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**Lesson 2 – 8 Proving Angle Relationships**

Geometry Lesson 2 – 8 Proving Angle Relationships Objective: Write proofs involving supplementary angles. Write proofs involving congruent and right angles.

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**Postulate 2.10 Protractor Postulate**

Given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180.

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Postulate 2.11 Angle Addition Postulate

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**Use Angle Addition Postulate**

Find

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Example If Justify each step. Angle Add. Post. Sub Sub Subt. Prop. Sub

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**Theorems Supplement Theorem Complement 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 angles.

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**Example Angles 6 & 7 form a linear pair. 3x + 32 + 5x + 12 = 180**

Justify each step. Supplement Thm. 3x x + 12 = 180 Sub 8x + 44 = 180 Sub 8x = Subt. Prop. 8x = 136 Sub Division Prop. x = 17 Sub

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**Properties of Angle Congruence**

Reflexive Symmetric Transitive

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**Theorem Congruent Supplement Theorem Abbreviation:**

Angles supplementary to the same angle or to congruent angles are congruent. Abbreviation:

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**Theorem Congruent Complements Theorem Abbreviation**

Angles complementary to the same angle or congruent angles are congruent. Abbreviation

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**Prove that the vertical angles 2 and 4 are congruent.**

Given: Prove:

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**Theorem 2.8 Vertical Angle Theorem**

If two angles are vertical angles, then they are congruent.

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**Prove that if DB bisects**

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**Right Angle Theorems Theorem 2.9 Theorem 2.10 Theorem 2.11**

Perpendicular lines intersect to form 4 right angles Theorem 2.10 All right angles are congruent. Theorem 2.11 Perpendicular lines from congruent adjacent angles.

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Theorem 2.12 If two angles are congruent and supplementary, then each angle is a right angle. Theorem 2.13 If two congruent angles form a linear pair, then they are right angles.

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Homework Pg – 4 all, 6, 8 – 14, all

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