Chapter 5.1, Problem 52HP

To determine

To prove: The relation $\angle ADB\cong \angle ACB$ .

Explanation of Solution

Given information:

The given triangle shown in figure (1).

  

Figure (1)

Plane $\gamma$ is perpendicular bisector of $\overline{DC}$ .

Proof:

Using two column proof.

Statement	Reason
Plane $\gamma$ is perpendicular bisector of $\overline{DC}$	Given
$\angle DBA$ and $\angle CBA$ are right angles	Definition of perpendicular lines
$\angle DBA\cong \angle CBA$	Right angles are congruent
$\overline{AB}\cong \overline{AB}$	Reflexive property of congruence
$\Delta DAB\cong \Delta CBA$	SAS Congruence theorem
$\angle ADB\cong \angle ACB$	CPCTC

From the above, $\angle ADB\cong \angle ACB$ .

Hence, proved.