Triangle Similarity 8Fdfbb

1. **State the problem:** Determine if $\triangle ABC$ is similar to $\triangle DEC$ based on the given diagram and information. 2. **Recall similarity criteria:** Triangles are similar if they satisfy one of the following: - Angle-Angle (AA): Two pairs of corresponding angles are equal. - Side-Angle-Side (SAS): Two pairs of sides are proportional and the included angles are equal. - Side-Side-Side (SSS): All three pairs of sides are proportional. 3. **Analyze the given information:** - Both triangles share point $C$. - Right angles are marked at $B$ in $\triangle ABC$ and at $E$ in $\triangle DEC$. - Lines $AD$ and $BC/DE$ intersect at $C$. 4. **Check angles:** - $\angle B$ in $\triangle ABC$ and $\angle E$ in $\triangle DEC$ are both right angles, so $\angle B = \angle E = 90^\circ$. - $\angle A$ in $\triangle ABC$ and $\angle D$ in $\triangle DEC$ are vertical angles formed by intersecting lines $AD$ and $BC/DE$, so $\angle A = \angle D$. 5. **Conclusion:** Since two pairs of corresponding angles are equal ($\angle B = \angle E$ and $\angle A = \angle D$), by the AA criterion, $\triangle ABC$ is similar to $\triangle DEC$. **Final answer:** Yes, $\triangle ABC$ is similar to $\triangle DEC$ by the Angle-Angle (AA) similarity criterion.