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`

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

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)

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

In Figure, it is given that A B=B C a n d A D=E Cdot Prove that a b e ~= C B D (ii) B D=B E

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

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

A point D is taken on the side B C of a \ A B C such that B D=2D Cdot Prove that a r\ (\ A B D)=\ 2\ a r\ (\ A D C)

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C E

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