Chapter 2.6, Problem 5WE

To determine

To state: The theorem that justifies "the line $\overline{DF}$ bisects $\angle CDB$ then $\angle I\cong \angle 2$ "about thediagram.

Answer to Problem 5WE

The answer is Angle Bisector theorem.

Explanation of Solution

Given information:

  

  $\overrightarrow{DF}$ bisects $\angle CDB$

From Angle Bisector Theorem

The angle $\angle 1=\frac{1}{2}\angle CDB$ and $\angle 2=\frac{1}{2}\angle CDB$

From Substitution Property

  $\angle 1=\angle 2$

From property that equal angles are congruent

  $\angle \text{I}\cong \angle 2$

Hence, the answer is Angle Bisector theorem.