 Hi and how are you all today? The question says xy is a line parallel to side bc of a triangle a b c. If b e is parallel to a c and c f is parallel to a b meet xy at e and f respectively show that area of triangle a b e is equal to area of triangle a c f. Now these are the two points which are given to us as xy also in the question we have given that xy is a line which is parallel to bc since xy is a line parallel to bc that means e f will also be parallel to bc right and also b e is parallel to a c this line and c f is parallel to now let us start with our solution now we know that if and between parallel lines the triangle the parallelogram right so we know that triangle a b e parallelogram b c y e are having a common base between the same parallel lines that is we know that triangle a b e and parallelogram b c y e are on the same base that is b c between the same parallel lines that is b e is parallel to say that area of a b e is half area of the parallelogram b c y e let this be the first equation of which parallelogram exactly it is half of parallelogram similarly parallelogram b c y x is equal to area of parallelogram b c y e right so we can see that the left hand side of these two equations are equal right hand side so their left hand sides will also be equal so we can say that therefore area of a b e will be equal to area of a c f that is by the first and the second equation we have right so this is what we were supposed to prove defense my session hope you enjoyed and have a very nice day