Question

E is the midpoint of median AD of triangle ABC and BE is is produced to meet AC at f .show that AF = 1/3AC . if AC =9cm find AF
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Answer 1

Answer:

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 will get

AF=FG=GC........3

AF+FG+GC=AC

AF+AF+AF=AC ......... from eq 3

AF=AC

AF=(1/3)AC