Question

Statements and Reasons

Answer 1

1) Quadrilateral
`ABCD` with diagonal
`\overline{AEC}` bisecting
`\angle DAB`,
`\overline{BE}`,
`\overline{DE}`,
`\angle 1 \cong \angle 2` (given)

2)
`\angle BAE \cong \angle EAD` (definition of an angle bisector)

3)
`\overline{AE} \cong \overline{AE}` (reflexive property)

4)
`\triangle BAE \cong \triangle DAE` (AAS)

5)
`\overline{AB} \cong \overline{AD}` (CPCTC)

6)
`\overline{AC} \cong \overline{AC}` (reflexive property)

7)
`\triangle BAC \cong \triangle DAC` (SAS)

8)
`\overline{BC} \cong \overline{DC}` (CPCTC)