Mathematics
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) ΔAPB is similar to ΔCPD.
(ii) PA x PD = PB x PC.
Related Questions
In the given figure, OD = 2 × OB, OC = 2 × OA and CD = 2 × AB then △ AOB ~ △ COD by :
AA
SS
SAS
SSS
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.
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.
In ΔABC, 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 x BC = BP x CA