Question

Triangle A E C is shown. Line segment B D is drawn near point C to form triangle B D C.
Which piece of additional information can be used to prove △CEA ~ △CDB?

∠BDC and ∠AED are right angles
AE ≅ ED
△BDC is a right triangle
∠DBC ≅ ∠DCB

Answer 1

∠BDC and ∠AED are right angles.

Reason: If ∠AED and ∠BDC are right, then ∠CEA = ∠CDB (both are 90°) and the triangles share ∠C, so they have two equal angles. By AA, △CEA ~ △CDB.