Properties of Triangles (Exercise 15.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

 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: 
 
(i) The side opposite to ?B is AC 
 
(ii) The angle opposite to side AB is ?C 
 
(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 note book. Join AB. BC and 
CA. Is the figure a triangle? If not, why? 
 
Solution: 
 
No, the figure is not a triangle. By definition a triangle is a plane figure formed by three 
non-parallel line segments 
 
3. Distinguish between a triangle and its triangular region. 
 
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: 
 
(i) The side opposite to ?B is AC 
 
(ii) The angle opposite to side AB is ?C 
 
(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 note book. Join AB. BC and 
CA. Is the figure a triangle? If not, why? 
 
Solution: 
 
No, the figure is not a triangle. By definition a triangle is a plane figure formed by three 
non-parallel line segments 
 
3. Distinguish between a triangle and its triangular region. 
 
 
 
 
 
 
 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
4. D is a point on side BC of a ?CAD is joined. Name all the triangles that you can 
observe in the figure. How many are they? 
 
Solution: 
We can observe the following three triangles in the given figure 
? ABC 
? ACD 
? ADB 
 
5. 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: 
Given A, B, C and D are four points, and no three points are collinear 
? ABC 
? ACD 
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: 
 
(i) The side opposite to ?B is AC 
 
(ii) The angle opposite to side AB is ?C 
 
(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 note book. Join AB. BC and 
CA. Is the figure a triangle? If not, why? 
 
Solution: 
 
No, the figure is not a triangle. By definition a triangle is a plane figure formed by three 
non-parallel line segments 
 
3. Distinguish between a triangle and its triangular region. 
 
 
 
 
 
 
 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
4. D is a point on side BC of a ?CAD is joined. Name all the triangles that you can 
observe in the figure. How many are they? 
 
Solution: 
We can observe the following three triangles in the given figure 
? ABC 
? ACD 
? ADB 
 
5. 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: 
Given A, B, C and D are four points, and no three points are collinear 
? ABC 
? ACD 
 
 
 
 
 
 
 
? DBC 
? ABD 
? AOB 
? BOC 
? COD 
? AOD 
 
6. What is the difference between a triangle and triangular region? 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
7. Explain the following terms: 
(i) Triangle 
(a) 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) A triangle is a plane figure formed by three non-parallel line segments. 
 
(ii) The three sides and the three angles of a triangle are together known as the parts or 
elements of that triangle. 
 
(iii) A scalene triangle is a triangle in which no two sides are equal. 
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: 
 
(i) The side opposite to ?B is AC 
 
(ii) The angle opposite to side AB is ?C 
 
(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 note book. Join AB. BC and 
CA. Is the figure a triangle? If not, why? 
 
Solution: 
 
No, the figure is not a triangle. By definition a triangle is a plane figure formed by three 
non-parallel line segments 
 
3. Distinguish between a triangle and its triangular region. 
 
 
 
 
 
 
 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
4. D is a point on side BC of a ?CAD is joined. Name all the triangles that you can 
observe in the figure. How many are they? 
 
Solution: 
We can observe the following three triangles in the given figure 
? ABC 
? ACD 
? ADB 
 
5. 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: 
Given A, B, C and D are four points, and no three points are collinear 
? ABC 
? ACD 
 
 
 
 
 
 
 
? DBC 
? ABD 
? AOB 
? BOC 
? COD 
? AOD 
 
6. What is the difference between a triangle and triangular region? 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
7. Explain the following terms: 
(i) Triangle 
(a) 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) A triangle is a plane figure formed by three non-parallel line segments. 
 
(ii) The three sides and the three angles of a triangle are together known as the parts or 
elements of that triangle. 
 
(iii) A scalene triangle is a triangle in which no two sides are equal. 
 
 
 
 
 
 
 
 
 
 
(iv) An isosceles triangle is a triangle in which two sides are equal.  
 
 
(v) An equilateral triangle is a triangle in which all three sides are equal.  
 
 
(vi) An acute triangle is a triangle in which all the angles are less than 90
o
. 
 
 
(vii) A right angled triangle is a triangle in which one angle should be equal to 90
o
. 
 
 
(viii) An obtuse triangle is a triangle in which one angle is more than 90
o
. 
 
 
(ix)  The interior of a triangle is made up of all such points that are enclosed within the 
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: 
 
(i) The side opposite to ?B is AC 
 
(ii) The angle opposite to side AB is ?C 
 
(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 note book. Join AB. BC and 
CA. Is the figure a triangle? If not, why? 
 
Solution: 
 
No, the figure is not a triangle. By definition a triangle is a plane figure formed by three 
non-parallel line segments 
 
3. Distinguish between a triangle and its triangular region. 
 
 
 
 
 
 
 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
4. D is a point on side BC of a ?CAD is joined. Name all the triangles that you can 
observe in the figure. How many are they? 
 
Solution: 
We can observe the following three triangles in the given figure 
? ABC 
? ACD 
? ADB 
 
5. 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: 
Given A, B, C and D are four points, and no three points are collinear 
? ABC 
? ACD 
 
 
 
 
 
 
 
? DBC 
? ABD 
? AOB 
? BOC 
? COD 
? AOD 
 
6. What is the difference between a triangle and triangular region? 
 
Solution: 
Triangle: 
A triangle is a plane figure formed by three non-parallel line segments. 
Triangular region: 
Whereas, it’s triangular region includes the interior of the triangle along with the 
triangle itself. 
 
7. Explain the following terms: 
(i) Triangle 
(a) 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) A triangle is a plane figure formed by three non-parallel line segments. 
 
(ii) The three sides and the three angles of a triangle are together known as the parts or 
elements of that triangle. 
 
(iii) A scalene triangle is a triangle in which no two sides are equal. 
 
 
 
 
 
 
 
 
 
 
(iv) An isosceles triangle is a triangle in which two sides are equal.  
 
 
(v) An equilateral triangle is a triangle in which all three sides are equal.  
 
 
(vi) An acute triangle is a triangle in which all the angles are less than 90
o
. 
 
 
(vii) A right angled triangle is a triangle in which one angle should be equal to 90
o
. 
 
 
(viii) An obtuse triangle is a triangle in which one angle is more than 90
o
. 
 
 
(ix)  The interior of a triangle is made up of all such points that are enclosed within the 
 
 
 
 
 
 
 
triangle. 
 
(x) The exterior of a triangle is made up of all such points that are not enclosed within 
the triangle. 
  
8. In Fig. 11, the length (in cm) of each side has been indicated along the side. State for 
each triangle angle whether it is scalene, isosceles or equilateral: 
 
 
Solution: 
(i) The given triangle is a scalene triangle because no two sides are equal. 
 
(ii) The given triangle is an isosceles triangle because two of its sides, viz. PQ and PR, are 
equal. 
(iii) The given triangle is an equilateral triangle because all its three sides are equal. 
 
(iv) The given triangle is a scalene triangle because no two sides are equal. 
 
(v) The given triangle is an isosceles triangle because two of its sides are equal. 
 
9. In Fig. 12, 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.