NCERT Solutions, Exercise 6.3: Triangles, Class 10 (Mathematics) Notes - Class 10

Class 10: NCERT Solutions, Exercise 6.3: Triangles, Class 10 (Mathematics) Notes - Class 10

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Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
Exercise 6.3 
Question 1:  
State which pairs of triangles in the following figure are similar? Write the similarity 
criterion used by you for answering the question and also write the pairs of similar 
triangles in the symbolic form:  
(i)  
  
(ii)  
 
(iii)  
 
 
 
 
 
 
 
Page 2


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
Exercise 6.3 
Question 1:  
State which pairs of triangles in the following figure are similar? Write the similarity 
criterion used by you for answering the question and also write the pairs of similar 
triangles in the symbolic form:  
(i)  
  
(ii)  
 
(iii)  
 
 
 
 
 
 
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
(iv)  
  
(v)   
 
(vi)   
  
 
Answer 1:  
 (i) ?A = ?P = 60°  
?B = ?Q = 80°  
?C = ?R = 40°  
Therefore, ?ABC ~ ?PQR [By AAA similarity criterion]  
  
(iii)The given triangles are not similar as the corresponding sides are not proportional.  
( ii)    
Page 3


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
Exercise 6.3 
Question 1:  
State which pairs of triangles in the following figure are similar? Write the similarity 
criterion used by you for answering the question and also write the pairs of similar 
triangles in the symbolic form:  
(i)  
  
(ii)  
 
(iii)  
 
 
 
 
 
 
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
(iv)  
  
(v)   
 
(vi)   
  
 
Answer 1:  
 (i) ?A = ?P = 60°  
?B = ?Q = 80°  
?C = ?R = 40°  
Therefore, ?ABC ~ ?PQR [By AAA similarity criterion]  
  
(iii)The given triangles are not similar as the corresponding sides are not proportional.  
( ii)    
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
(iv)The given triangles are not similar as the corresponding sides are not proportional.  
(v)The given triangles are not similar as the corresponding sides are not proportional.  
(vi) In ?DEF,  
?D + ?E + ?F = 180º  (Sum of the measures of the angles of a triangle is 180º.)  
70º + 80º + ?F = 180º  
?F = 30º  
Similarly, in ?PQR,  
?P + ?Q + ?R = 180º  
(Sum of the measures of the angles of a triangle is 180º.)  
?P + 80º +30º = 180º  
?P = 70º   
In ?DEF and ?PQR,  
?D = ?P (Each 70°)  
?E = ?Q (Each 80°)  
?F = ?R (Each 30°)  
? ?DEF ~ ?PQR [By AAA similarity criterion]  
  
 
 
Question 2:  
In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC,  
?DCO and ?OAB  
 
Page 4


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
Exercise 6.3 
Question 1:  
State which pairs of triangles in the following figure are similar? Write the similarity 
criterion used by you for answering the question and also write the pairs of similar 
triangles in the symbolic form:  
(i)  
  
(ii)  
 
(iii)  
 
 
 
 
 
 
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
(iv)  
  
(v)   
 
(vi)   
  
 
Answer 1:  
 (i) ?A = ?P = 60°  
?B = ?Q = 80°  
?C = ?R = 40°  
Therefore, ?ABC ~ ?PQR [By AAA similarity criterion]  
  
(iii)The given triangles are not similar as the corresponding sides are not proportional.  
( ii)    
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
(iv)The given triangles are not similar as the corresponding sides are not proportional.  
(v)The given triangles are not similar as the corresponding sides are not proportional.  
(vi) In ?DEF,  
?D + ?E + ?F = 180º  (Sum of the measures of the angles of a triangle is 180º.)  
70º + 80º + ?F = 180º  
?F = 30º  
Similarly, in ?PQR,  
?P + ?Q + ?R = 180º  
(Sum of the measures of the angles of a triangle is 180º.)  
?P + 80º +30º = 180º  
?P = 70º   
In ?DEF and ?PQR,  
?D = ?P (Each 70°)  
?E = ?Q (Each 80°)  
?F = ?R (Each 30°)  
? ?DEF ~ ?PQR [By AAA similarity criterion]  
  
 
 
Question 2:  
In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC,  
?DCO and ?OAB  
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
4 
Answer 2:  
DOB is a straight line.  
? ?DOC + ?COB = 180°  
? ?DOC = 180° - 125° = 55°  
In ?DOC,  
?DCO + ?CDO + ?DOC = 180°  
(Sum of the measures of the angles of a triangle is 180º.)  
? ?DCO + 70º + 55º = 180°  
? ?DCO = 55°  
It is given that ?ODC ~ ?OBA.  
? ?OAB = ? OCD [Corresponding angles are equal in similar triangles.]  
? ?OAB = 55°  
  
Question 3:  
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the  
 
point O. Using a similarity criterion for two triangles, show that   
 
Answer 3:  
 
In ?DOC and ?BOA,  
?CDO = ?ABO [Alternate interior angles as AB || CD]  
?DCO = ?BAO [Alternate interior angles as AB || CD]  
?DOC = ?BOA [Vertically opposite angles]  
Page 5


Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
1 
Exercise 6.3 
Question 1:  
State which pairs of triangles in the following figure are similar? Write the similarity 
criterion used by you for answering the question and also write the pairs of similar 
triangles in the symbolic form:  
(i)  
  
(ii)  
 
(iii)  
 
 
 
 
 
 
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
2 
(iv)  
  
(v)   
 
(vi)   
  
 
Answer 1:  
 (i) ?A = ?P = 60°  
?B = ?Q = 80°  
?C = ?R = 40°  
Therefore, ?ABC ~ ?PQR [By AAA similarity criterion]  
  
(iii)The given triangles are not similar as the corresponding sides are not proportional.  
( ii)    
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
3 
(iv)The given triangles are not similar as the corresponding sides are not proportional.  
(v)The given triangles are not similar as the corresponding sides are not proportional.  
(vi) In ?DEF,  
?D + ?E + ?F = 180º  (Sum of the measures of the angles of a triangle is 180º.)  
70º + 80º + ?F = 180º  
?F = 30º  
Similarly, in ?PQR,  
?P + ?Q + ?R = 180º  
(Sum of the measures of the angles of a triangle is 180º.)  
?P + 80º +30º = 180º  
?P = 70º   
In ?DEF and ?PQR,  
?D = ?P (Each 70°)  
?E = ?Q (Each 80°)  
?F = ?R (Each 30°)  
? ?DEF ~ ?PQR [By AAA similarity criterion]  
  
 
 
Question 2:  
In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC,  
?DCO and ?OAB  
 
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
4 
Answer 2:  
DOB is a straight line.  
? ?DOC + ?COB = 180°  
? ?DOC = 180° - 125° = 55°  
In ?DOC,  
?DCO + ?CDO + ?DOC = 180°  
(Sum of the measures of the angles of a triangle is 180º.)  
? ?DCO + 70º + 55º = 180°  
? ?DCO = 55°  
It is given that ?ODC ~ ?OBA.  
? ?OAB = ? OCD [Corresponding angles are equal in similar triangles.]  
? ?OAB = 55°  
  
Question 3:  
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the  
 
point O. Using a similarity criterion for two triangles, show that   
 
Answer 3:  
 
In ?DOC and ?BOA,  
?CDO = ?ABO [Alternate interior angles as AB || CD]  
?DCO = ?BAO [Alternate interior angles as AB || CD]  
?DOC = ?BOA [Vertically opposite angles]  
Mathematics 
(www.tiwariacademy.com) 
(Chapter – 6) (Triangles)  
(Class – X) 
 
www.tiwariacademy.com  
5 
? ?DOC ~ ?BOA [AAA similarity criterion]  
  
 
Question 4:  
 
 
Show that    
 
 
Answer 4:  
 
In ?PQR, ?PQR = ?PRQ  
? PQ = PR ………………(i)  
In the following figure,  
  
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