Chapter 5 Test

Happy Holidays.

Due: Jan 4, 2012

5.6 Inequalities in Two Triangles and Indirect Proof

Click for 5.6 notes

Chapter 5 Relationships in a Triangles Test Review

Chapter 5 practice Test

Practice Quizzes
5.1
5.2
5.3
5.4
5.5
5.6

5.4-5.6 Practice Problems

5.6 Inequalities in Two Triangles and Indirect Proof

5.5 Use Inequalities in a Triangle

Goal: You will find possible side lengths of a triangle.

5.5 practice Quiz

In class examples

Canon Blue

Chapter 5 Quiz review

5.4 Altitude And Median

Goal: How do you find the Centroid of a Triangle?

5.4 Altitude And Median Ppt

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5.3 Use Angle Bisectors of Triangles

How each theorem works: lesson 5 examples 1-3

5.3 practice quiz 1

5.3 practice quiz 2

5.2 Perpendicular Bisector

Goal: You will use perpendicular bisector to solve problems

5.2 practice Quiz 1
5.2 practice Quiz 2






Example 1:

Example 2:

more in class examples...
- click the link
- Select Prentice Hall Geometry 2011
- Select ch 5 section 2

Chapter 5 Relationships within Triangles



In class examples:

Day 1: Midsegment Theorem

Midsegment of a Triangle

Practice with midsegment #'s 1-4

Day 2: Coordinate Proof



practice with proofs #'s 5-7

Ch 4 test Review

Ch 4 test review outline


try pg 282 - 285 #'s 1-26 all. Good Luck and Happy studying!!



CPCTC and base angle theorem practice problems

5.7 Quiz

Practice with Proofs

Review homework problems.

Use Congruent Triangles

What you need to know for the quiz tomorrow. How to use and identify the following:

1. SSS
2. SAS
3. AAS
4. ASA
5. HL
6. CPCTC
7. Use Isosceles and Equilateral Triangles

Try the following quizzes for homework tonight.

• 4.3 Prove Triangles Congruent by SSS
• 4.4 Prove Triangles Congruent by SAS and HL
• 4.5 Prove Triangles Congruent by ASA and AAS
• 4.6 Use Congruent Triangles
• 4.7 Use Isosceles and Equilateral Triangles

4.7 Use Isosceles and Equilateral Triangles

Goal • Use theorems about isosceles and equilateral triangles.

Vocabulary

When an isosceles triangle has exactly two congruent sides, these two sides are the legs. The angle formed by the legs is the vertex angle. The third side is the base of the isosceles triangles. The two angles adjacent to the base are called base angles.

Legs
The legs of an isosceles triangle are the two congruent sides.

Vertex angle
The vertex angle of an isosceles triangle is the angle formed by the legs.

Base
The base of an isosceles triangle is the side that is not a leg.

Base angles
The base angles of an isosceles triangle are the two angles adjacent to the base.

In class examples (click for link)


Lesson 7 Examples 1-4

4.6 Use Congruent Triangles

Key Concept

Once you have proved that two triangles are congruent, you know that their corresponding parts must be congruent as well. This will allow you to find the unknown measures of angles , objects and distances, as well as prove that constructions of copying angles are valid.

Goal: Use congruent triangles to prove corresponding parts congruent.

4.5 using congruent triangles

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Working with Congruent Triangles in Proofs

Remember when working with congruent triangles...

1. Mark any given information on your diagram.
2. Look to see if the pieces you need are "parts" of the triangles that can be proven congruent.
3. If not given all needed pieces to prove the triangles congruent, look to see what else you might know about the diagram.
4. Know your definitions! If the given information contains definitions, consider these as "hints" to the solution and be sure to use them.
5. Stay open-minded. There may be more than one way to solve a problem.
6. Look to see if your triangles "share" parts. These common parts are automatically one set of congruent parts.

Example 1: How do we decide which method we should be using?

Example 2: Numerical Practice with Congruence


Quiz Monday

Practice with Congruent Triangle Proofs

Practice with Beginning Congruent Triangle Proofs

Directions: When attempting to prove triangles congruent, it is important to satisfy all of the conditions of the congruent triangle method you are using. This activity is designed to help you organize your thinking about how the parts of a congruent triangle proof will come together. In each problem below, examine the diagram and the GIVEN information. You may wish to draw the diagrams on paper so that you can mark off the information.

• Determine the method needed to prove the triangles congruent.
  (ASA, SAS, AAS, SSS, or HL for right triangles only)

• Check to see if you have the correct method by looking at the Method for Congruent Triangles box at the bottom of the chart.

• Each of the three components needed to support the chosen method appear to the left of their corresponding Statement.

• Decide what Reasons can be used to support your decisions.

Recognizing Congruent Triangles (click to see in class examples)

Example 1: Prove Triangles are Congruent

Homework:
Do the following problems below. I will collect this assignment Monday.

Directions:

1. Copy down each diagram or print the sheet.
2. Mark up the diagram.
3. Fill in all the blanks.
4. 
   

4.1 and 4.2 Quiz

Triangles Congruence Theorems (SSS, SAS, ASA, HL)

Methods for Proving Triangles Congruent

Goal:

Learn Different methods to prove triangles are congruent using:

1. Side Lengths
   
2. Side Lengths and Angles
   

Provingtrianglescongruentssssasasa

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In summary, when working with congruent triangles, remember to:

1. Mark any given information on your diagram.
2. Look to see if the pieces you need are "parts" of the triangles that can be proven congruent.
3. If not given all needed pieces to prove the triangles congruent, look to see what else you might know about the diagram.
4. Know your definitions! If the given information contains definitions, consider these as "hints" to the solution and be sure to use them.
5. Stay open-minded. There may be more than one way to solve a problem.
6. Look to see if your triangles "share" parts. These common parts are automatically one set of congruent parts.
   

Remember that proving triangles congruent is like solving a puzzle. Look carefully at the "puzzle" and use all of your geometrical strategies to arrive at an answer.

4.2 Apply Congruence and Triangles

In class examples: lesson 2 examples 1-5

4.1 practice Quiz

4.2 practice Quiz

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TRIANGLES

Triangles Representation



Triangle Song


4.1 Apply Triangle Sum Properties

Chapter 4 Congruent Triangles

Big Ideas

1. Classifying triangles by sides and angles
2. Proving that triangles are congruent
3. Using coordinate geometry to investigate triangle relationships
   

In class problems: Do workbook pg 61-63 #'s 5-8, 11-15 odd 21 -26 all.

Finish workbook problems for homework.

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