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Day 40 Warm Up. Use the law of syllogism to establish new information: If I go to the beach, then I’ll surf. If I surf, then I’ll nearly kill myself. Aside from surfing, what will happen if I go to the beach?. Monday, October 6, 2008. Objectives.

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day 40 warm up
Day 40 Warm Up
  • Use the law of syllogism to establish new information:
  • If I go to the beach, then I’ll surf.
  • If I surf, then I’ll nearly kill myself.
  • Aside from surfing, what will happen if I go to the beach?

Monday, October 6, 2008

objectives
Objectives
  • Use the law of syllogism to reason deductively
scooby doo
Scooby Doo
  • Tips:
  • Restate all in if-then form: If the ghosts chase Scooby Doo, then he will run.
  • Write all with => notation.
  • Look for spots to apply syllogism, rearranging if necessary.
scooby doo1
Scooby Doo
  • Therefore, if Scooby Doo asks for snacks, then he will share them with Shaggy. (After being chased by ghosts and followed by Shaggy).

The rearranged statements:

Scooby asks for snacks => ghosts chase Scooby

ghosts chase Scooby => Scooby runs

Scooby runs => Shaggy follows

Shaggy follows Scooby => Scooby finds snacks

Scooby finds snacks => Scooby shares

classwork
Classwork
  • Complete the logic worksheet

Home Studies

  • pp. 123-4
    • 10, 14, 15, 24, 25
    • Due Tuesday
in closing
In Closing
  • Syllogism:
    • p => q
    • q => r
    • p => r

Next Time We Meet

  • Pulling it all together: definitions, theorems, and logic => PROOFS
day 41 warm up
Day 41 Warm Up
  • If m and n are whole numbers,
  • 49 < n < 101 and 19 < m < 51,
  • then what is the greatest value for

Image: Lori Spindler’s photostream, http://www.flickr.com/photos/lorispindler/2569943966/

check home studies
Check Home Studies
  • 10. Contrapositive: “If the key is not in the ignition, then the car is not running.”
    • Converse: “If the key is in the ignition, then the car is running.”
  • 14. “If the moon is full, then the cattle will be nervous.”
  • 15. c., a., b., e., d. “kingdom was lost”
  • 24. b., e., c., a., d. “measure of <5 = 120°”
  • 25. c., b., e., a., d. “measure of <2 = 60°”
objectives1
Objectives
  • Learn to read and create 3 styles of proofs:
  • Paragraph proof
  • Flow proof
  • Two-column proof
  • Use logical reasoning to solve puzzles.
theorem 3 3
Theorem 3.3
  • “If two lines are perpendicular, then they intersect to form four right angles.”

Source: cdw9’s photostream http://www.flickr.com/photos/wainwright/168429619/

theorem 3 31
Theorem 3.3
  • “If two lines are perpendicular, then they intersect to form four right angles.”

Prove it!

p. 126 in your book

Source: cdw9’s photostream http://www.flickr.com/photos/wainwright/168429619/

classwork1
Classwork
  • Page 129, #9 and 10

Home Studies

None

Paragraph proof source: http://www.themathlab.com/geometry/mathcourt/writeproofs.htm#paragraph

in closing1
In Closing
  • Paragraph proofs use full sentences for justifying steps to a conclusion.

Next Time We Meet

Two other forms of proof: flow & two-column.

These are certainly shorter to write!

day 42 warm up
Jerry and Rachel are two strangers thrown together by a mysterious phone call from a woman they have never met.

A doctor who is traveling to see his estranged son sparks with an unhappily married woman at a North Carolina inn.

An LAPD officer will stop at nothing to force out the interracial couple who just moved in next door.

A firefighter and his wife begin a 40-day experiment known as "The Love Dare" in an attempt to save their marriage.

A disk containing the memoirs of a CIA agent ends up in the hands of two unscrupulous gym employees who attempt to sell it.

Burn After Reading

Nights in Rodanthe

Fireproof

Lakeview Terrace

Eagle Eye

Day 42 Warm Up

Match the weekend’s top 5 movies with their plots.

Source: http://www.imdb.com

objectives2
Objectives
  • Learn to read and create 3 styles of proofs:
  • Paragraph proof
  • Flow proof
  • Two-column proof
  • Use logical reasoning to solve puzzles.
paragraph proof
Paragraph Proof
  • Note: SAS is a theorem about triangles. We’ll learn it later.

Source: http://www.homeschoolmath.net/teaching/proof.php

theorems 3 4 3 5
Theorems 3.4 & 3.5
  • Thm 3.4: “All right angles are congruent.”
  • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.”

Source: Tim Caynes’ photostream http://www.flickr.com/photos/timcaynes/351502040/

theorems 3 4 3 51
Theorems 3.4 & 3.5
  • Thm 3.4: “All right angles are congruent.”
  • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.”

Prove it!

p. 127 in your book

Source: Tim Caynes’ photostream http://www.flickr.com/photos/timcaynes/351502040/

flow proof for thm 3 4
Flow Proof for Thm 3.4

Thm 3.4: “All right angles are congruent.”

2

1

Given

Given

two column proof for thm 3 5
Two-Column Proof for Thm 3.5
  • Thm 3.5: “If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.”

1

2

Statements Reasons

1. 1. Given

classwork2
Classwork
  • p. 129
  • Guided Practice 1-6

Home Studies

pp. 129-131

13-19 odd

classwork3
Classwork
  • Solutions for p. 129, #1-6
  • Four right
  • perpendicular
  • congruent
  • flow
  • two-column
  • paragraph
in closing2
In Closing
  • Two new theorems today – what were they?
  • Two new proof styles – which do you like better? Why?

Next Time We Meet

Proving theorems about parallel lines.

day 43 warm up
Day 43 Warm Up
  • Substitute teacher, Megan’s observing Yom Kippur.
  • Identify the pairs of angles that are:
  • Supplementary
  • Congruent

1

2

3

4

5

6

7

8

objectives3
Objectives
  • Identify angles formed by two lines and a transversal.
  • Use properties of parallel lines, including:
    • Corresponding angles
    • Alternate interior angles
    • Consecutive interior angles
    • Alternate exterior angles
    • Perpendicular transversals
classwork4
Classwork
  • Read and carefully study page 134 in the text.
  • Then solve p. 137, #1-4

Home Studies

None

classwork5
Classwork
  • Solutions to p. 137, #1-4
  • (answers vary on all)
  • <1 and <5
  • <3 and <5 or <4 and <6
  • <1 and <7 or <2 and <8
  • <4 and <5 or <3 and <6
objectives4
Objectives
  • Identify angles formed by two lines and a transversal.
  • Use properties of parallel lines, including:
    • Corresponding angles
    • Alternate interior angles
    • Consecutive interior angles
    • Alternate exterior angles
    • Perpendicular transversals
parallel lines cut by transversal
Parallel Lines Cut by Transversal

1

2

3

5

4

6

Red: Transversal

7

8

Yellow: Parallel lines

Image: evansville’s photostream http://www.flickr.com/photos/evansville/93945229/

properties of parallel lines
Properties of Parallel Lines
  • P15: Corresponding Angles Postulate
  • Thm 3.6: Alternate Interior Angles Thm.
  • Thm 3.7: Consecutive Interior Angles Thm.
  • Thm 3.8: Alternate Exterior Angles Thm.
  • Thm 3.9: Perpendicular Transversal Thm.

See page 135 in the textbook.

properties of parallel lines1
Properties of Parallel Lines
  • P15: Corresponding Angles Postulate

1

1 & 5 are congruent

5

properties of parallel lines2
Properties of Parallel Lines
  • Thm 3.6: Alternate Interior Angles Thm.

2

2 & 7 are congruent

7

properties of parallel lines3
Properties of Parallel Lines
  • Thm 3.7: Consecutive Interior Angles Thm.

4 & 7 are supplementary

4

7

properties of parallel lines4
Properties of Parallel Lines
  • Thm 3.8: Alternate Exterior Angles Thm.

1

2

1 & 8 are congruent

3

5

4

6

7

8

properties of parallel lines5
Properties of Parallel Lines
  • Thm 3.9: Perpendicular Transversal Thm.

If the red line is perpendicular to the “black dog” line then it’s also perpendicular to the “brown dog” line.

classwork6
Classwork
  • p. 137, #5-8

Home Studies

Starting p. 123

10, 14, 15, 24, 25

Due Monday

classwork7
Classwork
  • Solutions
  • Perpendicular Transversal Theorem
  • Alternate Exterior Angles Theorem
  • Alternate Interior Angles Theorem
  • Consecutive Interior Angles Theorem
  • Corresponding Angles Postulate
in closing3
In Closing
  • What’s a transversal?
  • Lots of vocabulary: corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles.

Next Time We Meet

We’ll explore the problems on pages 138-9.