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Geometry

Chapter 3: Parallel and Perpendicular Lines
3.4: Proofs with Perpendicular Lines

EQ: How do you write equations of parallel and perpendicular lines?

Parallel lines have the same slope and perpendicular lines have slopes that are opposite reciprocals (see theorems on p157).
Examples #2, 3 and 4 will help on the prep work.

Prep work:  p160(7-15, 17-19, 25-28)

Retake for Ch. 2 Test: p116(1-24, 26)
(On 1-4, skip inverse and contrapositive)

Chapter 3: Parallel and Perpendicular Lines
3.4: Proofs with Perpendicular Lines

EQ: How do you bisect a segment with a compass?

Constructions (p.149) were covered in class along with three new perpendicular related theorems (p.150)(that aren’t too essential in my opinion since we can easily work around them with previous theorems).

Prep work:  p152(3-12, 17-20, 23, 27, 28) and Worksheet 3.4

Retake for Ch. 2 Test: p116(1-24, 26)
(On 1-4, skip inverse and contrapositive)

Chapter 3: Parallel and Perpendicular Lines
3.3: Proving Parallel Lines

EQ: What is the converse of the theorems learned from last class?

Theorems 3.5 – 3.9 (p. 138-141) are the most important ideas to know. Most of these are Converse theorems of the ones from last class (Corresponding, Alternate Interior and Alternate Exterior and Consecutive Interior angles).  Just one new theorem using the Transitive property.

Prep work:  p142(3-8, 13-25, 28, 29, 33-36)

Retake for Ch. 2 Test: p116(1-24, 26)
(On 1-4, skip inverse and contrapositive)

Chapter 3: Parallel and Perpendicular Lines
3.1 and 3.2: Parallel Lines and Transversals

EQ: What special angle relations arise from two parallel lines cut by a transversal?

Theorems 3.1 – 3.4 (p. 132) are the most important ideas to know. Know that Corresponding, Alternate Interior and Alternate Exterior angles are congruent and that Consecutive Interior angles are supplementary.

Prep work: Worksheet 3.1-3.2 and p135(6-8, 11-13, 21, 22, 24)

 

Chapter 3: Parallel and Perpendicular Lines
3.1: Pairs of Lines and Angles

EQ: Are parallel lines the only ones that don’t intersect?

Core Concept boxes (p. 126 and 129) are the most important ideas to know. Know the difference between parallel and skew lines. You also need to know the 4 pairs of angles formed when any 2 lines (not necessarily parallel — that’s the next lesson) are crossed by a transversal. Look at examples 1 and 3 (the ones after the Core Concept boxes).

Prep work:  p129(3-31)

2.6 Proving Geometric Relationships

EQ: Why can theorems be a great shortcut for other proofs?

Four new theorems and one postulate today.  They are the last ones listed under their sections in the handout below.  You will get to use a similar handout for the next assessment.

Prep work:  p111(3-6, 13-16, 18, 23, 31-36)

Handout: Ch 1/2 Definitions, Postulates, Properties and Theorems

2.5 Two Column Proofs

EQ: How can you show your geometric reasoning in a 2-column proof format?

Important gateway between Algebraic properties and Geometric properties is the Definition of Congruence.  Additional properties covered include reflexive, symmetric and transitive of congruence for segments and angles.

Prep work:  p103(3, 4, 13-15, 23-26)

Retake assignment for Ch. 1 – only for those wanting to retake the Ch. 1 Assessment.  You also need to complete a majority of the problems on any missing assignment.  Retake must be done by Friday, Oct. 18th.