Warm-Up Exercises ANSWER x = 60; y = 60 ANSWER x = 35; y = 35 1. Find x and y. 2.

Warm-Up Exercises

ANSWER x = 60; y = 60

ANSWER x = 35; y = 35

1.

Find x and y.

2.

Warm-Up ExercisesEXAMPLE 1 Find measures of arcs

RSa. RTSb. RSTc.

SOLUTION

RS is a minor arc, so mRS = m RPS = 110o.a.

RTS is a major arc, so mRTS = 360o 110o = 250o.b. –

Find the measure of each arc of P, where RT is a diameter.

c. RT is a diameter, so RST is a semicircle, and mRST = 180o.

Warm-Up ExercisesEXAMPLE 2 Find measures of arcs

A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.

Survey

a. mAC

SOLUTION

a. mAC mAB= + mBC

= 29o + 108o

= 137o

Warm-Up ExercisesEXAMPLE 2 Find measures of arcs

b. mACD = mAC + mCD= 137o + 83o

= 220o

A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.

Survey

SOLUTION

b. mACD

Warm-Up ExercisesEXAMPLE 2 Find measures of arcs

mADC mAC= 360o – c.

= 360o – 137o

= 223o

A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.

Survey

SOLUTION

c. mADC

Warm-Up ExercisesEXAMPLE 2 Find measures of arcs

d. mEBD = 360o – mED

= 360o – 61o

= 299o

d. mEBD

A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.

Survey

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Identify the given arc as a major arc, minor arc, or

semicircle, and find the measure of the arc.

Warm-Up Exercises

TQ is a minor arc, so m TQ = 120o.

GUIDED PRACTICE for Examples 1 and 2

1. TQ

SOLUTION

. QRT2

SOLUTION

QRT is a major arc, so m QRT= 240o.

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

. TQR3

SOLUTION

TQR is a semicircle, so m TQR = 180o.

. QS4

SOLUTION

QS is a minor arc, so m QS = 160o.

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

. TS5

SOLUTION

TS is a minor arc, so m TS = 80o.

. RST6

SOLUTION

RST is a semicircle, so m RST = 180o.

Warm-Up ExercisesEXAMPLE 3 Identify congruent arcs

Tell whether the red arcs are congruent. Explain why or why not.

a. b.

SOLUTION

a. CD EF because they are in the same circle and mCD = mEF

b. RS and TU have the same measure, but are not congruent because they are arcs of circles that are not congruent.

Warm-Up Exercises

c. VX YZ because they are in congruent circles and mVX = mYZ .

EXAMPLE 3 Identify congruent arcs

Tell whether the red arcs are congruent. Explain why or why not.

c.

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Tell whether the red arcs are congruent. Explain why or why not.

7.

AB CD because they are in congruent circles and mAB = mCD .

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Tell whether the red arcs are congruent. Explain why or why not.

8.

SOLUTION

MN and PQ have the same measure, but are not congruent because they are arcs of circles that are not congruent.

Warm-Up ExercisesDaily Homework Quiz

Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure.

1. BC

ANSWER minor arc, 32o

Warm-Up ExercisesDaily Homework Quiz

2.

Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure.

CBE

ANSWER major arc, 212o

Warm-Up ExercisesDaily Homework Quiz

3.

Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure.

BCE

ANSWER semicircle, 180o

Warm-Up ExercisesDaily Homework Quiz

4.

Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure.

BCAEExplain why =~ .

ANSWER

BCAE =~

m AFE = m BFC because the angles are vertical angles, so AFE BFC.Then arcs and are arcs that have the same measure in the same circle. By definition .

=~AE BC

Warm-Up ExercisesDaily Homework Quiz

5.ACD AC

Two diameters of P are AB and CD.If m = 50 , find m and m .

. ADo

ANSWERo

310 ; 130o