sides ab and ac and median ad of a triangle abc are respectively proportional to sides pq and pr and median pm of another triangle pqr show that triangle ABC is similar to triangle pqr .
Answers
Answer:
ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC ∼ ΔPQR. ... Ex 6.3, 14 - Sides AB, AC and median AD of a triangle ABC ...
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Answer:
Given two triangles. ΔABC and ΔPQR in which AB, BC and median AD of ΔABC are proportional to sides PQ, QR and median PM of ΔPQR
AB/PQ = BC/QR = AD/PM
To Prove: ΔABC ~ ΔPQR
Proof: AB/PQ = BC/QR = AD/PM
 AB/PQ = BC/QR = AD/PM (D is the mid-point of BC. M is the mid point of QR)
ΔABD ~ ΔPQM [SSS similarity criterion]
Therefore, ∠ABD = ∠PQM [Corresponding angles of two similar triangles are equal]
∠ABC = ∠PQR
In ΔABC and ΔPQR
AB/PQ = BC/QR ———(i)
∠ABC = ∠PQR ——-(ii)
From above equation (i) and (ii), we get
ΔABC ~ ΔPQR [By SAS similarity criterion]
Hence Proved