which piece of additional information can be used to prove △cea ~ △cdb?\n∠bdc and ∠aed are right angles\nae…

Explanation:

Step1: Recall similarity - criteria

For two triangles $\triangle CEA$ and $\triangle CDB$, they already share $\angle C$ (common - angle). To prove similarity, we can use AA (angle - angle) similarity criterion.

Step2: Analyze each option

• Option 1: If $\angle BDC$ and $\angle AEC$ are right - angles, and we already have $\angle C$ common. By AA similarity criterion, $\triangle CEA\sim\triangle CDB$.
• Option 2: $AE\cong ED$ gives information about the lengths within $\triangle AED$ and is not relevant to the similarity of $\triangle CEA$ and $\triangle CDB$.
• Option 3: Just knowing that $\triangle BDC$ is a right - triangle is not enough. We need to know the relationship between the angles of $\triangle BDC$ and $\triangle CEA$.
• Option 4: $\angle DBC\cong\angle DCB$ gives information about the base - angles of $\triangle BDC$ and is not relevant to proving the similarity of $\triangle CEA$ and $\triangle CDB$.

Answer:

$\angle BDC$ and $\angle AEC$ are right angles