Math, asked by darshnaraval13, 5 months ago

please answer the question it's very urgent.please guy's​

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Answers

Answered by hp658198
1

Step-by-step explanation:

Given:- In the given figure i.e. inside the parallelogram PQRS, T and M are two points.

PT = MR

PT || MR

  1. To Prove:- ∆PTR ~ ∆RMP

Proof:- In ∆PTR and ∆RMP,

  • PT = MR (given)
  • PR = PR (common)
  • TPR = MRP (alternative interior angle)
  • TRP = MPR (alternative interior angle)

Therefore,

∆PTR ~ ∆RMP

hence proved.

2. To Prove :- RT || PM and RT = PM

Proof :- Since,

∆PTR ~ ∆RMP,

by CPCT,

RT || PM,

RT = PM.

Hence, proved.

Answered by joelpaulabraham
1

Step-by-step explanation:

Given:-

In Parallelogram PQRS, T and M are points inside it.

PT = MR

PT || MR

To Prove:-

(i) ΔPTR ≅ ΔRMP

(ii) RT || PM and RT = PM

Proof:-

We know that,

PT || MR

So,

In ΔPTR and ΔRMP,

  • PT = MR (Given)
  • ∠TPR = ∠PRM [Alternate Interior Angles]

[PT || MR and PR is the Tranversal]

  • PR = PR (Common Side)

∴ ΔPTR ≅ ΔRMP (By S.A.S Congruency)

(ii)

Then,

RT = PM (Corresponding Parts of Congruent Triangles)

[From above]

Hence,

We have,

RT = PM

PT = MR

We know that,

In a Quadrilateral, if two pairs of opposite sides are equal, then they must be parallel.

∴ RT || PM

Hence proved.

Hope it helped and believing you understood it........All the best

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