Question

d is the midpoint of \\( \overline { a c } \\)
reason:
given
\\( \overline { a d } \cong \overline { c d } \\)
\\( \angle a \cong \angle c \\)
\\( \overline { a b } \cong \overline { c b } \\)
reason:
reason:
reason:
select reason
reflexive property
select reason

Explanation:

Step1: Midpoint Definition

By the definition of a midpoint, if \(D\) is the midpoint of \(\overline{AC}\), then \(AD = CD\). In terms of congruence, \(\overline{AD}\cong\overline{CD}\).

Step2: Given Information

From the figure, we can see that the marks on \(\angle A\) and \(\angle C\) indicate they are congruent. So, \(\angle A\cong\angle C\) (given).

Step3: Given Information

The marks on \(\overline{AB}\) and \(\overline{CB}\) in the figure show that they are congruent. So, \(\overline{AB}\cong\overline{CB}\) (given).

Answer:

For \(\overline{AD}\cong\overline{CD}\), the reason is "Definition of Midpoint". For \(\angle A\cong\angle C\), the reason is "Given". For \(\overline{AB}\cong\overline{CB}\), the reason is "Given".