Question

20. Write a two-column proof:
Given: BAC = DAC, DCA = BCA
Prove: BC = CD

Answer 1

Given:

`\angle BAC\cong \angle DAC, \angle DCA\cong \angle BCA`

To prove:

`\overline{BC} \cong \overline{CD}`

Solution:

The two-column proof is:

Statement Reason

1.
`\angle BAC\cong \angle DAC` 1. Given

2.
`\angle BCA\cong \angle DCA` 2. Given

3.
`\overline{AC} \cong \overline{AC}` 3. Common side

4.
`\Delta ABC\cong \Delta ADC` 4. ASA congruent postulate

5.
`\overline{BC} \cong \overline{CD}` 5. CPCTC

Hence proved.