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

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

A B C D is a trapezium with A B||D C . A line parallel to A C intersects A B\ at X\ a n d\ B C at Ydot Prove that a r( A D X)=a r(\ A C Y)dot

A B C D is a trapezium with A B || D C . A line parallel to A C intersects A B at X and B C at Y . Prove that a r( triangle A D X)=a r(triangle A C Y) .

ABCD is a trapezium with A B|| D C . A line parallel to AC intersects AB at X and BC at Y. Prove that a r\ (A D X)\ =\ a r\ (A C Y) .

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) .

X Y is a line parallel to side B C of /_\ A B C . B E || AC and C F || A B meet X Y in E and F respectively. Show that a r( A B E)=a r( A C F) .

X Y is a line parallel to side B C of triangle A B C . If B E II A C and C F II A B meet X Y at E and F respectively.Show that a r( A B E)=a r( A C F)dot

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D) GIVEN : A parallelogram A B C D in which X and Y are the mid-points of B C and C D respectively. TO PROVE : a r( A X Y)=3/8a r(^(gm)a b c d) CONSTRUCTION : Join B Ddot

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D)

In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q are extended to X\ a n d\ Y respectively and /_A B X=/_P Q Y . Prove that A B C~=\ P Q R .