Chapter 9.4, Problem 1CE

To determine

To write: Whether $\stackrel{⌢}{PQ}\cong \stackrel{⌢}{XY}$ or not

Answer to Problem 1CE

Yes, $\stackrel{⌢}{PQ}\cong \stackrel{⌢}{XY}$

Explanation of Solution

Given information: $\overline{PQ}\cong \overline{XY}$

  

A minor arc is a shorter arc joining any two points on the circle.

Use the fact that if two chords are equal then their corresponding minor arcs are equal in measure.

As $\overline{PQ}\cong \overline{XY}$ , $\stackrel{⌢}{PQ}\cong \stackrel{⌢}{XY}$ .

So, answer is Yes, if $\overline{PQ}\cong \overline{XY}$ then $\stackrel{⌢}{PQ}\cong \stackrel{⌢}{XY}$ .