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Lesson 9.4 Inscribed 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. Theorem 9.13 - PowerPoint PPT Presentation
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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
