Question

Given: AC and BD bisect each other.
Prove: AB | CD and BC || AD.

Answer 1

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

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

4)
`\angle AEB \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 BEC \cong \angle AED` (vertical angles are congruent)

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

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

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