Chapter 6.3, Problem 10WE

To determine

To prove: that $\overrightarrow{OE}$ doesn’t bisect $\angle JOK$ .

Explanation of Solution

Given information:

  $\overline{OJ}\cong \overline{OK}$ ; $\overline{JE}\cancel{\cong }\overline{KE}$

Given figure,

  

Calculation:

Consider the following statement:

  $\overline{OJ}\cong \overline{OK}$ ; $\overline{JE}\cancel{\cong }\overline{KE}$ .

Prove that $\overrightarrow{OE}$ Doesn’t bisect $\angle JOK$ as follows:

An indirect proof is initiated by assuming temporarily that need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $\overrightarrow{OE}$ bisect $\angle JOK$ .

For this, $\Delta JOE$ and $\Delta KOE$ should be congruent by the SSS axiom.

However, it cannot be prove that they are congruent as it is given that $\overline{JE}\cancel{\cong }\overline{KE}$ .

Hence, $\angle 1\ne \angle 2$

Hence, it is proved that $\overrightarrow{OE}$ Doesn’t bisect $\angle JOK$ .