
3. Can you have a triangle with two acute angles?
Yes! It is possible. In a right-angle triangle with one angle is 90 degree but other two angles are always acute angles.
4. Can you have a triangle with all the three angles greater than 60º?
It is not possible! We know that angle sum property of any triangle, the sum of all angles of a triangle are 180 degree. Let we take all angles greater than 60 degree then the sum of all angles will greater than 180 degree. Which is contradict the angle sum property. Therefore all the three angles of the triangle will greater than 60º, it is not possible.
5. Can you have a triangle with all the three angles equal to 60º?
I have the triangle named equilateral triangle, which all the three angles are 60 degree.
6. Can you have a triangle with all the three angles less than 60º?
Reading the above statement in the question, It is not possible that all the three angles of the triangle are less than 60 degree. Because it is known that the sum of all the three angles of the triangle are 180 degree. But if we take all the angles less than 60 degree, then the sum will be less than 180 degrees. Therefore it is not possible that all the three angles will less than 60 degrees. class 7 maths chapter 6.
7. Is the sum of any two angles of a triangle always greater than the third angle?
The sum of any two angles of a triangle is not always greater than third angles. For Example, If we take right angle triangle, in this case this condition is not followed. In equilateral triangle this condition will followed.