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Question
Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that : `("AB")/("PQ") = ("AD")/("PM")`.
Solution
Given, ΔABC ∼ ΔPQR; AD and PM are the medians of ΔABC and ΔPQR respectively.
To prove: `("AB")/("PQ") = ("AD")/("PM")`
Proof: Since, ΔABC ∼ ΔPQR
∴ ∠B = ∠Q and
`("AB")/("PQ") = ("BC")/("QR") = (2"BD")/(2"QM") = ("BD")/("QM")` ...(∵ D and M are mid-points of BC and QR)
Now in ΔABD and ΔPQM
`("AB")/("PQ") = ("BD")/("QM")` ...(Proved)
∠B = ∠Q ...(Given)
∴ ΔABD ∼ ΔPQM ...(SAS axiom of similarity)
∴ `("AB")/("PQ") = ("AD")/("PM")` ...(Corresponding sides of Δ's are proportional)
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