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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.
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True
Given: ΔABC ~ ΔDEF
To prove=`(Ar(ΔABC))/(Ar(ΔDEF))=((AP)/(DQ))^2`
Proof: in ΔABP and ΔDEQ
∠ЁЭР╡ЁЭР┤ЁЭСГ= ∠ЁЭР╕ЁЭР╖ЁЭСД (ЁЭР┤ЁЭСа ∠ЁЭР┤= ∠ЁЭР╖,ЁЭСаЁЭСЬ ЁЭСбтДОЁЭСТЁЭСЦЁЭСЯ ЁЭР╗ЁЭСОЁЭСЩЁЭСУ ЁЭСЦЁЭСа ЁЭСОЁЭСЩЁЭСаЁЭСЬ ЁЭСТЁЭСЮЁЭСвЁЭСОЁЭСЩ)
∠ЁЭР╡= ∠ЁЭР╕ (∠ЁЭР┤ЁЭР╡ЁЭР╢ ~ ΔЁЭР╖ЁЭР╕ЁЭР╣)
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` [ЁЭСИЁЭСаЁЭСЦЁЭСЫЁЭСФ (1)]
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