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)