Chapter 9.4, Problem 6ST1

(a)

To determine

To Find: the $m\stackrel{⌢}{EF}\cong ?\text{ and }m\stackrel{⌢}{EHF}\cong ?$ in the figure shown such that point $E,F,G,H\text{ and }J\text{ lie on}\odot O$ .

Answer to Problem 6ST1

  ${50}^{\circ }\text{ and }{310}^{\circ }$

Explanation of Solution

Given:

Figure is shown below.

  

point $E,F,G,H\text{ and }J\text{ lie on}\odot O$ .

Calculation:

  $m\stackrel{⌢}{EF}$ is the measure of minor arc EF which is equal to the central angle ${50}^{\circ }$ .

And $m\stackrel{⌢}{EHF}$ represents the measure of major arc which is equal to the minus the measure of its minor arc therefore.

  $\begin{array}{l}m\stackrel{⌢}{EHF}=360-50\\ m\stackrel{⌢}{EHF}={310}^{\circ }\end{array}$

Therefore, the answer is ${50}^{\circ }\text{ and }{310}^{\circ }$ .

(b)

To determine

To State: the theorem which support the conclusion that $\stackrel{⌢}{JH}\cong \stackrel{⌢}{HG}$ in the figure shown such that $\overline{JH}\cong \overline{HG}$ .

Explanation of Solution

Given:

Figure is shown below.

  

point $E,F,G,H\text{ and }J\text{ lie on}\odot O$ .

Calculation:

Theorem 9-4 state that in a same circle or in congruent circles ,congruent chords have congruent arc.