Question

In triangle abc pq p and q are point in a b and ac respectively and pq parallel to bc prove that the median bisect pq

Answer 1

Given: ∆ABC in which P and Q are points on sides AB and AC respectively such that PQ || BC and AD is a median.

To Prove : AD bisects PQ.

Proof: In ∆APE and ∆ABD

∠APE = ∠ABD

[corresponding angles]

and ∠PAE = ∠BAD [common]

Therefore, by using AA similar condition

ΔAPE~ΔABD

=> AE/AD=PE/BD

Now, In ∆AQE and ∆ACD

∠AQE = ∠ACD

[corresponding angles]

∠QAE = ∠CAD [common]

Therefore, by using A.A. condition

ΔAQE~ΔACD

=>AE/AD=EQ/DC......(ii)

Comparing (i) and (ii), we have

PE/BD = EQ/DC

but BD=DC

=>PE=EQ

[∵ AD is a median]

Hence AD bisects PQ.

Step-by-step explanation:

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