ICSE Class 10th Mathematics Chapter 15 - Similarity Important Questions with Answers

In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: ?APC and ?BPD are similar.

In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: 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.

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 :

1. ?APB is similar to ?CPD.
2. PA × PD = PB × PC. 

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DP : PL = DC : BL.

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DL : DP = AL : DC.

In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: ?AOB is similar to ?COD.

In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: OA × OD = OB × OC.

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: CB : BA = CP : PA

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: AB × BC = BP × CA 

In ?ABC; BM ? AC and CN ? AB; show that:

`(AB)/(AC) = (BM)/(CN) = (AM)/(AN)`