Geometry H/GT
August 22 to September 1
Date
Monday
8/22
Tuesday
8/23
Wednesday
8/24
Thursday
8/25
Friday
8/26
Monday
8/29
Tuesday
8/30
Wednesday
8/31
Thursday
9/1
Topic
Introductions
WS: Do you remember? Review of
Algebra skills
1.1 Patterns and Inductive reasoning
2.1 Conditional Statements
5.4 Venn Diagrams, Inverses and
Contrapositives
2.2 Biconditional statements
2.3 Deductive reasoning
2.3 Deductive Reasoning: Law of
detachment and law of Law of
Syllogism
Quiz 1.1 , 2.1, 5.4
2.4 Reasoning in Algebra
2.4 Reasoning in Algebra
Review for Test
Test #1
Assignment
Complete the ‘Review of Algebra
Skills’ worksheet started in class
Page 83-84: # 1 to 35(even)
Page84-86: 36-61 (even)
Page 283-285: # 1-9 (all),10-18(even),
22,23,26-31(all),34-36(all)
Page 90-93: # 1-30 (even),3840(all),42,43,48
Pg. 96-98: # 1-8,10,12,15,16-24(even)
Pg. 106-107: #5-23 (all), 27, 29, 38,
40, 42, 43
Pg. 106-107: #5-23 (all), 27, 29, 38,
40, 42, 43
Review for test
Points, Lines and Planes - Review of
middle school Geometry
Page 19-21: # 2-24(even), 25-29(odd),
38,40,48,49,51,52
Homework: Tuesday, Aug 24
Homework: Wednesday, Aug 25
5.4 Converse, Inverse, Contrapositive, and Indirect Argument
p. 283-286 #12-16 (e); 20, 24, 26-29 (a), 30-40 (e)
Write the first step of an indirect proof.
12. ∆PEN is an isosceles triangle.
Identify the two statements that contradict each other.
16. I. ∆PQR is equilateral.
II. ∆PQR is a right triangle.
III. ∆PQR is isosceles.
Write an indirect proof.
20. Given: The total membership of the Debate Club and the Chess Club is fewer than 20. The Chess Club has
10 members.
Prove: The Debate Club has fewer than 10 members.
Write (a) the inverse and (b) the contrapositive of the following statement. Give the truth value of each.
24. If you live in El Paso, then you live in Texas.
Write a true conditional statement for each given condition. If such a statement is not possible, tell why.
26, The inverse is false.
27. The inverse is true.
28. The contrapositive is false.
29. The contrapositive is true.
Write an indirect proof.
30. Fresh skid marks appear behind a green car at the scene of an accident. Show that the driver of the green car
applied the brakes.
32. An obtuse triangle cannot contain a right triangle.
Write the conditional statement illustrated by each Venn Diagram. Then write its contrapositive.
34.
36.
Cats
Integer
Kittens
whole number
38. Earl lives near a noisy construction site at which work ends promptly at 5:00 each workday. Earl thinks, “Today is
Tuesday. It were before 5:00k I would hear construction noise, but I don’t hear any. So it must be later than 5:00.”
a) What does Earl prove?
b) What assumption does he make?
c) What fact would contradict the assumption?
40. Describe a real-life situation in which you sued an indirect argument to convince someone of your point of view.
Outline your argument.
Homework: Thursday, Aug 26
pp. 90-93 #6,10, 14, 18, 22, 24, 38, 40-46, 48
6. The conditional statement below is true. Write its converse. If the congruent is also true, combine the statements as a
biconditional. . If x = -10, then x2 = 100.
Write the two statements that form each biconditional.
10. Two lines are parallel if and only if they are coplanar and do not intersect.
Test the statement below to see if it is reversible. If so, write it as a true biconditional. If not, write “not reversible.”
14. Parallel planes are planes that do not intersect.
Is the statement below a good definition? If not, explain.
18. A cat is an animal with whiskers.
22. A square is a figure with two pairs of parallel sides.
24. An obtuse angle is an angle whose measure is greater than 90 o.
Write each statement as a biconditional.
38. Congruent angles are angles with equal measure.
40. The whole numbers are the nonnegative numbers.
Let statements of p, q, and r be as follows. p: A and B are right angles. q:
A and B are supplementary angles.
r: the sum of the measures of angles A and B is 180o. Substitute for p, q, and r, and write each statement the way you
would read it.
41. p  q
42. q  p 43. p  q 44. q  p
45. p  r
46. r  q
48. You have illustrated true conditional statements with Venn diagrams. You can do the same thing with true
biconditionals. Consider the following statements. An integer is divisible by 10 if and only if its last digit is 0.
a) Write the two conditional statements that make up this Biconditional.
b) Illustrate the first conditional from part (a) with a Venn diagram.
c) Illustrate the second conditional from part (a) with a Venn diagram.
d) Combine your two Venn Diagrams from parts (b) and (c) to form a Venn diagram representing the
biconditional statement.
e) What must be true of the Venn diagram for any true biconditional statements?
f) How does your conclusion in part (e) help to explain why a good definition can be written as a
biconditional?
Homework: Friday, Aug 27
pp. 97-98 # 10,12,-15, 16-24 (e)
Use the Law of Syllogism to draw a conclusion.
10. If an animal is a red wolf, then its scientific name is Canis rufus. If an animal’s name is Canis rufus, it is an
endangered animal.
12. If you read a good book, then you enjoy yourself. If you enjoy yourself, then your time is well spent.
13. If you’re studying biology, you are studying a science. If you are studying botany, then you are studying biology.
Use the Law of Detachment and the Law of Syllogism to draw a conclusion about the following statements
14. If a mountain is the highest in Alaska, then it is the highest in the United States. If an Alaskan mountain is 20,300 ft
high, then it is the highest in Alaska. Alaska’s Mount McKinley is 20,300 ft. high.
15. If you live in Lubbock, then you live in Texas. Levon lives in Lubbock. If you live in Texas, then you live in the
28th state to enter the Union.
For problems 16-20, assume the following statements are true.
A. If Maria is drinking juice, then it is breakfast time.
B. If it is lunchtime, then Kira is drinking milk and nothing else.
C. If it is mealtime, then Curtis is drinking water and nothing else.
D. If it is breakfast time, then Julio is drinking juice and nothing else.
E. Maria is drinking juice.
Use only the information given above. For each statement, write must be true, may be true, or is not true. Explain your
reasoning.
16. Julio is drinking juice.
18. Kira is drinking milk.
20. Maria is drinking water.
For each of the following, write the first statement as a conditional. If possible, use the Law of Detachment to make a
conclusion. If not possible, write not possible.
22. All national parks are interesting. Mammoth Cave is a national park.
24. Every high school student likes music. Ling likes music.
Homework starting Monday, Aug 30, look at your Textbook