Answer :

1. line AB is congruent to line BC : given

2. angle AEB is congruent to angle CEB : given

3. line BE is congruent to line BE : reflexive property of congruency

4. line AE is congruent to line EC : CPCTC

5. angle BAD is congruent to angle BCD : corresponding angles

6. line AD is corresponding to line DC : corresponding line of congruent triangles.

Congruent triangles are triangles are with equal corresponding angles and equal corresponding sides.

To prove line AD is congruent to line CD

1. line AB is congruent to line BC : given

2. angle AEB is congruent to angle CEB : given

3. line BE is congruent to line BE : reflexive property of congruency

4. line AE is congruent to line EC : CPCTC

5. angle BAD is congruent to angle BCD : corresponding angles.

6. Triangle AED is congruent to triangle CED ( HL postulate)

7. line AD is corresponding to line DC : corresponding line of congruent triangles.

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