Chapter 4.5, Problem 1CYU

To determine

To prove:

  $\Delta ABC\cong \Delta DBC$ by two-column.

Explanation of Solution

Given Information:

  $\overline{CB}$ bisects $\angle ABD$ and $\angle ACD$ .

  

Proof:

The two-column proof can be given as:

Proof	Reason
$\overline{CB}$ bisects $\angle ABD$ and $\angle ACD$	Given.
$\angle ABC\cong \angle DBC$	Definition of angular bisector.
$\overline{BC}\cong \overline{BC}$	Reflexive property.
$\angle ABC\cong \angle DCB$	Definition of angular bisector.
$\Delta ABC\cong \Delta DBC$	ASA − Angle, Side, Angle.