Chapter 9.4, Problem 15WE

To determine

To find:In given figure, to prove if arcs $JZ$ and $KZ$ are congruent to each other.

Answer to Problem 15WE

Thus, by below statements it proves that arcs

  $JZ$ and $KZ$ are congruent as corresponding chords of given circle are proved congruent.

Explanation of Solution

Giveninformation: In below given figure, $\angle J\cong \angle K$ .

  

Concept used:Use the statement of theorem 9.4 that congruent chords have congruent corresponding arcs. Also use the fact that in an isosceles triangle, if any two angles are congruent, then their opposite sides are also congruent.

Proof: In given triangle, $\Delta JZK$ , as $\angle J\cong \angle K$ , so their opposite sides will also be congruent. Or, $\overrightarrow{JZ}\cong \overline{ZK}$ . And using statement of theorem 9.4, the corresponding arcs of these chords will also be congruent, so, $JZ$ and $KZ$ are congruent.

Conclusion: Thus,It proves that if the two angles of triangle inside a circle are congruent, their opposite sides will be congruent and hence their corresponding arcs will also be congruent.