Question

d e and f are mid points of the sides bc ca and ab respectively of a triangle abc. prove that : area of triangle def = 1/4 area of triangle abc

Answer 1

F AND E ARE THE MID POINTS OF THE TRIANGLE. SO, FE IS PARALLEL TO BC AND ALSO FE IS EQUAL TO HALF OF BC.
FE IS EQUAL TO BD ND FE IS EQUAL TO CD.
IN QUADRI. FEBD,
OPP. SIDES ARE PARALLEL AND EQUAL, SO IT IS A PARALLELOGRAM.
BY DOING SAME, WE CAN PROOVE ALL OF THE PARALLELOGRAMS.
NOW,
WE KNOW THAT THE DIAGONALS OF A PARALLELOGRAMS BIS CT IT INTO TWO TRIANGLES OF EQUAL AREA OR CONGRUENT TRIANGLES.
Hence triangle FBD is congruent to all the triangles.
We Can write it as DEF=1/4 of ABC
as all the triangles are equal..