Triangles `A B C` and +DBC are on the same base `B C` with A, D on opposite side of line `B C ,` such that `a r(_|_ A B C)=a r( D B C)dot` Show that `B C` bisects `A Ddot`

Triangles A B C and DBC are on the same base B C with A, D on opposite side of line B C , such that a r(triangle A B C)=a r( triangle D B C) . Show that B C bisects A D .

In Figure, D , E are points on sides A B and A C respectively of A B C , such that a r( B C E)=a r( B C D)dot Show that DE ll BC .

In figure ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (a r(A B C))/(a r(D B C))=(A O)/(D O) .

In figure ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (a r(A B C))/(a r(D B C))=(A O)/(D O) .

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

Triangles on the same base and between the same parallels are equal in area. GIVEN : Two triangles A B C and P B C on the same base B C and between the same parallel lines B C and A Pdot TO PROVE : a r( A B C)=a r( P B C) CONSTRUCTION : Through B , draw B D C A intersecting P A produced in D and through C , draw C Q B P , intersecting line A P in Q.

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 a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

D and E are points on sides AB and AC respectively of Delta A B C such that a r\ (D B C)\ =\ a r\ (E B C) . Prove that D E||B C .