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`

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that /_A B D\ =/_A C D

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

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

In Figure, A B C\ a n d\ ABD are two triangles on the base A Bdot If line segment C D is bisected by A B\ a t\ O , show that a r\ ( A B C)=a r\ (\ A B D)

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

In Figure, it is given that A B=C F , E F=B D a n d /_A F E= /_C B Ddot Prove that A F E= ~= C B D

In Fig. 4.124, E is a point on side C B produced of an isosceles triangle A B C with A B=A C . If A D_|_B C and E F_|_A C , prove that (i) A B D E C F (ii) A BxxE F=A DxxE C . (FIGURE)

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure