Question

given: c is the mid - point of bd. prove: δacb≅δacd. complete the two - column proof.

Explanation:

Step1: Definition of mid - point

If a point $C$ is the mid - point of a line segment $\overline{BD}$, then by the definition of a mid - point, the two sub - segments formed are congruent. So, $\overline{BC}\cong\overline{CD}$.

Step2: Right - angle congruence

Since $\angle BCA$ and $\angle DCA$ are right angles, and all right angles are congruent, we can write $\angle BCA\cong\angle DCA$.

Answer:

♣: Definition of mid - point
♦: $\angle BCA\cong\angle DCA$