Question

given c is the midpoint of bd
prove \\( \triangle a c b \cong \triangle a c d \\)
complete the two - column proof

Explanation:

Step1: Reason for \(BC\cong CD\)

By the definition of a midpoint, if \(C\) is the mid - point of \(BD\), then \(BC = CD\) (in terms of length) and \(BC\cong CD\) (in terms of congruence).

Step2: Missing statement for \(\angle BCA\cong\angle DCA\)

Since \(\angle BCA\) and \(\angle DCA\) are right angles (given in step 4) and all right angles are congruent (reason 5), the statement for step 5 is \(\angle BCA\cong\angle DCA\).

Answer:

1. Definition of midpoint
2. \(\angle BCA\cong\angle DCA\)