Question

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

Explanation:

Step1: Find ∠BDC in △BCD

In right triangle $\triangle BCD$, $\angle C=90^\circ$, $\angle B=49^\circ$.
$\angle BDC = 180^\circ - 90^\circ - 49^\circ = 41^\circ$

Step2: Find ∠F in △FED

In right triangle $\triangle FED$, $\angle E=90^\circ$, $\angle FDE=41^\circ$.
$\angle F = 180^\circ - 90^\circ - 41^\circ = 49^\circ$

Step3: Match corresponding angles

For $\triangle BCD$ and $\triangle FED$:
$\angle C = \angle E = 90^\circ$, $\angle B = \angle F = 49^\circ$, $\angle BDC = \angle FDE = 41^\circ$.
All corresponding angles are equal, so the triangles are similar.

Answer:

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