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, Δ ABC ∼ Δ DEF. Find the lengths of the sides of both the triangles (Each side is in cm).
In Δ ABC and Δ DEF, AB = 3 x DF, BC = 3 x DE and AC = 3 x EF. Show that the given triangle are similar. Name the two similar triangle on a proper way.
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