Question

△abc and △ecd are shown below.
which statement is true?
△abc is similar to △ecd.
△abc is not similar to △ecd.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Analyze △ABC properties

△ABC has AB=AC (marked congruent sides), so it is isosceles with ∠B = ∠ACB.

Step2: Analyze △ECD properties

△ECD has EC⊥CD, so ∠ECD=90°. Also BC=CD (marked congruent segments), EC is one leg, CD=BC.

Step3: Check similarity conditions

For similarity, corresponding angles must be equal, or sides in proportion with included equal angle. In △ABC, base angles are equal, but ∠ACB is not 90° (it's the base angle of an isosceles triangle, so less than 90°), while ∠ECD=90°. The side ratios: $\frac{AB}{EC}$ ≠ $\frac{BC}{CD}$ (since AB=AC≠EC, BC=CD). No matching AA (Angle-Angle) or SAS (Side-Angle-Side) similarity criteria are met.

Answer:

△ABC is not similar to △ECD.