ABCD is a trapezium such that `A B||C Da n dC B` is perpendicular to them. If `/_A D B=theta,B C=p ,a n dC D=q` , show that `A B=((p^2+q^2)sintheta)/(pcostheta+qsintheta)`

In Figure, A B C D is a trapezium with AB||DC . If /_\ A E D is similar to /_\ B E C , prove that A D=B C .

A B C D is a trapezium in which A B D C . P and Q are points on sides A D and B C such that P Q A B . If P D=18 , B Q=35 and Q C=15 , find A D .

In Figure, A P\ a n d\ B Q are perpendiculars to the line segment A B\ a n d\ A P=B Q . Prove that O is the mid-point of line segment A B\ a n d\ P Q

In Figure, line l is the bisector of angle A\ a n d\ B is any point on ldotB P\ a n d\ B Q are perpendiculars from B to the arms of Adot Show that: A P B\ ~= A Q B BP=BQ or B is equidistant from the arms of /_A

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C D . Prove that : (i) A D N~= C B P (ii) A N=C P

In Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /_A B D=/_A C D

In Figure, if A B=A C\ a n d\ /_B=/_Cdot Prove that B Q=C P

In Figure, A D\ _|_C D\ and C B\ _|_ CD If A Q=B P\ a n d\ D P=C Q , prove that /_D A Q=/_C B P dot

In a \ A B C ,\ A D bisects /_A\ a n d\ /_C >/_Bdot Prove that /_A D B >\ /_A D C .

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A P bisects " "/_A as well as /_D and A P is the perpendicular bisector of B C