Download Geometry Lesson 2.8.notebook

Geometry Lesson 2.8.notebook
October 20, 2014
Proving Angle Relationships
Protractor Postulate ­ Given any angle, the measure can be put into a one­to­one crrespondence with real numbers between 0 and 180.
ANGLE ADDITION POSTULATE ­ D is in the interior of if and only if Find if
If and Find 1
Geometry Lesson 2.8.notebook
October 20, 2014
SUPPLEMENT THEOREM ­ If two angles form a linear pair, then they are supplementary angles.
COMPLEMENT THEOREM ­ If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary. form a linear pair. If 2
Geometry Lesson 2.8.notebook
October 20, 2014
Properties of Angle Congruence
Theorem ­ Reflexive Property of Congruence Theorem ­ Symmetric Property of Congruence
Theorem ­ Transitive Property of Congruence
CONGRUENT SUPPLEMENT THEOREM ­ Angles supplementary to the same angle or congruent angles are congruent.
If Congruent Complement Theorems ­ Angles complementary to the same or congruent angles are complementary.
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Geometry Lesson 2.8.notebook
October 20, 2014
GIVEN ­ Angles 2 and 4 are vertical angles.
Prove: are vertical
angles.
are nonadjcent angles formed by 2 interecting lines.
form a linear pair.
Definition of vertical angles
Definition of a linear pair.
form a linear pair.
are supplementary
Supplement Theorem
are supplementary
Congruent Supplement Theorem
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Geometry Lesson 2.8.notebook
October 20, 2014
VERTICAL ANGLE THEOREM ­ If two angles are verical angles, then they are congruent.
bisects Given: PROVE: bisects 5
Geometry Lesson 2.8.notebook
October 20, 2014
Right Angle Theorems
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Perpendicular lines intersect to form 4 right angles.
All right angles are congruent.
Perpendicular lines form congruent adjacent angles.
If two angles are congruent and supplementary, then each angle is a right angle.
If two congruent angles form a linear pair, then they are right angles.
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Geometry Lesson 2.8.notebook
October 20, 2014
P. 154 6­14
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