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Chapter 3 – Parallel and Perpendicular

Chapter 3: Parallel and Perpendicular Lines

EQ: Can you remember all we’ve covered in this chapter?

Prep work: p236(3-6, 11-14, 19-24, 29-36, 43-44)
Look at examples starting on page 232.  This is just review of middle school topics on classifying triangles by their sides (scalene, isosceles or equilateral) and angles (acute, right, obtuse or equiangular) .  These problems also use the fact that the interior angles of a triangle add to 180 degrees.

Retake for Ch. 3 Test: Geo Ch3 Review for Retest

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

EQ: How do you find the distance between a point and a line?

Example #5 on p.159 is similar to Cornell notes from class.

Prep work:  p160(21-23, 36)

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 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)