Question

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

Explanation:

Step1: Find ∠C in △CDE

In right △CDE, $\angle C = 90^\circ - 46^\circ = 44^\circ$

Step2: Find ∠FEG in △FGE

In right △FGE, $\angle FEG = 90^\circ - 44^\circ = 46^\circ$

Step3: Match corresponding angles

$\angle D = \angle G = 90^\circ$, $\angle CED = \angle FEG = 46^\circ$, $\angle C = \angle F = 44^\circ$. All corresponding angles are congruent.

Answer:

△CDE is similar to △FGE.