Fall Review Worksheet

ACP Topics to review

The ACP Test is closed notes!  Before you take the Test this week, be sure to review the following topics:

1.  Make conjectures - remember when we describe what we see.  Be sure to know these words and what they look like:  point, line, plane, skew lines, collinear, coplanar, supplemental, linear pair, vertical lines, complementary, segment.

2.  Constructions - what they look like, the order to make them, and what they do.  Remember the angle bisector, segment bisector, copying angles, copying line segments, constructing perpendiculars on and off the line.

3.  Patterns - how to get the equation that describes the pattern.  We did this in class last Thursday and Friday.

4.  Slopes and equations of lines.  Look at this blog's entries on this topic.  Make sure you can calculate slope, find equations of parallel and perpendicular lines.

5. Use the formulas for slope, midpoint, distance.  Remember that if you get asked for length, you need to use the distance formula!  And if you get a perimeter question, that you need to calculate the distance of each side and then add them up.

6. Transversal relationships - remember the corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles.

7.  Triangle congruence - be sure to be able to determine which one is used:  SSS, SAS, ASA, AAS.

8. Transformations - remember to multiply when you see the word "scale factor"

9. Similarity - use those proportions and ratios!

10.  Proofs.  Review that proofs packet.

Review on Conditional Statements

Be sure to know your conditional statements!

Each sentence can be re-written in "If __(hypothesis)_____, then ___(conclusion)_________" form.

Let's look at this sentence:  "Scoring more than 70% on the test will let you pass"

First, identify the conclusion:  "you pass"
Then identify the hypothesis:  "scoring more than 70% on the test"

Next, put them into an If-Then statement:   "If  scoring more than 70% on the test Then you pass"

Note that this sentence doesn't make sense, nor does it have good English grammar.  So we change and add some words for it to makes sense.  Here's what it becomes:

 "If you score more than 70% on the test, then you will pass."

This If-Then statement is called the Conditional Statement.  We can rearrange the hypothesis and conclusion as well as negate them to have the 4 types of Logic statements in Geometry.

Conditional:  

 "If you score more than 70% on the test, then you will pass."

Inverse Statement:

 "If you do NOT score more than 70% on the test, then you will NOT pass."  <--- notice the addition of the word NOT, meaning they got negated.

Converse Statement:

 "If  you will pass, then you score more than 70% on the test."  <--- notice the hypothesis and conclusion got swapped.

Contrapositive Statement"

 "If  you will NOT pass, then you will NOT score more than 70% on the test."  <-- notice that the hypothesis and conclusion got swapped AND each part got negated by using the word NOT.

Be sure you can remember which is which.

Review on Perpendicular Lines Equations

Review of Parallel Lines Equations

Now you try: 

Find an equation of the line that passes through (–1, –3) and is parallel

to y = 2x + 6.

Project - Map Practice with Distance and Midpoint

Map Practice with Distance and Midpoint                        Name: ________________________

 

Restaurants: ·       Burger King ·       Hardee's ·       McDonald's ·       Chick-Fil-A ·       Bojangles

Buildings: ·       City Hall ·       Post Office ·       Courthouse ·       Library ·       Armory

Stores: ·       Wal-Mart ·       Target ·       Food Lion ·       Lowe's ·       BP station

 

1.     Begin by drawing and labeling your x and y axes on your graph paper.  Make sure that your axes cover the entire area of the page.

 

2.     Plot and label the following locations on your map:

·       Burger King at (-2, 3) ·       Hardee's at (4, 1) ·       City Hall at (-9, -8) ·       Post Office at (-3, 8)

·       Wal-Mart at (4, -4) ·       Target at (-8, 6) ·       BP station at (1, -10)

 

 

3.     Bojangles is located at the midpoint of Burger King and Hardee's.  Plot and label Bojangles on the map and write the coordinates of Bojangles here _______.

4.     The library is located at the midpoint of City Hall and the post office.  Plot and label the library on the map and write the coordinates of the library here _______.

5.     Food Lion is located at the midpoint of Wal-Mart and Target.  Plot and label Food Lion on the map and write the coordinates of Food Lion here _______.

6.     Hardee's is the midpoint between Burger King and Chick-Fil-A.  Plot and label Chick-Fil-A on the map and write the coordinates of Chick-Fil-A here _______.

7.     The courthouse is the midpoint between the post office and the library.   Plot and label the courthouse on the map and write the coordinates of the courthouse here _______.

8.     Wal-Mart is the midpoint between Lowe's and the BP station.  Plot and label the Lowe's on the map and write the coordinates of Lowe's here _______.

9.     Burger King is the midpoint between Target and the armory.  Plot and label the armory on the map and write the coordinates of the armory here _______.

10.  (-2, -2) is the midpoint between McDonald's and City Hall.  Plot and label McDonald's on the map and write the coordinates of McDonald's here _______.

Use your map and your coordinates to find the distances between the following points of interest:

11.  What is the distance between McDonald's and the BP station?  ____________

12.  What is the distance between Wal-Mart and Hardee's?  ____________

13.  What is the distance between Target and City Hall?  ____________

14.  What is the distance between the armory and the library?  ____________

15.  What is the distance between Chick-Fil-A and Food Lion?  ____________

16.  What is the distance between Lowe's and Burger King?  ____________

17.  What is the distance between the courthouse and Bojangles?  ____________

18.  What is the distance between McDonald's and the Chick-Fil-A?  ____________

19.  What is the distance between Wal-Mart and the BP station?  ____________

20.  What is the distance between the post office and Target?  ____________

26. Midpoint Practice

25. Midpoint Formula

24. Distance and Perimeter

23. Distance Formula

22. Transversals in Parallellograms (practice)

Homework: Page 152# 19-22

21. Transversal angles practice

20. Transversal

16. Parallel Lines

15. Slope-Intercept Form

14. Average rate of change

Unit 1 Test

13. Unit 1 Review

13.  UNIT 1 REVIEW
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LO:  I will review the concepts I learned about conjectures, angle relationships, logic and conditional statements.
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Handout is as follows:

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DOL:
I will have completed at least two problems from each category.

11. Informal Proofs

For 9/12 Class:

11.  INFORMAL PROOFS
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LO:  SWBAT will apply and use deductive reasoning, postulates and properties to prove mathematical statements.
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We will mostly work on the handout which we will add to your notebook.

12. Formal Proof

For 9/13/13 class day:

11.  FORMAL PROOF
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LO:  SWBAT apply and use deductive reasoning, postulates and properties to prove geometrical statements using formal proofs
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Today is about proofs using geometric concepts.  We will be looking at several examples and then it's your turn. 

 Here are two examples:

Now it's your turn.  Try to fill in the blanks in these two proofs.
If  you do not finish in class, this becomes homework.

10. Algebraic Proofs

10.  ALGEBRAIC PROOFS

LO:  SWBAT will apply and use deductive reasoning to justify and prove mathematical statements

 Today is all about proving algebraic equations.

 

9. Laws of Syllogism and Detachment

9.  Law of Detachment and Syllogism

LO:  SWBAT use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false

Venn Diagram

Can be used to represent a conditional statement

 

 

 

  

No Homework.

 

8. Conditional Statements

For September 9th class

8.  CONDITIONAL STATEMENTS
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LO:  SWBAT will determine the validity of a conditional statement, its converse, inverse
and contrapositive.
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(Textbook Chapter 2-3, starting from page 91)


1. Conditional Statements
To change a statement to an If-Then statement is to make a conditional statement.  

Let's look at the statement:  "Rain means it's cloudy."
Changing this to a conditional means identifying the hypothesis and conclusion then adding the if-then words to it like this:
 

The "if" is always followed by the hypothesis and the "then" is always followed by the conclusion.

Now you try.  Rewrite these advertisements into If-Then forms:

2.  Converse, Inverse, and Contrapositive
Other statements based on the conditional statements are Converse, Inverse and Contrapositive.  They are formed by exchanging and negating the hypothesis and conclusion of the conditional statements in various ways.

Notice that the symbols for the Conditional Statement reads as "p to q".

Now you try: using the same conditionals from the advertisements from section 1 above, write each one's converse, inverse and contrapositive.

3.  Counterexample
A Counterexample is a true example to prove a statement false.

For example:
Statement:  "If it has four right angles, then it's a square"
This is a false statement.  We then give the counterexample:  A rectangle.

The counterexample proves that the statement was false.

Now you try:  for each false statement from #2 above, provide a counterexample.

4.  Biconditional Statements

A conjunction of two statements where both the conditional and its converse are true is called biconditional. 

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Homework
Page 94, questions 1-10

7. Logical Reasoning

7. LOGICAL REASONING
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LO:  SWBAT use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false.
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Before we start, let's look at the format we will be using:

• Lower case letters will be used to name a statement.

 1. NEGATION

Negation is changing the truth value of a statement to its opposite value.  We designate the negated value with the symbol "~".

Example Statement:

p:  Austin is the capital city of Texas.    The truth value of this statement is True.  

~p:  Austin is NOT the capital city of Texas.  The truth value is now False.

Again, the ~p statement is the negated statement.

2. CONJUNCTION

A conjunction is a compound statement formed by joining two or more statements with the word and.  We then use the statements to write a compound statement.  (Compound just means mixing two things together in one). 

p:  Parallel lines have the same slopes

q:  Vertical angles are congruent

r:  The expression -5x + 11x simplifies to -6x

To write the compound statement, we use the symbol ∧.

So now we write our compound statements:

• p∧q (read as "p and q"):  Parallel lines have the same slope and vertical angles are congruent.
• ~p ∧ ~q (read as "not p and not q"):  Parallel lines DOES NOT have the same slope and vertical lines are NOT congruent.
• ~q ∧ r (read as "not q and r"):  Vertical angles are NOT congruent and the expression -5x + 11x simplifies to -6x.

3. DISJUNCTION

A disjunction is a compound statement formed by joining two or more statements with the word or.  We then use the statements to write a compound statement.

Let's use the same statements from above

p:  Parallel lines have the same slopes

q:  Vertical angles are congruent

r:  The expression -5x + 11x simplifies to -6x

To write the compound statement, we use the symbol  ˅ .

So now we write our compound statements:

So now we write our compound statements:

• p ˅ q (read as "p or q"):  Parallel lines have the same slope or vertical angles are congruent.
• ~p ˅ ~q (read as "not p or not q"):  Parallel lines DOES NOT have the same slope or vertical lines are NOT congruent.
• ~q ˅ r (read as "not q or r"):  Vertical angles are NOT congruent or the expression -5x + 11x simplifies to -6x.

Note that the statements are identical except they are now joined by the word "OR" instead of "AND".

4.  TRUTH TABLES

We will fill in this table in class and discuss it.

5.  VENN Diagrams

We will examine the Venn Diagram and interpret data from it.

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Class Activity:

Handouts will be provided in class. 

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Homework:

P.87, questions 1 to 9.  The book is as below: