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 BACandBDC, right angled at Aand D respectively,are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove that APxPC=DPxPB.

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 Fig. 4.179, 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) (FIGURE)

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.

Triangles A B C and +DBC are on the same base B C with A, D on opposite side of line B C , such that a r(_|_ A B C)=a r( D B C)dot Show that B C bisects A Ddot

In right triangle A B C , right angle at C , M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Ddot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B