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.

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=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.

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

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

ABC is a right triangle such that AB=AC and bisector of angle C intersects the side AB at D. prove that AC+AD=BC.

ABCD is a cyclic quadrilateral .The side BC is extended to E .The bisectors of the angles angleBADandangleDCE intersect at the point P .Prove that angleADC=angleAPC .

In a trapezium ABCD, if E and F be the mid-points of diagonal AC and BD respectively. Prove that EF=1/2(AB-CD).