To prove that △ ADC and △ BEC are similar, knowing that they have one congruent angle, we can use either SAS Similarity Theorem or AA Similarity Theorem. However, none of the given options is enough to use the first theorem because to use it we would need to know that AC BC= CD CE.
To use Angle-Angle Similarity Postulate, we need to prove that these triangles have at least two congruent angles. Let's recall the Alternate Interior Angles Theorem.
If parallel lines are cut by a transversal,
then the pairs of alternate interior angles are congruent.
This means if AD and BE were parallel, then ∠ CAD would be congruent to ∠ CBE and ∠ CDA would be congruent to ∠ CEB.
With this we can say that these two triangles are similar by AA Similarity Postulate. Therefore, it would be enough information if we knew that AD is parallel to EB. This corresponds with answer C.
