Question

alyssa has written the following proof. given: e is the mid - point of ac. ab∥dc. prove: △aeb≅△ced. proof: statements reasons 1. e is the mid - point of ac. 1. given 2. ab∥dc 2. given 3. ae = ec 3. definition of midpoint 4. ∠aeb = ∠ced 4. vertical angles are congruent. 5. ∠eab = ∠ecd 5. if two parallel lines are intersected by a transversal, then alternate interior angles are congruent. 6. △aeb≅△ced 6. which of the following would correctly complete statement 6? sss aas asa sas

Explanation:

Step1: Identify congruent parts

We have $AE = EC$ (from mid - point definition), $\angle AEB=\angle CED$ (vertical angles), and $\angle EAB=\angle ECD$ (alternate interior angles).

Step2: Recall congruence postulates

The Angle - Side - Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Here, side $AE$ is included between $\angle EAB$ and $\angle AEB$, and side $EC$ is included between $\angle ECD$ and $\angle CED$.

Answer:

C. ASA