Question

the triangles are similar by:
aa similarly postulate
sss similarity theorem
sas similarity theorem
the triangles are not similar

Explanation:

Step1: Identify Vertical Angles

Angles at \( C \) ( \( \angle ACB \) and \( \angle ECD \)) are vertical angles, so they are equal.

Step2: Identify Given Angles

\( \angle B = 50^\circ \) and \( \angle D = 50^\circ \), so \( \angle B = \angle D \). Also, \( \angle A = 55^\circ \), and we can find \( \angle E \) (since sum of angles in a triangle is \( 180^\circ \), but we already have two angles: vertical angle and \( 50^\circ \), and one triangle has \( 55^\circ \), \( 50^\circ \), so the third angle in both triangles will be equal). By AA (Angle - Angle) similarity postulate, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, we have two pairs of equal angles (vertical angles and \( 50^\circ \) angles, and the third angle will also be equal due to angle - sum property), so the triangles are similar by AA similarity postulate.

Answer:

AA similarity postulate