Pair of Lines & Transversal (Exercise 15.2) RD Sharma Solutions | Mathematics for Class 6 PDF Download

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1. In Fig. 15.17, line n is a transversal to lines l and m. Identify the following: 
(i) Alternate and corresponding angles in Fig. 15.17 (i). 
(ii) Angles alternate to ?d and ?g and angles corresponding to ?f and ?h in Fig. 15.17 (ii). 
(iii) Angle alternative to ?PQR, angle corresponding to ?RQF and angle alternate to ?PQE in Fig. 15.17 
(iii). 
(iv) Pairs of interior and exterior angles on the same side of the transversal in Fig. 15.17 (ii). 
 
Solution: 
 
(i) Alternate interior angles are ?BGH and ?CHG; ?AGH and ?CHF 
Alternate exterior angles are ?AGE and ?DHF; ?EGB and ?CHF 
Corresponding angles are ?EGB and ?GHD; ?EGA and ?GHC; ?BGH and ?DHF; ?AGF and ?CHF. 
 
(ii) Angles alternate to ?d and ?g are ?e and ?b and angles corresponding to ?f and ?h are ?c and ?a. 
 
(iii) From the figure we know that l is transversal to m and n. 
Angle alternate to ?PQR is ?QRA  
Angle corresponding to ?RQF is ?BRA  
Angle alternate to ?PQE is ?BRA 
 
(iv) Interior angles are ?d, ?f and ?a, ?e and exterior angles are ?c, ?g and ?b, ?h 
 
2. Match column A and column B with the help of the Fig. 15.18: 
 Column A     Column B 
(i) Vertically opposite angles   (i) ?PAB and ?ABS 
(ii) Alternate angles    (ii) ?PAB and ?RBY
 
(iii) Corresponding angles   (iii) ?PAB and ?XAQ 
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1. In Fig. 15.17, line n is a transversal to lines l and m. Identify the following: 
(i) Alternate and corresponding angles in Fig. 15.17 (i). 
(ii) Angles alternate to ?d and ?g and angles corresponding to ?f and ?h in Fig. 15.17 (ii). 
(iii) Angle alternative to ?PQR, angle corresponding to ?RQF and angle alternate to ?PQE in Fig. 15.17 
(iii). 
(iv) Pairs of interior and exterior angles on the same side of the transversal in Fig. 15.17 (ii). 
 
Solution: 
 
(i) Alternate interior angles are ?BGH and ?CHG; ?AGH and ?CHF 
Alternate exterior angles are ?AGE and ?DHF; ?EGB and ?CHF 
Corresponding angles are ?EGB and ?GHD; ?EGA and ?GHC; ?BGH and ?DHF; ?AGF and ?CHF. 
 
(ii) Angles alternate to ?d and ?g are ?e and ?b and angles corresponding to ?f and ?h are ?c and ?a. 
 
(iii) From the figure we know that l is transversal to m and n. 
Angle alternate to ?PQR is ?QRA  
Angle corresponding to ?RQF is ?BRA  
Angle alternate to ?PQE is ?BRA 
 
(iv) Interior angles are ?d, ?f and ?a, ?e and exterior angles are ?c, ?g and ?b, ?h 
 
2. Match column A and column B with the help of the Fig. 15.18: 
 Column A     Column B 
(i) Vertically opposite angles   (i) ?PAB and ?ABS 
(ii) Alternate angles    (ii) ?PAB and ?RBY
 
(iii) Corresponding angles   (iii) ?PAB and ?XAQ 
 
 
 
 
 
 
 
Solution: 
 
(i) ?PAB and ?XAQ are vertically opposite angles 
 
(ii) ?PAB and ?ABS are alternate angles 
 
(iii) ?PAB and ?RBY are corresponding angles