Question

given: c is the mid - point of bd. prove: △acb≅△acd. complete the two - column proof. 1. c is the midpoint of bd. 1. given 2. bc≅cd 2. 3. ac≅ac 3. reflexive property 4. ∠bca and ∠dca are right 4. given 5. 5. all right ∠s are ≅ 6. △acb≅△acd 6. sas

Explanation:

Step1: Identify midpoint implication

C is midpoint of $\overline{BD}$ ⇒ $\overline{BC} \cong \overline{CD}$ (definition of midpoint).

Step2: Recognize right angles congruence

$\angle BCA$ and $\angle DCA$ are right ⇒ $\angle BCA \cong \angle DCA$ (all right angles ≅).

Step3: Apply SAS congruence

$\overline{BC} \cong \overline{CD}$, $\angle BCA \cong \angle DCA$, $\overline{AC} \cong \overline{AC}$ (reflexive) ⇒ $\triangle ACB \cong \triangle ACD$ (SAS).

Answer:

♣: definition of midpoint, ♦: $\angle BCA \cong \angle DCA$