Final answer:
Triangles AEB and DEC are congruent because angle AEB is congruent to angle DEC due to being vertical angles, as stated in option (A).
Step-by-step explanation:
The student's question pertains to determining why triangles AEB and DEC are congruent given the ratio AE/ED = BE/EC. Among the choices provided, the correct justification involves understanding that angle AEB is congruent to angle DEC due to them being vertical angles, which are always congruent. The given ratios imply proportional segments but do not directly establish congruency of sides. As such, the correct choice is (A) Angle AEB is congruent to angle DEC (Vertical angles).
The statement "AE/ED = BE/EC" indicates that the triangles AEB and DEC are similar by the Side-Angle-Side (SAS) similarity criterion. This is because the ratios of corresponding sides are equal.
Now, to justify that triangle AEB is congruent to triangle DEC, you need to establish more than just similarity. You need to show that corresponding angles are congruent.
From the given information, the correct choice is:
A) Angle AEB is congruent to angle DEC (Vertical angles)
This is because vertical angles are congruent, and if AEB and DEC are similar triangles, the corresponding angles are congruent, including the vertical angles.