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.


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


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

= 220o


Survey

SOLUTION

b. mACD


mADC mAC= 360o – c.

= 360o – 137o

= 223o


Survey

SOLUTION

c. mADC


d. mEBD = 360o – mED

= 360o – 61o

= 299o

d. mEBD


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.


. TQR3

SOLUTION

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

. QS4

SOLUTION

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


. 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


c.

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Example 3


7.

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

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Example 3


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


2.


CBE

ANSWER major arc, 212o


3.


BCE

ANSWER semicircle, 180o


4.


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


5.ACD AC

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

. ADo

ANSWERo

310 ; 130o

warm-up exercises answer x = 60; y = 60 answer x = 35; y = 35 1. find x and y. 2

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