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

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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.

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

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

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

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

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

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)

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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