10.5.2011

Another day of Geometry.
We made sure everyone understood the homework,   especially p 133 # 43-46.

Then we moved on to page one of the  Lines, Transversals and angle handout. (see below)

Geometry                                                                                                Name _____________________

Lines, transversals, and angles                                                                                                               10.4.2011

1. Review: Use a protractor to measure an angle

Use a protractor to find the measures of the four angles in the figure below

 2. review Graphing linear equations.

     Graph the following lines:  a) y = x + 3
                                                 b) x - y = 2
                                                 c) x + 4y = 12

     d) which of the two lines are parallel and which line is the transversal? 

Next, we returned to our Ch 2 review  #3 & 4 (See below)

               Hwk #14 due Oct. 6:          Ch2 Review Sheet #3 and 4 below Color coded below

                                                             AND     Do p 121 #1-8

                                                                                p 122 # 1,2,6,8,9, 11

Geometry                                                                                                Name ­­­­­­­­­­­­­                                           

Ch 2 Test Date: A block Tuesday, October 11

When studying for math you should work problems!  “Looking over” your notes or reading through the book will do little or nothing to help you prepare.  The best sources of problems are this review, quizzes, problems worked during class, and then the book (generally in that order).  Copy a problem onto a separate sheet of paper, or cover up the solution, and then try to rework the problem.  When finished, compare your new solution to the original to confirm you correctly answered the question.  The following words, formulas, and topics should not be a surprise to you, but they are assembled in one place to help ensure that you cover everything.

Summary 

1.    If a, then b is a conditional statement.  The hypothesis is a, and the conclusion is b.  Conditional

statements come in many forms but all can be rewritten in if-then form.  Conditional statements can be illustrated by an Euler diagram.

2.   The converse of If a, then b is If b, then a.  The inverse is If not a, then not b, and the

contrapositive is If not b, then not a.  The statement a if and only if b is a biconditional that means that both the conditional and its converse are true.

3.   Law of Detachment: Given an if then statement,  if the hypothesis is true, then the conclusion of the conditional is valid.    Given:         If a, then b  and also given a,.

 Conclusion:   b

           

4.   Law of Syllogism:  Given: if a, then b  and  if b, then c

                                  Conclusions:   if a, then c

Vocabulary

Conditional statement

Hypothesis

Conclusion

Euler diagram

Converse

Inverse

Contrapositive

Biconditional

Chapter 2 Review     Practice Problems

     

1.     Write each of the following in if-then form

a.     Adjacent angles have a common vertex.

b.     Through any two points, there is exactly one line.

c.     Waste not, want not.

2.  Answer each of the following questions based on the given conditional statement.  Draw an Euler Diagram to illustrate the given conditional statement.

            If two lines both have slopes of 3/7 then they are parallel.

     Hypothesis:

            Conclusion:

a.      Is this conditional true or false?  If false, give a counterexample.

           

b.     Write the converse of the given conditional

c.     Is the converse true or false?  If false, give a counterexample. If true write the biconditional.

d.     Write the inverse of the given conditional

e.     Is the inverse true or false?  If false, give a counterexample

f.      Write the contrapositive of the given conditional

g.     Is the contrapositive true or false?  If false, give a counterexample

3.   Answer each of the following questions based on the given conditional statement. Draw an Euler Diagram to illustrate the given conditional statement.

            If an angle is a right angle, then its measure is 90°.

            Hypothesis:

            Conclusion:

a.     Is this conditional true or false?  If false, give a counterexample.

           

b.     Write the converse of the given conditional

c.     Is the converse true or false?  If false, give a counterexample. If true write the biconditional.

d.     Write the inverse of the given conditional

e.     Is the inverse true or false?  If false, give a counterexample

f.      Write the contrapositive of the given conditional

g.     Is the contrapositive true or false?  If false, give a counterexample

4. Assuming that the following three conditional statements are true answer the following questions. Draw an Euler Diagram for each conditional. Then draw a nested Euler Diagram for all three conditionals.

If it is Conference on Democracy then we will have a keynote speaker.

If we have a keynote speaker then there will be an extended assembly.

If we have an extended assembly then tutorial will be at the end of the day.

a.     If you hear that we had an extended assembly, what can you logically conclude?

b.     If you look at your planner and see today is NOT Conference on Democracy what can you logically conclude?

c.     If tutorial is not at the end of the day, what can you logically conclude?

4d) Write the following statements in order

A. If it looks like rain, then I will bring my umbrella to school with me.

B. If there are clouds in the sky and the sky is dark, then it looks like rain.

C. If I bring my umbrella to school with me, then I will hang it in the classroom closet.

4e) This morning, there are clouds in the sky and the sky is dark. What conclusion can be made from the conditionals in part 4a?