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Question
For each of the following statements state whether true(T) or false (F)
the ratio of the perimeter of two similar triangles is the same as the ratio of the their corresponding medians.
Solution
True
Given: ΔABC ~ ΔDEF
To prove=`(Ar(ΔABC))/(Ar(ΔDEF))=((AP)/(DQ))^2`
Proof: in ΔABP and ΔDEQ
∠๐ต๐ด๐= ∠๐ธ๐ท๐ (๐ด๐ ∠๐ด= ∠๐ท,๐ ๐ ๐กโ๐๐๐ ๐ป๐๐๐ ๐๐ ๐๐๐ ๐ ๐๐๐ข๐๐)
∠๐ต= ∠๐ธ (∠๐ด๐ต๐ถ ~ Δ๐ท๐ธ๐น)
By AA criterion, ΔABP and ΔDEQ
`(AB)/(DE)=(AP)/(DQ)` .................(1)
Since, ΔABC ~ ΔDEF
∴ `(Ar(ΔABC))/(Ar(ΔDEF))=((AB)/(DE))^2`
⇒ `(Ar(ΔABC))/(Ar(ΔDEF))=((AP)/(DQ))^2` [๐๐ ๐๐๐ (1)]
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