Chapter 5.1, Problem 11PSB

To determine

To Prove: $\overline{AB}\ne \overline{BC}$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}\overrightarrow{BD}\text{bisects}\angle ABC\\ \angle ADB\text{is acute}\end{array}$

Concept Used:

Two line segments are said to be congruent if they are of the same measure.

Proof:

Here, we have

  $\begin{array}{l}\text{In }\Delta ABD\text{and }\Delta CBD\\ \overline{BD}\cong \overline{BD}\left(\because \text{Common side}\right)\\ \Rightarrow \angle ABD\cong \angle CBD\left(\because \overrightarrow{BD}\text{bisects}\angle ABC\right)\\ \Rightarrow \Delta ABD\cancel{\cong }\Delta CBD\\ \therefore \overline{AB}\ne \overline{BC}\end{array}$