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

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 Find A B : A D

In Figure, A B C D is a trapezium in which A B||D C ,\ \ D C is produced to E such that C E=A B , prove that a r( A B D)=a r\ ( B C E)dot Construction: Draw D M\ on B A produced and B N_|_D C

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

In Figure, A B C D is a trapezium in which A B||C D . Prove that: a r( A O D)=a r( B O C)dot