Perpendicularity Section 2'1

1
PerpendicularitySection 2.1

• Lines, rays, or segments that intersect at right
  angles are perpendicular.

2
Objectives Chapter 2

• Understand the concept of perpendicularity
• Recognize the concept of complementary and
  supplementary angles
• Prove angles congruent by means of four new
  theorems
• Apply the addition/subtraction properties of
  segments and angles
• Apply the multiple/division properties of
  segments and angles
• Apply the transitive properties of angles and
  segments
• Apply the Substitution Property
• Recognize and use opposite rays and vertical
  angles

3
Illinois Learning Standards

• STATE GOAL 8 Use algebraic and analytical
  methods to identify and describe patterns and
  relationships in data, solve problems and predict
  results.
• D. Use algebraic concepts and procedures to
  represent and solve problems.
• 8.D.4 Formulate and solve linear and quadratic
  equations and linear inequalities algebraically
  and investigate nonlinear inequalities using
  graphs, tables, calculators and computers.

4
Illinois Learning Standards

• STATE GOAL 9 Use geometric methods to analyze,
  categorize and draw conclusions about points,
  lines, planes and space.
• B. Identify, describe, classify and compare
  relationships using points, lines, planes and
  solids.
• 9.B.4 Recognize and apply relationships within
  and among geometric figures.
• C. Construct convincing arguments and proofs to
  solve problems.
• 9.C.4b Construct and communicate convincing
  arguments for geometric situations.

5
Homework

• Section Page Problems
• 2.1 64 8, 11, 14,
• 2.2 68 5, 9, 20
• 2.3 74 3, 6, 13,
• 2.4 79 1, 8, 10, 16, 20, 21,
• 2.5 87 1, 8, 11, 12, 13, 17
• 2.6 93 10, 13, 16
• 2.7 98 10, 11, 17,
• 2.8 102 3, 11, 12, 13, 15
• R 106 11, 15, 21, 24, 26, 27, 31, 33

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Theorem

• Theorem If two coplanar lines are each
  perpendicular to a third line, then these two
  lines are parallel to each other.

7

• Given 2 lines cut by a transversal.
• If the corresponding angles are congruent then
  the lines are _______.

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One Four

• If two lines, segments, or rays intersect to form
  a right angle then they intersect to form how
  many right angles?

9
2.1.3
10
2.1.11
11
2.1.14