Class 6 Exam > Class 6 Notes > Mathematics (Maths) Class 6 > RD Sharma Solutions: Triangles (Exercise 12.1)
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Page 1
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
Page 2
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
Page 3
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
Page 4
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
(x) Exterior of a triangle – The region which lies outside the triangle is called the exterior of a triangle.
8. In Fig. 12.13, the length (in cm) of each side has been indicated along the side. State for each triangle
whether it is scalene, isosceles or equilateral.
Solution:
(i) It is a scalene triangle having sides of different lengths.
(ii) It is an isosceles triangle having two sides of same length i.e. 5.6 cm.
(iii) It is an equilateral triangle having all sides of same length i.e. 5 cm.
(iv) It is a scalene triangle having sides of different lengths.
(v) It is an isosceles triangle having two sides of same length i.e. 6.2 cm.
9. In Fig. 12.14, there are five triangles. The measures of some of their angles have been indicated. State for
each triangle whether it is acute, right or obtuse.
Solution:
Page 5
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
(x) Exterior of a triangle – The region which lies outside the triangle is called the exterior of a triangle.
8. In Fig. 12.13, the length (in cm) of each side has been indicated along the side. State for each triangle
whether it is scalene, isosceles or equilateral.
Solution:
(i) It is a scalene triangle having sides of different lengths.
(ii) It is an isosceles triangle having two sides of same length i.e. 5.6 cm.
(iii) It is an equilateral triangle having all sides of same length i.e. 5 cm.
(iv) It is a scalene triangle having sides of different lengths.
(v) It is an isosceles triangle having two sides of same length i.e. 6.2 cm.
9. In Fig. 12.14, there are five triangles. The measures of some of their angles have been indicated. State for
each triangle whether it is acute, right or obtuse.
Solution:
(i) It is a right triangle with one angle as 90
o
.
(ii) It is an obtuse triangle with one angle as 120
o
.
(iii) It is an acute triangle with one angle as 60
o
.
(iv) It is a right triangle with one angle as 90
o
.
(v) It is an obtuse triangle with one angle as 110
o
.
10. Fill in the blanks with the correct word/symbol to make it a true statement:
(i) A triangle has ……. sides.
(ii) A triangle has …….. verticals.
(iii) A triangle has …….. angles.
(iv) A triangle has …….. parts.
(v) A triangle whose no two sides are equal is known as ……..
(vi) A triangle whose two sides are equal is known as ……..
(vii) A triangle whose all the sides are equal is known as …….
(viii) A triangle whose one angle is a right angle is known as ……..
(ix) A triangle whose all the angles are of measures less than 90
o
is known as …….
(x) A triangle whose one angle is more than 90
o
is known as …….
Solution:
(i) A triangle has three sides.
(ii) A triangle has three verticals.
(iii) A triangle has three angles.
(iv) A triangle has six parts.
(v) A triangle whose no two sides are equal is known as scalene.
(vi) A triangle whose two sides are equal is known as isosceles.
(vii) A triangle whose all the sides are equal is known as equilateral.
(viii) A triangle whose one angle is a right angle is known as right triangle.
(ix) A triangle whose all the angles are of measures less than 90
o
is known as acute triangle.
(x) A triangle whose one angle is more than 90
o
is known as obtuse triangle.
11. In each of the following, state if the statement is true (T) or false (F):
(i) A triangle has three sides.
(ii) A triangle may have four vertices.
(iii) Any three line-segments make up a triangle.
(iv) The interior of a triangle includes its vertices.
(v) The triangular region includes the vertices of the corresponding triangle.
(vi) The vertices of a triangle are three collinear points.
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FAQs on Triangles (Exercise 12.1) RD Sharma Solutions - Mathematics (Maths) Class 6
| 1. How to find the area of a triangle? |  |
Ans. To find the area of a triangle, multiply the length of the base by the height and divide the result by 2. The formula for the area of a triangle is A = (base * height) / 2.
| 2. What is the Pythagorean theorem and how is it used in triangles? | |
Ans. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is often used to find the length of one side of a right-angled triangle when the lengths of the other two sides are known.
| 3. How do we classify triangles based on their angles? | |
Ans. Triangles can be classified based on their angles as follows:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
| 4. What is the difference between an equilateral triangle and an isosceles triangle? | |
Ans. An equilateral triangle has all three sides and angles equal in length and measure, while an isosceles triangle has two sides and angles equal in length and measure.
| 5. How can we determine if two triangles are similar? | |
Ans. Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. This means that the ratio of the lengths of corresponding sides in the two triangles will be the same.
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Dec 30, 2024 Last updated |
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