Question

If △ ABC ∼ △ DEF, then ______.

Options

• \[\frac{AB}{EF} = \frac{AC}{DF}\]

• \[\frac{AB}{DE} = \frac{BC}{DF}\]

• \[\frac{AC}{DF} = \frac{AB}{DE}\]

• \[\frac{BC}{EF} = \frac{AC}{DE}\]

Answer 1

If △ ABC ∼ △ DEF, then \[\underline{\mathbf{\frac{AC}{DF} = \frac{AB}{DE}}}\].

Explanation:

In Δ ABC ∼ Δ DEF, we can conclude:

AB corresponds to DE, BC corresponds to EF and AC corresponds to DF.

We know that,

Corresponding sides of similar triangles are equal.

∴ `(AB)/(DE) = (BC)/(EF) = (AC)/(DF)` 

⇒ `(AB)/(DE) = (AC)/(DF)`