In ` A B C` , if `A D` is the bisector of `/_A` , prove that: `(A r e a( A B D))/(A r e a( A C D))=(A B)/(A C)`

In triangle A B C , if A D is the bisector of /_A , prove that: (A r e a( A B D))/(A r e a( A C D))=(A B)/(A C)

In Figure, /_\ A B C and /_\ D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) .

In Fig. 4.179, A B C and D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) (FIGURE)

In Figure, /_B A C=90^0,A D is its bisector. If D E_|_A c , prove that DE ×(A B+A C)=A B×A C

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot Prove that A D=2A B

In a parallelogram A B C D , the bisector of /_A also bisects B C at X . Prove that A D=2A B .

In a \ A B C ,\ A D bisects /_A\ a n d\ /_C >/_Bdot Prove that /_A D B >\ /_A D C .

A B C D is a trapezium in which A B C D . The diagonals A C and B D intersect at O . Prove that (i) A O B C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a ( A O B))/(A r e a ( C O D)) (b) (A r e a ( A O D))/(A r e a ( C O D))

If A B C D is a parallelogram, then prove that a r\ (\ A B D)=\ a r\ (\ B C D)=\ a r\ (\ A B C)=\ a r\ (\ A C D)=1/2\ a r\ (|""|^(gm)A B C D)

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot prove that A D=2A Bdot