swbat find the measure of an inscribed angle. p a b c central angle : an angle whose vertex is at...

SWBAT ﬁnd the measure of an inscribed angle

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SWBAT find the measure of an inscribed angle

Central Angle : An Angle whose vertex is at the center of the

circleMinor ArcMajor Arc

Less than 180°

More than 180°

ABACB

To name: use 2 letters

To name: use 3 letters

<APB is a Central Angle

Page 3: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Semicircle: An Arc that equals 180°

EDF

To name: use 3 letters

EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of

180°

Page 4: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

THINGS TO KNOW AND REMEMBER ALWAYS

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal

Page 5: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

measure of an arc = measure of central angle

Q 96

m AB

m ACB

m AE

96°

264°

84°

Page 6: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Arc Addition PostulateA

m ABC =

m AB + m BC

Page 7: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Tell me the measure of the following arcs.

80100

140A

m DAB =

m BCA =

240

260

Page 8: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles.

4545

110

Page 9: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

let’s practice

•Page 606 #9-18 You have 7 minutes.You have 7 minutes.

Page 10: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Inscribed Angle: An angle whose

vertex is on the circle and

whose sides are chords of the circle

INSCRIBEDANGLE

INTER

CEP

TED

ARC

Page 11: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

T1.

YES; CL

Page 12: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

V2. NO;

QVR

Page 13: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Let’s investigate

Page 607

Page 14: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

ArcdIntercepteAngleInscribed

160°

80°

To find the measure of an inscribed angle…

Page 15: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

120

What do we call this type of angle?What is the value of x?

What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the

measure of the inscribed arc!!

Page 16: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Examples

3. If m JK = 80, find m <JMK.

4. If m <MKS = 56, find m MS.

112

Page 17: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

If two inscribed angles intercept the same arc, then they are congruent.

Page 18: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Example 5

In J, m<A= 5x and m<B = 2x + 9.Find the value of x.

m<A = m<B 5x = 2x+9x = 3

Page 19: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Let’s practice

•Page 611 #5-16

Page 20: SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Homework

• Page 612 # 23 - 27

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swbat find the measure of an inscribed angle. p a b c central angle : an angle whose vertex is at...

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