Question

△bcd and △bef are shown below.
which statement is true?
△bcd is similar to △bef.
△bcd is not similar to △bef.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify shared angle

$\angle B$ is common to $\triangle BCD$ and $\triangle BEF$.

Step2: Identify equal corresponding angles

$\angle BCD = \angle BEF$ (marked congruent), $\angle BDC = \angle BFE$ (marked congruent).

Step3: Apply AA similarity criterion

If two pairs of corresponding angles of two triangles are congruent, the triangles are similar by AA (Angle-Angle) similarity.

Answer:

$\triangle BCD$ is similar to $\triangle BEF$.