Selina Textbook Solutions: Similarity | Mathematics Class 10 ICSE PDF Download

 Page 1


Similarity (With Applications to Maps & Models) 
 
Exercise 15A 
Question 1. 
In the figure, given below, straight lines AB and CD intersect at P; and AC // BD. Prove 
that: 
 
(i) ?APC and ?BPD are similar. 
(ii) If BD = 2.4 cm AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and 
PC. 
 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
Page 2


Similarity (With Applications to Maps & Models) 
 
Exercise 15A 
Question 1. 
In the figure, given below, straight lines AB and CD intersect at P; and AC // BD. Prove 
that: 
 
(i) ?APC and ?BPD are similar. 
(ii) If BD = 2.4 cm AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and 
PC. 
 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 2. 
In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD 
intersect each other at point P. Prove that: 
 
(i) ?APB is similar to ?CPD 
(ii) PA × PD = PB × PC 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
Page 3


Similarity (With Applications to Maps & Models) 
 
Exercise 15A 
Question 1. 
In the figure, given below, straight lines AB and CD intersect at P; and AC // BD. Prove 
that: 
 
(i) ?APC and ?BPD are similar. 
(ii) If BD = 2.4 cm AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and 
PC. 
 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 2. 
In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD 
intersect each other at point P. Prove that: 
 
(i) ?APB is similar to ?CPD 
(ii) PA × PD = PB × PC 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 3. 
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at 
point L, prove that: 
(i) DP: PL = DC: BL. 
(ii) DL: DP=AL: DC. 
 
Solution: 
(i) 
 
 
 
Page 4


Similarity (With Applications to Maps & Models) 
 
Exercise 15A 
Question 1. 
In the figure, given below, straight lines AB and CD intersect at P; and AC // BD. Prove 
that: 
 
(i) ?APC and ?BPD are similar. 
(ii) If BD = 2.4 cm AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and 
PC. 
 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 2. 
In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD 
intersect each other at point P. Prove that: 
 
(i) ?APB is similar to ?CPD 
(ii) PA × PD = PB × PC 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 3. 
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at 
point L, prove that: 
(i) DP: PL = DC: BL. 
(ii) DL: DP=AL: DC. 
 
Solution: 
(i) 
 
 
 
(ii) 
 
 
Question 4. 
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 
2CO and BO=2DO; show that: 
 
(i) ?AOB is similar to ?COD. 
(ii) OA × OD – OB × OC. 
 
Solution: 
 
(i) 
 
Page 5


Similarity (With Applications to Maps & Models) 
 
Exercise 15A 
Question 1. 
In the figure, given below, straight lines AB and CD intersect at P; and AC // BD. Prove 
that: 
 
(i) ?APC and ?BPD are similar. 
(ii) If BD = 2.4 cm AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and 
PC. 
 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 2. 
In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD 
intersect each other at point P. Prove that: 
 
(i) ?APB is similar to ?CPD 
(ii) PA × PD = PB × PC 
 
Solution: 
 
(i) 
 
 
(ii) 
 
 
 
Question 3. 
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at 
point L, prove that: 
(i) DP: PL = DC: BL. 
(ii) DL: DP=AL: DC. 
 
Solution: 
(i) 
 
 
 
(ii) 
 
 
Question 4. 
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 
2CO and BO=2DO; show that: 
 
(i) ?AOB is similar to ?COD. 
(ii) OA × OD – OB × OC. 
 
Solution: 
 
(i) 
 
 
 
(ii) 
 
 
Question 5. 
In ?ABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets 
the opposite side at point P. Show that: 
(i) CB: BA=CP: PA 
(ii) AB × BC = BP × CA 
 
Solution: 
(i)