Question

given:
\\( \angle a e d \cong \angle b e d \\)
and
\\( \angle e a d \cong \angle c b f \\)
prove \\( \triangle a e d \cong \triangle b e d \\) by moving justifications into the table.
\\( \angle c b f \cong \angle d b e \\)
\\( \angle e a d \cong \angle d b e \\)
\\( \overline{d e} \cong \overline{d e} \\)
\\( \triangle a e d \cong \triangle b e d \\)
vertical angles are congruent. reflexive property symmetric property transitive property triangle sum theorem

Explanation:

Step1: Justify \(\angle CBF\cong\angle DBE\)

Vertical angles are congruent.

Step2: Justify \(\angle EAD\cong\angle DBE\)

Transitive Property (Since \(\angle EAD\cong\angle CBF\) (given) and \(\angle CBF\cong\angle DBE\) (from Step 1)).

Step3: Justify \(\overline{DE}\cong\overline{DE}\)

Reflexive Property.

Answer:

For \(\angle CBF\cong\angle DBE\): Vertical angles are congruent.
For \(\angle EAD\cong\angle DBE\): Transitive Property.
For \(\overline{DE}\cong\overline{DE}\): Reflexive Property.