Math, asked by 1ankush2007, 1 month ago

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Answered by kamalhajare543
17

Answer:

GIVEN:-

  • T and M are two points inside a parallelogram PQRS.
  • PT = MR and PT || MR.

TO FIND:-

  • ∆PTR = ∆RMP
  • RT || PM and RT = RM

CONCEPT USED:-

  • When the two angles of transversal lines are alternate interior then the lines are Parallel.

When two triangles are Congurent then Corresponding part of Congurent triangles are also equal.

Now,

In ∆PTR and ∆RMP.

 \sf \: \implies\angle \: TRP = \angle \: MPR \: (Alt.int.angle).

\implies\rm{PT = MR } (Given).

 \sf \: \implies\rm{ PR = RP} \:  \:  (common \:  sides).

So, By S-A-S Congurence criteria ∆PTR ≈ ∆RMP.

Therefore,

\sf \implies PT = MR (By CPCT) \\ \\ \sf \: \implies\rm{ PT || MR }  \:  \: (Concept  \: Used).

Hence Proved.

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