If `DeltaABC~DeltaEDF` and `DeltaABC` is not similar to `DeltaDEF`, then which of the following is not true?

Options

A. `BCcdotEF=ACcdotFD`
B. `ABcdotEF=ACcdotDE`
C. `BCcdotDE=ABcdotEF`
D. `BCcdotDE=ABcdotFD`

Answer

C

Explanation

Given, `DeltaABC~DeltaEDF`
`therefore (AB)/(ED)=(BC)/(DF)=(AC)/(EF)`

Taking first two terms, we get
`(AB)/(ED)=(BC)/(DF)`
`rArrABcdotDF=EDcdotBC`
or `BCcdotDE=ABcdotDF`
So option (d) is true.
Taking last two terms, we get
`(BC)/(DF)=(AC)/(EF)`
`rArrBCcdotEF=ACcdotDF`
So option is also true.
Taking first and last terms, we get
`(AB)/(ED)=(AC)/(EF)`
`rArrABcdotEF=EDcdotAC`
hence, option (b) is true.