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Irina-Kira [14]
2 years ago
5

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

Mathematics
1 answer:
Art [367]2 years ago
4 0

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)

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