Lesson 9.4 Inscribed Angles pp. 390-393

Lesson 9.4Inscribed Angles

pp. 390-393

Lesson 9.4Inscribed Angles

pp. 390-393

Objectives:1. To identify and prove theorems

relating inscribed angles to the measure of their intercepted arcs.

2. To state other relationships that involve inscribed angles.

Objectives:1. To identify and prove theorems

relating inscribed angles to the measure of their intercepted arcs.

2. To state other relationships that involve inscribed angles.

Theorem 9.13

The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.

Theorem 9.13

The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.

AA

BBCCKK

KK

AA

BB

CC

DD

KK

AA

BB

CC

DD

OO

BB

AACC

If mAC = 60, then mABC = 30.If mAC = 60, then mABC = 30.

Theorem 9.14

If two inscribed angles intercept congruent arcs, then the angles are congruent.

Theorem 9.14

If two inscribed angles intercept congruent arcs, then the angles are congruent.

OO

BB

AACC

DD

ABC ADC ABC ADC

Theorem 9.15

An angle inscribed in a semicircle is a right angle.

Theorem 9.15

An angle inscribed in a semicircle is a right angle.

OOAA

BB

CC

mABC = 90.mABC = 90.

Theorem 9.16

The opposite angles of an inscribed quadrilateral are supplementary.

Theorem 9.16

The opposite angles of an inscribed quadrilateral are supplementary.

OOAA

BB

CC

DD

ABC and ADC are supplementary.BAD and BCD are supplementary.ABC and ADC are supplementary.BAD and BCD are supplementary.

MM

PPSSTT

UU

RRQQ

Given: In circle M, mRT = 80,

mSQ = 64. Find mQTS.

Given: In circle M, mRT = 80,

mSQ = 64. Find mQTS.

MM

PPSSTT

UU

RRQQ

Given: In circle M, mRT = 80,

mSQ = 64. Find mTQR.

Given: In circle M, mRT = 80,

mSQ = 64. Find mTQR.

MM

PPSSTT

UU

RRQQ

Given: In circle M, mRT = 80,

mSQ = 64. Find mTQP.

Given: In circle M, mRT = 80,

mSQ = 64. Find mTQP.

MM

PPSSTT

UU

RRQQ

Given: In circle M, mRT = 80,

mSQ = 64. Find mTPR.

Given: In circle M, mRT = 80,

mSQ = 64. Find mTPR.

AA BB

DD CC EE

KK

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mAC.

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mAC.

AA BB

DD CC EE

KK

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mBC.

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mBC.

AA BB

DD CC EE

KK

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mACB.

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mACB.

AA BB

DD CC EE

KK

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mABC.

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mABC.

AA BB

DD CC EE

KK

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mAB.

Given: In circle K, AB || DE,

AC BC; mBAC = 56°. Find mAB.

Homeworkpp. 392-393Homeworkpp. 392-393

D C

AB

O

X1

3

2

4

►A. Exercises1. If mDC = 60°, find m4.

►A. Exercises1. If mDC = 60°, find m4.

D C

AB

O

X1

3

2

4

►A. Exercises3. If m3 = 25°, find mDC.

►A. Exercises3. If m3 = 25°, find mDC.

D C

AB

O

X1

3

2

4

►A. Exercises5. If m3 = 28°, find m4.

►A. Exercises5. If m3 = 28°, find m4.

D C

AB

O

X1

3

2

4

►A. Exercises7. If mDC = 55°, find mDBC.

►A. Exercises7. If mDC = 55°, find mDBC.

D C

AB

O

X1

3

2

4

►A. Exercises9. If mADB = 290°, find m1.

►A. Exercises9. If mADB = 290°, find m1.

D C

AB

O

X1

3

2

4

►B. Exercises11. If mDC = 68° and mAB =

134°, find mDXA.

►B. Exercises11. If mDC = 68° and mAB =

134°, find mDXA.

►B. ExercisesUse the following figure for exercises 12-16.

13. If mMLO = 240°, find mMLO.

►B. ExercisesUse the following figure for exercises 12-16.

13. If mMLO = 240°, find mMLO.

MM LL

PP

YY

NN OO

►B. ExercisesUse the following figure for exercises 12-16.

15. If mMLO = 212°, find mMNO and mMLO.

►B. ExercisesUse the following figure for exercises 12-16.

15. If mMLO = 212°, find mMNO and mMLO.

MM LL

PP

YY

NN OO

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

E

A D B

C

27. CDA and CDB are right angles.27. CDA and CDB are right angles.

28. BC BD28. BC BD

E

A D B

C

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

29. mACE = mB + mCAD29. mACE = mB + mCAD

E

A D B

C

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

30. AE + AB BE30. AE + AB BE

E

A D B

C

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

31. mBAE + mABE + mE = 180°31. mBAE + mABE + mE = 180°

E

A D B

C

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D

■ Cumulative ReviewJustify each statement with a reason.Given: ABC is obtuse; CD AB at D