Question

proving triangles congruent

given: c is the midpoint of \\( \overline{bd} \\)
prove \\( \triangle a c b \cong \triangle a c d \\)

complete the two - column proof.

Explanation:

Step1: Midpoint Definition

Since \(C\) is the midpoint of \(\overline{BD}\), by the definition of a midpoint, \(BC = CD\). In congruence notation, \(BC\cong CD\) (Reason 2: Definition of midpoint).

Step2: Right - Angle Congruence

Given that \(\angle BCA\) and \(\angle DCA\) are right angles (Reason 4: given). By the property that all right angles are congruent, \(\angle BCA\cong\angle DCA\) (Reason 5: All right \(\angle\)s are \(\cong\)).

Answer:

For Reason 2: Definition of midpoint; For Statement 5: \(\angle BCA\cong\angle DCA\)