Q. 34.6( 8 Votes )
If ∆ABC ∼ ∆EDF and ∆ABC is not similar to ∆DEF, then which of the following is not true?
A. BC.EF = AC.FD
B. AB.EF = AC.DE
C. BC.DE = AB.EF
D. BC.DE = AB.FD
We know that, sides of one triangle are proportional to the side of the other triangle, and then their corresponding angles are also equal, so by SSS similarity, triangles are similar.
∆ABC ∼ ∆EDF
AB/ED = BC/DF = AC/EF
(By similarity property)
Taking first two terms, we get
AB/ED = BC/DF
⇒ AB.DF = ED.BC
So, option (d) is true
Taking last two terms, we get
BC/DF = AC/EF
⇒ BC.EF = AC.DF
So, option (A) is true
Taking first and last terms, we get,
AB/ED = AC/EF
⇒ AB.EF = ED.AC
Hence, option (b) is true.
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