Q. 124.2( 260 Votes )

Sides AB and BC a

Answer :


To Prove: Δ ABC ∼ Δ PQR

Given:


Proof:
Median divides the opposite side

BD = and,


QM =


Now, 

Multiplying and dividing by 2, we get,

=



In Δ ABD and Δ PQM,


Side-Side-Side (SSS) Similarity Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar.

ΔABD ΔPQM (By SSS similarity)


ABD = PQM (Corresponding angles of similar triangles)


In ΔABC and ΔPQR,


ABD = PQM (Proved above)


The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

ΔABC ΔPQR (By SAS similarity)

Hence, Proved.

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