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.