Question

What are the missing statements in steps 6 and 10 of the proof?

Answer 1

Second option. The converse of the alternate interior angles theorem is that equal alternate angles -> parallel lines. The steps before show which angles and consequently which lines they are referring to.

Answer 2

Answer:

(B)

Step-by-step explanation:

Given: AC and BD bisect each other.

To prove: ABCD is a parallelogram.

Proof:

Statement                                                                    Reason

1. AC and BD bisect each other                                  Given

2. AE=EC and BE=ED                                    Definition of bisection

3.m∠AEB=m∠CED                                    Vertically opposite angles

4.ΔABE≅ΔCDE                                                   SAS criterion

5.∠ACD≅∠CAB                       Corresponding angles of congruent triangles   are congruent

6. AB║CD                              Converse of alternate interior angles theorem

7.m∠BEC=m∠AED                                       Vertical angles theorem

8.ΔBEC≅ΔDEA                                              SAs criterion

9. ∠DBC≅∠BDA Corresponding angles of congruent triangles   are congruent

10.BC║AD                             Converse of alternate interior angles theorem

11. ABCD is a parallelogram              Definition of parallelogram

Hence proved.