lesson 4.3 angle bisectors pp. 129-134
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Lesson 4.3 Angle Bisectors pp. 129-134. Objectives: 1.To identify and apply the Angle Addition Postulate. 2.To define and apply angle bisectors. 3.To define and identify perpendicular lines. Definition. - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 4.3Angle Bisectors
pp. 129-134
Lesson 4.3Angle Bisectors
pp. 129-134
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Objectives:1. To identify and apply the Angle
Addition Postulate.2. To define and apply angle
bisectors.3. To define and identify
perpendicular lines.
Objectives:1. To identify and apply the Angle
Addition Postulate.2. To define and apply angle
bisectors.3. To define and identify
perpendicular lines.
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Adjacent angles are two coplanar angles that have a common side and common vertex but no common interior points.
Adjacent angles are two coplanar angles that have a common side and common vertex but no common interior points.
DefinitionDefinitionDefinitionDefinition
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DAB and DAC are called adjacent angles.
DAB and DAC are called adjacent angles.
BB
DD
CCAA
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BB
DD
CCAA
BAC and DAC are NOT adjacent angles.
BAC and DAC are NOT adjacent angles.
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BB
CC
EEAA DD
BAC and CDE are NOT adjacent angles.
BAC and CDE are NOT adjacent angles.
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Postulate 4.3Angle Addition Postulate. If K lies in the interior of MNP, then mMNP = mMNK + mKNP.
Postulate 4.3Angle Addition Postulate. If K lies in the interior of MNP, then mMNP = mMNK + mKNP.
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Find mXYZ if mXYT = 25° and mTYZ = 15°.
mXYZ = mXYT + mTYZ
mXYZ = 25 + 15
mXYZ = 40°
Find mXYZ if mXYT = 25° and mTYZ = 15°.
mXYZ = mXYT + mTYZ
mXYZ = 25 + 15
mXYZ = 40°
Example 1Example 1Example 1Example 1
ZZ
TT
XX
YY
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Find mDBC if mABC = 90° and mABD = 70°.
mABC = mABD + mDBC
90 = 70 + mDBC
20° = mDBC
Find mDBC if mABC = 90° and mABD = 70°.
mABC = mABD + mDBC
90 = 70 + mDBC
20° = mDBC
Example 2Example 2Example 2Example 2
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DDCC
BB
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BB
DD
CCAA
Find mBAC if mBAD = 35 and mDAC = 15.
Find mBAC if mBAD = 35 and mDAC = 15.
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Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV.
Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV.
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Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV.
Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV.
AA
RRQQ
VV
30°30° 70°70°
40°40°
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Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV.
Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV.
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Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV.
Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV.
AA
RRQQ
VV
30°30°
70°70°100°100°
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An angle bisector is a ray that (except for its origin) is in the interior of an angle and forms congruent adjacent angles.
An angle bisector is a ray that (except for its origin) is in the interior of an angle and forms congruent adjacent angles.
DefinitionDefinitionDefinitionDefinition
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Perpendicular lines are lines that intersect to form right angles. The symbol for perpendicular is .
Perpendicular lines are lines that intersect to form right angles. The symbol for perpendicular is .
DefinitionDefinitionDefinitionDefinition
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Homeworkpp. 133-134Homeworkpp. 133-134
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►A. Exercises11. Find mUYX if mUYW = 75° and
mWYX = 35°.
►A. Exercises11. Find mUYX if mUYW = 75° and
mWYX = 35°.
ZZ YY XX
UU
VVWW
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►B. Exercises13. Find mUYV if mUYW = 85° and
mVYW = 15°.
►B. Exercises13. Find mUYV if mUYW = 85° and
mVYW = 15°.
ZZ YY XX
UU
VVWW
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AABB
CC
DDEE
FF11 55
443322
►B. Exercises
15. If FD is the bisector of EFC, what is true about 1 and 5?
►B. Exercises
15. If FD is the bisector of EFC, what is true about 1 and 5?
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AABB
CC
DDEE
FF11 55
443322
►B. Exercises
17. If FC bisects DFB and mDFB = 92°, what is m5?
►B. Exercises
17. If FC bisects DFB and mDFB = 92°, what is m5?
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■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.26. plane, space
■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.26. plane, space
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■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.27. point, line
■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.27. point, line
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■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.28. polygon, plane
■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.28. polygon, plane
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■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.29. line, plane
■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.29. line, plane
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■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.30. polyhedron, space
■ Cumulative ReviewIn each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem.30. polyhedron, space