Math, asked by pchandrakala777, 10 months ago

side Ac of triangle ABC is produced
to D such that CD = 1/2AE if E is
the mid point of BC and DE
Produced meets AB at F prove
that Ef = 1/3 DF​

Answers

Answered by Anonymous
3

Answer:

heya

Step-by-step explanation:

Given,

ABC is a triangle.

D is midpoint of BC and DQ.

They're drawn parallel to BA.

Then, Q is midpoint of AC.

∴AQ = DC

∴ FA parallel to DQ||PC.

AQC, is a transversal so, AQ = QC and FDP also a transveral on them.

∴FD = DP .......(1) [ intercept theorem]

EC = 1/2 AC = QC

Now, triangle EQD, here C is midpoint of EQ and CP which is parallel to DQ.

And, P is midpoint of DE.

DP = PE..........(2)

Therefore, From (1) and (2)

FD = DP = PE

∴ FD = 1/3 FE

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