Question

given: c is the midpoint of \\( \overline{bd} \\).
prove: \\( \triangle acb \cong \triangle acd \\)

complete the two - column proof.

Explanation:

Step1: Midpoint definition

By the definition of a midpoint, if \(C\) is the midpoint of \(\overline{BD}\), then \(BC = CD\), which means \(\overline{BC}\cong\overline{CD}\).

Step2: Right - angle congruence

Since \(\angle BCA\) and \(\angle DCA\) are right angles (\(\angle BCA = 90^{\circ}\) and \(\angle DCA=90^{\circ}\)), we can say \(\angle BCA\cong\angle DCA\) (because all right angles are equal in measure, so they are congruent).

Answer:

1. definition of midpoint; 5. \(\angle BCA\cong\angle DCA\)