Question

E is the mid point of a median AD of Triangle ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC

Answer 1

Question:

E is the mid point of a median AD of Triangle ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC?

Answer:

Given:

In ABC

AD is an median.

E is thr mid point of AD

To Show: AF = 1/3AC

Construction: Draw DF||EF

Proof: In ∆ADP,

E is the mid point of AD.

And EF||DP

So, F is the mid point of AP -- ( By converse of Mid Point Theorem)

In ∆FBC,

D is the mid point of BC

And DP||BF

So, P is the mid point of FC -- ( By converse of Mid Point Theorem)

Thus, AF = FP = PC

AF = 1/3 AC -- (Hence Proved)

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