In Figure, `X ,\ Y\ ` are two points on equal sides `A B\ a n d\ A C` of a ` A B C` such that `A X=A Ydot` Prove that `X C=Y B`

In Figure, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D C of a parallelogram A B C DdotA Y\ a n d\ D X are joined intersecting in P ; C X\ a n d\ B Y are joined intersecting in Q . Show that A X C Y is a parallelogram (ii) D X B Y\ is a parallelogram quadrilateral P X Q Y is a parallelogram

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, X ,Y are the mid-points of opposite sides A B and D C of a parallelogram A B C DdotA Y and D X are joined intersecting in P ; C X and B Y are joined intersecting in Qdot Show that DXBY is a parallelogram, P X Q Y is parallelogram.

A B is a line segment, A X and B Y are two equal line segments drawn on opposite sides of line A B such that A X B Ydot If A B and X Y intersect each other P , prove that A P X~=B P Y A B and X Y bisect each other.

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)

In figure D is a point on side BC of a DeltaA B C such that (B D)/(C D)=(A B)/(A C) . Prove that AD is the bisector of /_B A C .

In Figure, B C X Y ,\ B X C A and A B Y Cdot Prove that: a r( A B X)=a r( A C Y)

In Figure, A B C D is a parallelogram and X ,Y are the mid=points of sides A B and D C respectively. Show that A X C Y is a parallelogram. Figure

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B\ at X\ a n d\ D C at Ydot Prove that O X=O Y

In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extended to X and Y respectively and /_A B X =/_P Q Ydot Prove that A B C~=P Q Rdot Figure