Happy Halloween

Have a good weekend and be careful.

Make sure you complete the review sheet and bring some candy to class on Tuesday.

Graphing Linear Equations

NOTE:

1. There is a graph paper link to the right. It's under valuable links.
2. Make sure you change the equation from standard form to slope intercept form before you graph the equation.
   

Writing Liner Equations Quiz

3.5 Write and Graph Linear Equations

Example 1: Write an equation of a line from a graph



Example 2: Write an equation of parallel line



Example 3: Write an equation of perpendicular line

3.4 Find and Use slopes of a line and 3.5 Write and Graph equations of a line

Oh yeah...Algebra Review!!!


For the next few days we will be doing the following:

1. Find and compare slopes of lines.
2. Find Equations of Lines.

Vocab before we get started.

In class notes Ch 3 lesson 4, examples 1-4.

3.1-3.3 prove lines are parallel quiz

WOW Class Geometry is everywhere!!!

Practice Quizzes

3.1 Identify Pairs of Lines and Angles

3.2 Use Parallel Lines and Transversals

3.3 Prove Lines are Parallel

3.3 Prove Lines are Parallel

Do Now:

1. What do we have to know first to use the the following?

* Corresponding Angles Postulate
* Alternate Interior Angles Theorem
* Alternate Exterior Angles Theorem
* Consecutive Interior Angles Theorem


2. Write the converse of the following statement.

If it is raining, then Josh needs an umbrella.

4. How do you prove lines are parallel?




Example 1: Apply the converse theorems and postulate

Example 2: Transitive Property of Parallel Lines

Example 3: Using Algebra

3.2 Parallel Lines and Transversals

Goal: Use angles formed by parallel lines and transversals

3.2 Practice Quiz

Vocabulary

• Example 1 and 2
• Example 3 and 3
  

Key Applications:

• Science
• Parking Lots
• Windows

3.1 Identify Pairs of Lines and Angles

Chapter 3 Parallel and Perpendicular Lines

3.1 Identify Pairs of Lines and Angles

Goal • Identify angle pairs formed by three intersecting lines.


VOCABULARY
1.)Parallel lines
Two lines are parallel lines if they do not intersect and are coplanar.

2.)Skew lines
Two lines are skew lines if they do not intersect and are not coplanar.

3.)Parallel planes
Two planes that do not intersect are parallel planes.

4.)Transversal
A transversal is a line that intersects two or more coplanar lines at different points.

5.)Corresponding angles
Two angles are corresponding angles if they have corresponding positions.

6.)Alternate interior angles
Two angles are alternate interior angles if they lie between the two lines and on opposite sides of the transversal.

7.)Alternate exterior angles
Two angles are alternate exterior angles if they lie outside the two lines and on opposite sides of the transversal.

8.)Consecutive interior angles
Two angles are consecutive interior angles if they lie between the two lines and on the same side of the transversal.

Chapter 3
Lesson 1, Examples 1 Identify relationships in space,
Lesson 1, Examples 2Identify parallel and perpendicular lines
Lesson 1, Example 3 Identify angle relationships

Ch 2 Reasoning and Proof Review

Try problems in the the text book

• pg 134-137 #'s 6, 9, 10, 13, 18-20, 23.
  Note: study how to write a biconditional statement
  
• pg 138 #'s 9-13, 17-20
  

Practice Test

2.7 Prove Angle Pair Relationships

Before you learned how to identify relationships between pairs of angles.

Now you will learn properties of special pairs of angles.

Why? So you can describe angles found in a home.






Examples

1. Using the Right Angle Congruence Theorem
2. Find angle measure
3. Using algebra
   

Homework for Firday

I will collect this worksheet on Tuesday. Have a good weekend.

p.s.If you're free Sunday morning at 930 am, my game will be played live at www.tg4.ie then click on live.

2.6 Prove Statements about Segments and Angles

Goal · Write proofs using geometric theorems

VOCABULARY

Proof

A proof is a logical argument that shows a statement is true.

Two-column proof

A two-column proof has numbered statements and corresponding reasons that show an argument in logical order.

Theorem

A theorem is a statement that can be proven.




In class examples: Chapter 2 lesson 6, ex 1-4


You Try:

2.5 Reasoning Using Properties from Algebra

Goal: Use algebraic properties in logical arguments.

Key Concept

You can use properties of real numbers to write logical arguments about geometric figures like angle measures and segment lengths.

Those that can be applied include the algebraic properties of equality (addition, subtraction, multiplication, division, and substitution), the distributive property and the reflexive, symmetric, and transitive properties of equality (for real numbers, segment length, and angle measure).



Example1: Write reasons for each step.



Example2: Use properties of equality for angles
Example3: Use properties of equality for segments

2.4 Use Postulates and Diagrams

Goal: Use postulates involving points, lines and planes.

In class examples: Chapter 2: lesson 4, examples 1-4

Vocabulary

A line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

Postulate 5 Through any two points there exists exactly one line.

Postulate 6 A line contains at least two points.

Postulate 7 If two lines intersect, then their intersection is exactly one point.

Postulate 8 Through any three noncollinear points there exists exactly one plane.

Postulate 9 A plane contains at least three noncollinear points.

Postulate 10 If two points lie in a plane, then the line containing them lies in the plane.

Postulate 11 If two planes intersect, then their intersections is a line.