Question

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

Options

• BC . EF = A C. FD

• AB . EF = AC . DE

• BC . DE = AB . EF

• BC . DE = AB . FD

Answer 1

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)`

⇒ 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.