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**2-8: Proving Angle Relationships**

Geometry: Logic 2-8: Proving Angle Relationships

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Do Now:

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Homework

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Today Angle Addition Relationships Monday: Review

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Recall Angle Addition Postulate

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Recall Angle Addition Postulate: m<ABD+ m<DBC = m< ABC

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Example 1 Given: m<1=56 and m<JKL=145 Prove: m<1=89 K 2 J 1 L

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Theorems: Supplement Theorem: If two angles form a linear pair, then they are supplementary angles.

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Theorems 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 2: Given: m<1=73 Prove: m<2=17 1 2

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**Properties Reflexive Property: <1≅<1**

Symmetric Property: <1 ≅ <2 then <2 ≅ <1 Transitive Property: If <1 ≅ <2 and <2 ≅ <3 then <1 ≅ <3

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Theorems: Congruent Supplements Theorem: Angles supplementary to the same angle or to congruent angles are congruent themselves.

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Theorems Congruent Complements Theorem: Angles complementary to the same angle or to congruent angles are congruent themselves.

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Theorems: Vertical Angles Theorem: If two angles are vertical angles, then they are congruent.

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Example 3: Given: <1 and <2 are supplementary; <2 and <3 are supplementary Prove: <1 ≅ <3 1 2 3

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**Example 4: Given: 𝐷𝐵 bisects <ADC Prove: <2 ≅ <3 B A C 1 2 D**

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**Theorems Perpendicular lines intersect to form ______________.**

All right angles are ________________ Perpendicular lines form ____________ adjacent angles.

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**Theorems Perpendicular lines intersect to form four right angles.**

All right angles are congruent Perpendicular lines form congruent adjacent angles.

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Theorems Continued If two angles are congruent and supplementary, then each angle is ___________________ If two congruent angles form a linear pair, then they are ___________________

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Theorems Continued 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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**Example 5: Given: <5 ≅ <6**

Prove: <4 and <6 are supplementary 6 5 4

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Proving Theorems: Prove that perpendicular lines intersect to form four right angles.

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**Practice Problems Try some on your own!**

As always call me over if you are confused!

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Exit Ticket Given: <4 ≅ <7 Prove: <5 ≅ <6 5 6 4 7

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