Math, asked by Artee120, 8 months ago

PT is a median of a traingle PQR is PR+QR+PQ > 2PT​

Answers

Answered by Anonymous
1

Answer:

A ROUGH FIGURE FOR BETTER UNDERSTANDING

Step-by-step explanation:

A ∆PQR in which PT is a Median .

To Prove: PR + PQ > 2PT

Construction: produce PT to S , such that PT = TS. Join SR.

PROOF:

In ∆PTQ & ∆STR

PT=ST ( By construction).......(1)

∠PTQ = ∠STR (vertically opposite angles)

QT=RT (PT is a median, T is a midpoint of QR)

∆PTQ≅∆STR (By SAS congruence rule)

PQ= SR (By CPCT)...........(2)

In ∆PSR

PR +SR> PS

[Sum of any two sides of a triangle is greater than the third side]

PR +SR> PT + TS (PS= PT+TS)

PR + PQ >PT + TS (from eq 2)

PR + PQ >PT + PT (from eq 1)

PR + PQ > 2PT

Hence, the sum of any two sides of a triangle is greater than twice the median with respect to the third side.

HOPE THIS WILL HELP YOU...

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Answered by piyushkumar153
4

Answer:

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