Question

AC and BD bisect eachother prove AB || CD and BC ll AD

Answer 1

1)
`\overline{AC}` and
`\overline{BD}` bisect each other (given)

2)
`\overline{AE} \cong \overline{EC}` (a bisector splits a segment into two congruent parts)

3)
`\overline{BE} \cong \overline{ED}` (a bisector splits a segment into two congruent parts)

4)
`\angle BEA \cong \angle CED` (vertical angles are congruent)

5)
`\triangle BEA \cong \triangle DEC` (SAS)

6)
`\angle EBA \cong \angle EDC` (CPCTC)

7)
`\overline{AB} \parallel \overline{CD}` (converse of alternate interior angles theorem)

8)
`\angle DEA \cong \angle BEC` (vertical angles are congruent)

9)
`\triangle AED \cong \triangle BEC` (SAS)

10)
`\angle BCE \cong \angle EAD` (CPCTC)

11)
`\overline{BC} \parallel \overline{AD}` (converse of alternate interior angles theorem)