If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?

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KollegeApply · Accepted Answer

BC . DE = AB . EF Explanation: We know that, If sides of one triangle are proportional to the side of the other triangle and the corresponding angles are also equal, then the triangles are similar by SSS similarity. So, ∆ABC ∼ ∆EDF Using similarity property, `("AB")/("ED") = ("BC")/("DF") = ("AC")/("EF") Taking ("AB")/("ED") = ("BC")/("DF"), we get ("AB")/("ED") = ("BC")/("DF")` AB . DF = ED . BC So, option (d) BC . DE = AB . FD is true Taking `("BC")/("DF") = ("AC")/("EF"), we get ("BC")/("DF") = ("AC")/("EF")` $\Rightarrow$ BC . EF = AC . DF So, option (a) BC . EF = AC . FD is true Taking `("AB")/("ED") = ("AC")/("EF"), we get, ("AB")/("ED") = ("AC")/("EF")` AB . EF = ED . AC So, option (b) AB . EF = AC . DE is true. [Solution diagram: 267675_solution_1.png]

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