Question

statement
ab parallel cd; \frac{ab}{dc} = \frac{ac}{ce}
angle ecd cong angle cab
\triangle abc sim \triangle cde
reason
a
b
c

Explanation:

Step1: Identify the reason for \( \angle ECD\cong\angle CAB \)

Since \( AB\parallel CD \), by the property of parallel lines (alternate - interior angles), when a transversal \( AC \) intersects \( AB \) and \( CD \), \( \angle ECD\cong\angle CAB \) (corresponding angles).

Step2: Prove \( \triangle ABC\sim\triangle CDE \)

We know that \( \frac{AB}{DC}=\frac{AC}{CE} \) (given) and \( \angle ECD\cong\angle CAB \) (from Step 1). By the Side - Angle - Side (SAS) similarity criterion, if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar. So, \( \triangle ABC\sim\triangle CDE \) by the SAS similarity criterion.

Answer:

The reason for \( \angle ECD\cong\angle CAB \) (B) is "Corresponding angles (since \( AB\parallel CD \))". The reason for \( \triangle ABC\sim\triangle CDE \) (C) is "SAS (Side - Angle - Side) similarity criterion".