NCERT Solutions, Exercise 6.4, Triangles, Class 10 (Mathematics) Class 10 Notes | EduRev

Class 10 : NCERT Solutions, Exercise 6.4, Triangles, Class 10 (Mathematics) Class 10 Notes | EduRev

 Page 1


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
 
Exercise 6.4  
Question 1: 
Let and their areas be, respectively, 64 cm
2
 and 121 cm
2
. If EF =  
15.4 cm, find BC.  
 
Answer 1:  
  
  
 
  
  
Page 2


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
 
Exercise 6.4  
Question 1: 
Let and their areas be, respectively, 64 cm
2
 and 121 cm
2
. If EF =  
15.4 cm, find BC.  
 
Answer 1:  
  
  
 
  
  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
 
Question 2:  
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB 
= 2CD, find the ratio of the areas of triangles AOB and COD.  
 
 
Answer 2:  
 
 
 
Since AB || CD,  
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)  
In ?AOB and ?COD,  
?AOB = ?COD (Vertically opposite angles)  
?OAB = ?OCD (Alternate interior angles)  
?OBA = ?ODC (Alternate interior angles)  
? ?AOB ~ ?COD (By AAA similarity criterion)  
  
  
 
Page 3


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
 
Exercise 6.4  
Question 1: 
Let and their areas be, respectively, 64 cm
2
 and 121 cm
2
. If EF =  
15.4 cm, find BC.  
 
Answer 1:  
  
  
 
  
  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
 
Question 2:  
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB 
= 2CD, find the ratio of the areas of triangles AOB and COD.  
 
 
Answer 2:  
 
 
 
Since AB || CD,  
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)  
In ?AOB and ?COD,  
?AOB = ?COD (Vertically opposite angles)  
?OAB = ?OCD (Alternate interior angles)  
?OBA = ?ODC (Alternate interior angles)  
? ?AOB ~ ?COD (By AAA similarity criterion)  
  
  
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
Question 3:  
In the following figure, ABC and DBC are two triangles on the same base BC. If AD  
  
 
Answer 3:  
Let us draw two perpendiculars AP and DM on line BC.  
  
In ?APO and ?DMO,  
?APO = ?DMO (Each = 90°)  
?AOP = ?DOM (Vertically opposite angles)  
? ?APO ~ ?DMO (By AA similarity criterion)  
  
 
intersects BC at O, show that  
  
  
We know that area of a triangle =  
.  
Page 4


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
 
Exercise 6.4  
Question 1: 
Let and their areas be, respectively, 64 cm
2
 and 121 cm
2
. If EF =  
15.4 cm, find BC.  
 
Answer 1:  
  
  
 
  
  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
 
Question 2:  
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB 
= 2CD, find the ratio of the areas of triangles AOB and COD.  
 
 
Answer 2:  
 
 
 
Since AB || CD,  
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)  
In ?AOB and ?COD,  
?AOB = ?COD (Vertically opposite angles)  
?OAB = ?OCD (Alternate interior angles)  
?OBA = ?ODC (Alternate interior angles)  
? ?AOB ~ ?COD (By AAA similarity criterion)  
  
  
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
Question 3:  
In the following figure, ABC and DBC are two triangles on the same base BC. If AD  
  
 
Answer 3:  
Let us draw two perpendiculars AP and DM on line BC.  
  
In ?APO and ?DMO,  
?APO = ?DMO (Each = 90°)  
?AOP = ?DOM (Vertically opposite angles)  
? ?APO ~ ?DMO (By AA similarity criterion)  
  
 
intersects BC at O, show that  
  
  
We know that area of a triangle =  
.  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
4 
Question 4:  
If the areas of two similar triangles are equal, prove that they are congruent.  
 
Answer 4:  
Let us assume two similar triangles as ?ABC ~ ?PQR.  
  
 
Question 5:  
D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio 
of the area of ?DEF and ?ABC.  
 
Answer 5:  
 
D and E are the mid-points of ?ABC.  
Page 5


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
 
Exercise 6.4  
Question 1: 
Let and their areas be, respectively, 64 cm
2
 and 121 cm
2
. If EF =  
15.4 cm, find BC.  
 
Answer 1:  
  
  
 
  
  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
 
Question 2:  
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB 
= 2CD, find the ratio of the areas of triangles AOB and COD.  
 
 
Answer 2:  
 
 
 
Since AB || CD,  
? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles)  
In ?AOB and ?COD,  
?AOB = ?COD (Vertically opposite angles)  
?OAB = ?OCD (Alternate interior angles)  
?OBA = ?ODC (Alternate interior angles)  
? ?AOB ~ ?COD (By AAA similarity criterion)  
  
  
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
Question 3:  
In the following figure, ABC and DBC are two triangles on the same base BC. If AD  
  
 
Answer 3:  
Let us draw two perpendiculars AP and DM on line BC.  
  
In ?APO and ?DMO,  
?APO = ?DMO (Each = 90°)  
?AOP = ?DOM (Vertically opposite angles)  
? ?APO ~ ?DMO (By AA similarity criterion)  
  
 
intersects BC at O, show that  
  
  
We know that area of a triangle =  
.  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
4 
Question 4:  
If the areas of two similar triangles are equal, prove that they are congruent.  
 
Answer 4:  
Let us assume two similar triangles as ?ABC ~ ?PQR.  
  
 
Question 5:  
D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio 
of the area of ?DEF and ?ABC.  
 
Answer 5:  
 
D and E are the mid-points of ?ABC.  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
5 
 
 
  
 
 
Question 6:  
Prove that the ratio of the areas of two similar triangles is equal to the square  of 
the ratio of their corresponding medians.  
 
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