Question

Please help with this two-column proof.

Answer 1

Given:

$\overline {DC}$ bisects ∠ACB

$\overline {A C} \cong \overline{B C}$

To prove:

$\triangle A C D \cong \triangle B C D$

Solution:

Now writing statement with reason in step by step.

In $\triangle A C D\ \text{and} \ \triangle B C D,$

Step 1: Given

$\overline {DC}$ bisects ∠ACB

$\Rightarrow \angle ACD \cong \angle BCD$ (Angle)

Step 2: Given

$\overline {A C} \cong \overline{B C}$ (Side)

Step 3: By reflexive property,

$\overline {D C} \cong \overline{D C}$ (Side)

Step 4: By SAS congruence rule

$\triangle A C D \cong \triangle B C D$

Hence proved.