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

Answer :

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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