Question

Please help me prove that ED is congruent to BA! I thought I had it right by proving right and vertical angles, but I’m missing something

Answer 1

Step-by-step explanation:

$\overline{DA} \text{ bisects } \overline{EB}$     is given

$\overline{BC} \cong \overline{EC}$  definition of bisect

$\overline{EB} \perp \overline{ED}, \, \overline{EB} \perp \overline{BA}$  are both given

$\angle B, \, \angle E \text{ are right angles}$  definition of perpendicular

$\angle B \cong \angle E$   because all right angles are congruent

$\angle{ACB} \cong \angle{DCE}$  vertical angles are congruent

$\triangle{ACB} \cong \triangle{DCE}$   ASA (angle-side-angle)

$\overline{ED} \cong \overline{BA}$  CPCTC (corresponding parts of congruent triangles are congruent)