Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
EQ: How do we write proofs involving complementary, supplementary, congruent, and right angles?
Questions/Main IdeasLesson 2­8 Proving Angle Relationships
Postulate 2.10 Protractor Postulate
Given AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of AB, such that the measure of the angle formed is r.
Postulate 2.11 Angle Addition Postulate
If R is in the interior of PQS, then m PQR + m RQS = m PQS
Questions/Main IdeasExample 1
At 4 o'clock, the angle between the hour and minute hands of a clock is 120 . If the second hand stops where it bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second hand and hour hands?
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Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
Questions/Main IdeasTheorems
2.3 Supplement Theorem: If two angles form a linear pair, then they are supplementary.
2.4 Complement Theorem: If the noncommon side of two adjacent angles form a right angle, then the angle are complementary angles.
2.5 Congruence of angles is reflexive, symmetric, and transitive.
Questions/Main Ideas Example 2
If 1 and 2 form a linear pair and m 2 = 166, find m 1.
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Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
Questions/Main Ideas Theorems
2.6 Angles supplementary to the same angle or to congruent angles are congruent.
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1 + 2 = 180 and 2 + 3 = 180 so 1 = 3
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2.7 Angles complementary to the same angle or to congruent angles are congruent.
1 + 2 = 90
and 2 + 3 = 90 so 1 = 3
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Questions/Main Ideas Example 3
In the figure, angle 1 and angle 4 form a linear pair, and angle 3 and angle 1 are supplementary. Prove that angle 3 and angle 4 are congruent.
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Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
Questions/Main Ideas Theorem 2.8 Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
Example 4
If 1 and 2 are vertical angles and m 1 = d ­ 32 and m 2 = 175 ­ 2d, find m 1 and m 2.
Questions/Main IdeasTheorems
2.9 Perpendicular lines intersect to form four right angles.
2.10
All right angles are congruent.
2.11
Perpendicular lines form congruent adjacent angles.
2.12
If two angles are congruent and supplementary, then each angle is a right angle.
2.13
If two congruent angles form a linear pair, then they are right angles.
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Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
Summary
Assignment: page 112 16­32 all, 38­39
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Lesson 2­8 Proving Angle Relationships with answers.notebook
October 24, 2012
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