ABCD is a quadrilateral in which AB=AD . The bisector of  BAC AND CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.

ABCD is a quadrilateral in which AB=AD. The bisector of /_BAC AND /_CAD intersect the sides BCandCD at the points EandF respectively.Prove that EF/_BD

ABCD is a quadrilateral in which AB= AD, the bisector of angle BAC and angle CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF || BD.

If ABCD is a quadrilateral in which AB|CD and AD=BC, prove that /_A=/_B.

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects both the angle ABC and angle ADC .

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects boht the angle ABC and ADC

AD is a median of triangleABC . The bisectors of angleADB and angleADC meets AB and AC in E and F respectively prove that EF||BC.

ABCD is a quadrilateral in which AD=BC and angleADB=angleCBA . Prove that: BD=AC

In an isosceles right-angled triangle ABC, /_B=90^(@) . The bisector of /_BAC intersects the side BC at the point D. Prove that CD^(2) =2BD^(2)

AD is a median of Delta ABC. The bisector of /_ADB and /_ADC meet AB and AC in E and F respectively.Prove that EF |BC

In the following figure , ABCD is a cyclic quadrilateral in which AD is parallel to BC . If the bisector of angle A meets BC at point E and given circle at point F, prove that : (i) EF =FC (ii) BF = DF