Question

Given: AC BD and AC and BD bisect each other. Prove: BE EC

Answer 1

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

2) $ABCD$ is a parallelogram (a quadrilateral with diagonals that bisect each other is a parallelogram)

3) $ABCD$ is a rhombus (a parallelgoram with congruent diagonals is a rhombus)

4) $\overline{BE} \cong \overline{EC}$ (halves of congruent segments are congruent)