In Fig. 4.116, `A B C D` is a trapezium with `A B D C` . If ` A E D` is similar to ` B E C` , prove that `A D=B C` . (FIGURE)

In Figure, A B C D is a trapezium with AB||DC . If /_\ A E D is similar to /_\ B E C , prove that A D=B C .

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

In Fig. 4.170, A B C D is a trapezium in which A B∥ D C and A B=2\ D C . Determine the ratio of the areas of A O B and C O D . (FIGURE)

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

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(triangle A B D)=a r (triangle B C E) . Construction: Draw D M\ on B A produced and B N_|_D C

In Figure, if A B=A C\ a n d\ B E=C D , prove that A D=A Edot

In Fig. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E

In Fig. 4.145, if A B_|_B C , D C_|_B C and D E_|_A C , prove that C E D ∼ A B C . (FIGURE)

In Fig. if E F|| D C|| A Bdot Prove that (A E)/(E D)=(B F)/(F C) . (FIGURE)

In Fig. if E F|| D C|| A Bdot Prove that (A E)/(E D)=(B F)/(F C) . (FIGURE)