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

Sum of angles in a triangle is $180^\circ$.
$\angle BDC = 180^\circ - 90^\circ - 49^\circ = 41^\circ$

Step2: Match corresponding angles

In △BCD: $\angle C=90^\circ$, $\angle B=49^\circ$, $\angle BDC=41^\circ$
In △FED: $\angle E=90^\circ$, $\angle FDE=41^\circ$, $\angle F=180^\circ-90^\circ-41^\circ=49^\circ$
All corresponding angles are equal.

Step3: Apply AA similarity criterion

If two triangles have all corresponding angles equal, they are similar.

Answer:

△BCD is similar to △FED.