Question

proving triangles congruent
given: c is the midpoint of \\( \overline{bd} \\).
prove: \\( \triangle acb \cong \triangle acd \\)
complete the two - column proof.

Explanation:

Step1: Reason for \( \overline{BC}\cong\overline{CD} \)

By the definition of a mid - point, if \( C \) is the mid - point of \( \overline{BD} \), then \( BC = CD \), so \( \overline{BC}\cong\overline{CD} \).

Step2: Statement for Reason 5

Since \( \angle BCA \) and \( \angle DCA \) are right angles and all right angles are congruent, the statement is \( \angle BCA\cong\angle DCA \).

Answer:

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