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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 Presentation
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Lesson 4.3Angle Bisectors
pp. 129-134
Lesson 4.3Angle 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.
Objectives:1. To identify and apply the Angle
Addition Postulate.2. To define and apply angle
bisectors.3. To define and identify
perpendicular lines.
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
DAB and DAC are called adjacent angles.
DAB and DAC are called adjacent angles.
BB
DD
CCAA
BB
DD
CCAA
BAC and DAC are NOT adjacent angles.
BAC and DAC are NOT adjacent angles.
BB
CC
EEAA DD
BAC and CDE are NOT adjacent angles.
BAC and CDE are NOT adjacent angles.
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.
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
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
AA
DDCC
BB
BB
DD
CCAA
Find mBAC if mBAD = 35 and mDAC = 15.
Find mBAC if mBAD = 35 and mDAC = 15.
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.
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°
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.
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°
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
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
Homeworkpp. 133-134Homeworkpp. 133-134
►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
►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
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?
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?
■ 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
■ 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
■ 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
■ 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
■ 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
