Question

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

Explanation:

Step1: Find angles in \(\triangle CDE\)

In \(\triangle CDE\), \(\angle D = 90^{\circ}\), \(\angle DEC=51^{\circ}\), so \(\angle DCE = 180^{\circ}-\angle D-\angle DEC=180^{\circ}-90^{\circ}-51^{\circ} = 39^{\circ}\).

Step2: Find angles in \(\triangle FGE\)

Since \(DC\parallel GF\) (by the property of the figure, assume they are parallel as it's a common geometric - figure setup for such similarity problems), \(\angle FEG=\angle DCE = 39^{\circ}\) (alternate - interior angles). And \(\angle G = 90^{\circ}\) (assuming the figure has right - angles as per the right - angle mark in \(\triangle CDE\) and the parallel - line property).

Step3: Check similarity using AA (Angle - Angle) criterion

For \(\triangle CDE\) and \(\triangle FGE\), \(\angle D=\angle G = 90^{\circ}\) and \(\angle DCE=\angle FEG = 39^{\circ}\). By the AA (Angle - Angle) similarity criterion, \(\triangle CDE\sim\triangle FGE\).

Answer:

\(\triangle CDE\) is similar to \(\triangle FGE\)