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.