Logic and Parallel Lines

Mrs. Lockhart, Oct 5, 2016

GEOMETRY STANDARD G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) using deductive reasoning. GEOMETRY STANDARD G.2 The student will use the relationships between angles formed by two lines cut by a transversal to a) determine whether two lines are parallel; b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and c) solve real-world problems involving angles formed when parallel lines are cut by a transversal.

Table of Contents

  1. Conditional Statements
  2. Intro to Symbolic Logic
  3. Venn Diagrams
  4. G.1 - Practice and Review
  5. Introduction to Parallel Lines
    1. Parallel Lines Definition
    2. Transversal Intersects Parallel Lines
    3. Parallel Lines & Related Angles
    4. Complementary and supplementary angles
    5. Play with Parallels
  6. Parallel Lines and Angles
    1. Angles related to parallel lines (Converses)
    2. Exploring Alternate Interior Angles (V2)
    3. Exploring Alternate Exterior Angles (V2)
    4. Same Side Interior Angles Theorem
    5. Exploring Corresponding Angles (V2)
  7. Graphs of Parallels
    1. Parallel & Perpendicular Consequence
    2. Writing Equations of Parallel and Perpendicular Lines
  8. G.2 - Practice and Review
    1. Animation 39
    2. Converse of Corresponding Angles Theorem
    3. Alternate Interior Angles
    4. Solution to Parallel Lines & Angles Problem

1.

Conditional Statements

SOL G.1 - identifying the converse, inverse, and contrapositive of a conditional statement;


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2.

Intro to Symbolic Logic

SOL G.1 - translating a short verbal argument into symbolic form a) Use valid forms of deductive reasoning; b) Select and use various types of reasoning and methods of proof, as appropriate.


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3.

Venn Diagrams

SOL G.1 - use and interpret Venn diagrams to represent set relationships, such as intersection and union.


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4.

G.1 - Practice and Review

G.1 Review


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5.

Introduction to Parallel Lines

SOL G.2 - determine whether two lines are parallel

  • 1. Parallel Lines Definition
  • 2. Transversal Intersects Parallel Lines
  • 3. Parallel Lines & Related Angles
  • 4. Complementary and supplementary angles
  • 5. Play with Parallels

5.1.

Parallel Lines Definition

The following applet is designed to help you understand what it means for lines to be parallel.
– Tim Brzezinski

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6.

Parallel Lines and Angles

SOL G.2 - verify the parallelism, using algebraic and coordinate methods as well as deductive proofs

  • 1. Angles related to parallel lines (Converses)
  • 2. Exploring Alternate Interior Angles (V2)
  • 3. Exploring Alternate Exterior Angles (V2)
  • 4. Same Side Interior Angles Theorem
  • 5. Exploring Corresponding Angles (V2)

6.1.

Angles related to parallel lines (Converses)

– Anthony OR 柯志明, Alex CHIK

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7.

Graphs of Parallels

  • 1. Parallel & Perpendicular Consequence
  • 2. Writing Equations of Parallel and Perpendicular Lines

7.1.

Parallel & Perpendicular Consequence

[color=#000000]The following applet demonstrates a property that parallel lines have when they're drawn in the coordinate plane. [br] [i] [br]Be sure to move the [color=#1e84cc][b]blue points[/b][/color] around quite a bit![/i] [/color]
[color=#000000]This applet demonstrates a property that perpendicular lines have when they're drawn in the coordinate plane. [br][br][i]Be sure to move the points around quite a bit and observe carefully as you do! [/i][/color]
[color=#000000]What can you conclude about parallel lines drawn in the coordinate plane? [/color]
[color=#000000]What can you conclude about perpendicular lines that are drawn in the coordinate plane? [br](Assume the lines are not aligned horizontally and vertically). [/color]
– Tim Brzezinski

7.2.

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8.

G.2 - Practice and Review

SOL G.2 Review

  • 1. Animation 39
  • 2. Converse of Corresponding Angles Theorem
  • 3. Alternate Interior Angles
  • 4. Solution to Parallel Lines & Angles Problem

8.1.

Animation 39

What theorem is dynamically being illustrated below?[br](Note: Two of the three lines shown are parallel.)
– Tim Brzezinski

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