Question

If in ∆ABC and ∆DEF, `(AB)/(EF) = (AC)/(DE)` then they will be similar when ______.

Options

• ∠A = ∠D

• ∠A = ∠E

• ∠C = ∠F

• ∠B = ∠E

Answer 1

If in ∆ABC and ∆DEF, `(AB)/(EF) = (AC)/(DE)` then they will be similar when ∠A = ∠E.

Explanation:

To determine when ΔABC ∼ ΔDEF, we use the SAS similarity criterion:

If two pairs of corresponding sides are in proportion and the included angle between them is equal, then the triangles are similar.

Given, `(AB)/(EF) = (AC)/(DE)`

These are two pairs of sides.

The included angle between AB and AC is ∠A.

The included angle between EF and DE is ∠E.

So, for similarity:

⇒ ∠A = ∠E