Chapter 9.4, Problem 14WE

To determine

To prove: $\angle J\cong \angle K$

Explanation of Solution

Given information: $\stackrel{⌢}{JZ}\cong \stackrel{⌢}{KZ}$

Proof:

  

It is given that $\stackrel{⌢}{JZ}\cong \stackrel{⌢}{KZ}$ .

In a circle, if two minor arcs are equal in measure then their corresponding chords are also equal in measure.

So,

  $\overline{JZ}\cong \overline{KZ}$

In a triangle, if any two sides are found to be congruent then the included angles opposite to these sides respectively are congruent.

Therefore,

  $\angle J\cong \angle K$