Question

in figure ad is a median of triangle abc e is the midpoint of AD, DG is parallel to BF. prove that ac = 3 ae

Answer 1

Answer:

Given AD is the median of ΔABC and E is the midpoint of AD Through D, draw DG || BF In ΔADG, E is the midpoint of AD and EF || DG By converse of midpoint theorem we have F is midpoint of AG and AF = FG → (1) Similarly, in ΔBCF D is the midpoint of BC and DG || BF G is midpoint of CF and FG = GC → (2) From equations (1) and (2), we get AF = FG = GC → (3) From the figure we have, AF + FG + GC = AC AF + AF + AF = AC [from (3)] 3 AF = AC AF = (1/3) AC

Step-by-step explanation: