Q. 34.1( 329 Votes )

Two sides AB and

Answer :

It is given in the question that:

AB = PQ

BC = QR

And,

AM = PN


(i) To Prove:  
BC = BM  and   QR = QN             (AM and PN are medians)


BC = QR

BC = QR


In


AM = PN (Given)


AB = PQ (Given)


BM = QN (Proved above)

Side-Side-Side (SSSRule. Side-Side-Side is a rule used to prove whether a given set of triangles arecongruent. The SSS rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Therefore,

By SSS congruence rule,


(ii)
To Prove: 
Proof:
In
and

AB = PQ (Given)

ABC = PQR (By c.p.c.t)

BC = QR (Given)

Therefore,

Two sides and included angle (SAS) Definition: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. 

By SAS congruence rule,

Hence, Proved.

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