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 and D B C are two isosceles triangles on the same base B C and vertices A and D are on the same side of B D . 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 P bisects /_A as well as /_D A P is perpendicular bisector of B Cdot

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 A P is the perpendicular bisector of B C

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

Two triangle ABC and D B C lie on the same side of the base B C . From a point P on B C ,P Q A B AND P R B D ARE DRAWN. They meet A C in Q and D C in R respectively. Prove that Q R A Ddot

Triangles on the same base and between the same parallels are equal in area. GIVEN : Two triangles A B C and P B C on the same base B C and between the same parallel lines B C and A Pdot TO PROVE : a r( A B C)=a r( P B C) CONSTRUCTION : Through B , draw B D C A intersecting P A produced in D and through C , draw C Q B P , intersecting line A P in Q.

In figure ABC and AMP are two right triangles, right angles at B and M respectively. Prove that(i) DeltaA B C~ DeltaA M P (ii) (C A)/(P A)=(B C)/(M P)

A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersect at P . If A B=D C , Prove that : P A B~= P D C P A=P Da n dP C=P B A D B C

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H