Question

Q.No.6. E is the mid-point on median AD of AABC. (See given figure) Show that;
ar(DEC) = -ar(ABC)​

Answer 1

Step-by-step explanation:

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