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Answers
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
- 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.
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