Question

which piece of additional information can be used to prove △cea ~ △cdb?
○ ∠bdc and ∠aed are right angles
○ \\(\overline{ae} \cong \overline{ed}\\)
○ △bdc is a right triangle
○ ∠dbc ≅ ∠dcb

Explanation:

Step1: Identify common angle

△CEA and △CDB share ∠C.

Step2: Check AA similarity condition

AA similarity requires two equal angles. If ∠BDC and ∠AEC are right angles, then ∠BDC=∠AEC=90°, so AA is satisfied.

Step3: Evaluate other options

• $\overline{AE} \cong \overline{ED}$: Irrelevant to triangle similarity.
• △BDC is right triangle: Only one right angle, no match for △CEA.
• ∠DBC≅∠DCB: Makes △BDC isosceles, no relation to △CEA.

Answer:

A. ∠BDC and ∠AED are right angles