prove segment BA is congruent to segment EA, if the given is segment CB is parallel to segment ED & A is the midpoint of segment CD

Answer 1

To prove: BA=EA

Given: CB || ED

A is the midpoint of CD

Proof:

1. CB || ED Given
2. <BCA=<EDA When two parallel lines are cut by a transversal, alternate interior angles formed are congruent
3. CA=DA A midpoint divides the segment into two congruent parts
4. <CAB=<DAE Vertical angles are congruent
5. Triangle ACB is congruent to Triangle ADE By the SAS theorem
6. BA=EA CPCTC (Corresponding parts of congruent triangles are congruent)