Question

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

Explanation:

Step1: Determine the reason for \( \overline{BC}\cong\overline{CD} \)

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

Step2: Determine the statement for reason “all right \( \angle s \) are \( \cong \)”

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

Answer:

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