Two triangles `B A Ca n dB D C` , right angled at `Aa n dD` respectively, are drawn on the same base `B C` and on the same side of `B C` . If `A C` and `D B` intersect at `P ,` prove that `A PxP C=D PxP Bdot`

Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, are drawn on the same base B C and on the same side of B C . If A C and D B intersect at P , prove that A P*P C=D P*P Bdot

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 B D\ ~= A C D (ii) A B P\ ~= A C P

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

Two circle with centres A and B intersect at C and Ddot Prove that /_A C B=/_A D Bdot

In Figure, /_\ A B C and /_\ D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) .

A triangle A B C is right angled at A. AL is drawn perpendicular to B C . Prove that /_B A L=/_A C Bdot

In two triangles A B C\ a n d\ A D C , if A B=A D\ a n d\ B C=C Ddot Are they congruent?

In Figure, A B C\ a n d\ D B C are two isosceles triangles on the same base B C such that A B=A C\ a n d\ D B=C Ddot Prove that /_A B D=\ /_A C D

In Figure, A B C\ a n d\ D B C are two triangles on the same base B C such that A B=A C\ a n d\ D B=D Cdot Prove that /_A B D=/_A C D

If D is any point on the base B C produced, of an isosceles triangle A B C , prove that A D > A Bdot