Question

In triangle ABC , E is the mid point of side AB and D is a point on AC such that DE || BC . which of the following is true- AE|| AC , AE= AC , AE=½AC , AE =DE​

Answer 1

Answer:

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