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 90°) and the two triangles also share ∠ECA = ∠DCB (the angle at C). Thus the triangles have two equal angles and are similar by AA.