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
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
Similar questions
Social Sciences,
5 months ago
Math,
5 months ago
Math,
5 months ago
Biology,
10 months ago
Math,
10 months ago