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**Week 1 Warm Up 10.18.11 1) If 3 + 4 = 7, then 7 = 3 + 4,**

State the postulate or theorem: 1) If = 7, then 7 = 3 + 4, 2) If 2x + 5 = 17, then 2x = 12. Add theorem 2.1 here next year. 3) If ∠A and ∠B are vertical angles, then ∠A ≅ ∠B.

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Geometry 3.2 Day 1 I will prove results about perpendicular lines. Theorem 3.1 Linear Pairs of Congruent Angles If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular Ex g ⊥ h

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**1 2 Ex 1 Prove T3.1 Given: ∠ 1 ≅ ∠ 2 Given: ∠ 1 and ∠ 2**

are linear pairs Prove: g ⊥ h Step Reason ∠ 1 ≅ ∠ 2 Given ∠ 1 and ∠ 2 are linear pairs Given m∠ 1 + m∠ 2 = 180º Definition of Linear Pairs m∠ 1 = m∠ 2 Definition of congruent angles m∠ 1 + m∠ 1 = 180º Substitution property of equality 2m∠ 1 = 180º Simplify m∠ 1 = 90º Division property of equality m∠ 2 = 90º Substitution property of equality ∠ 1and ∠ 2 are right angles Definition of right angles g ⊥ h Definition of perpendicular lines

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**Perpendicular Adjacent Acute Angles**

Theorem 3.2 Perpendicular Adjacent Acute Angles If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Ex 90º

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Theorem 3.3 Four Right Angles If two lines are perpendicular, then they intersect to form four right angles. Ex 90º

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Theorem 3.3 Four Right Angles If two lines are perpendicular, then they intersect to form four right angles. 90º Ex

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**k j Ex 2 What can you conclude?: j ⊥ k 8 9 7 10**

1) ∠ 7 and ∠ 8 are complementary 2) ∠ 9 is a right angle 3) 4)

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**What is the value of x? 65º x Review**

A _______ is a line that intersects two or more coplanar lines. Do: 1 What is the value of x? 65º Add theorem 2.1 here next year. x Assignment: Handout - Section 3.2 B

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Chapter 3.6 Notes: Prove Theorems about Perpendicular Lines Goal: You will find the distance between a point and a line.

Chapter 3.6 Notes: Prove Theorems about Perpendicular Lines Goal: You will find the distance between a point and a line.

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