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

(B)

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.