In ` A B C` , a line `X Y` parallel to `B C` cuts `A B` at `X` and `A C` at `Y` . If `B Y` bisects `/_X Y C` , then `B C=C Y` (b) `B C=B Y` (c) `B C!=C Y` (d) `B C!=B Y`

In A B C , a line X Y parallel to B C cuts A B at X and A C at Y . If B Y bisects /_X Y C , then (a) B C=C Y (b) B C=B Y (c) B C!=C Y (d) B C!=B Y

X Y is drawn parallel to the base B C of a A B C cutting A B at X and A C at Y . If A B=4 B X and Y C=2c m , then A Y= 2c m (b) 4c m (c) 6c m (d) 8c m

X Y is drawn parallel to the base B C of Delta A B C cutting A B at X and A C at Y . If A B=4\ B X and Y C=2c m , then A Y= (a) 2c m (b) 4c m (c) 6c m (d) 8c m

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) .

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) .

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, 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, 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, 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) .

If x/(b + c -a) = y/(c + a - b) = z/(a + b -c) , then show that (b -c) x + (c-a) y + (a -b) z = 0 .