Question

In figure AD is median of triangle ABC ,E is a mid point on AD such that AE:ED=2:3 prove that BE=4EF

Answer 1

Please write the correct question

In figure AD is median of triangle ABC ,E is a mid point on AD such that AE:ED=2:3 prove that BE=4EF

But there is refrence of point F and if E is modpoint of AD then how can AE : ED = 2:3

Answer 2

BE=4EF

GIVEN: A Triangle ABC.

            AD is the Median.

            E is the midpoint of AD
TO PROVE: BE=4EF

CONSTRUCTION: A-line DG is to be drawn parallel to BF

                              To be made through D.
SOLUTION: As we know,

In Triangle ADG,

E is the midpoint of AD.

EF is parallel to DG.
Now, by using the Converse of Mid Point Theorem

We get,

F is the midpoint of AG and AF=FG                        -----Eq1

Similarly,

In Triangle BCF,

D is the midpoint of BC.

DG is parallel to BF

Therefore,

G is the midpoint of CF and FG=GC                       -----Eq2

Now, by using Equations 1 and 2,

We get,

AF = FG = GC                                                           ----Eq3

AF + FG +GC = AC

AF + AF + AF = AC                                       [  using Eq 3 ]

3 AF = AC

AF = AC/3  

Implying that,

BE=4EF

Hence Proved.

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