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Name___________________ Period ____
Geometry Agenda
Average ______
*** Reminder: Your test is this FRIDAY. All Unit 2 homework
and makeup work is due by the day of the test. NO LATE
WORK WILL BE ACCEPTED AFTER THE DAY OF THE
TEST.
Week 1.5 Objective Grade Monday
September 19, 2016
Deductive Reasoning
Practice Tuesday
September 20, 2016
Geometric Proof
Practice Wednesday
September 21, 2016
Geometric Proof Day 2
Practice Thursday
September 22, 2016
Review
STUDY Friday
September 23, 2016
Test
Relax
First Things First
Monday Tuesday
Wednesday Thursday
Friday
No Warm Up
Monday Tuesday
Wednesday Thursday
Friday
No Warm Up
Geometry: Unit 3 – Deductive Reasoning
Practice – Deductive Reasoning Pages 60-64 Name: _______________________________ Date: ___________________ Period: _________ Use the statements in the box below.
If Winnie reads the book by Friday, then she will write the report on Saturday. If Winnie writes the report on Saturday, then she will turn it in on Monday.
1. Assume that Winnies reads the book by Friday. What conclusion can you make? Why? 2. Suppose that Winnie does not turn the report in on Monday. What conclusion can you make?
Assume the following are true: * If David does not buy popcorn, then he did not shop. * If Ashley buys pizza, then she will have some left over. * If the store is open, then Ashley and David will shop. * If Ashley shops, then she will buy pizza. * The store is open.
3. Did Ashley buy popcorn?
4. Did Ashley have pizza left over?
5. Did David eat part of Ashley’s pizza?
6. Did David buy popcorn?
Order the statements in the two problems below. Then state the conclusion.
7. Given: 4 60om
________ a. If 7 120om , then 6 60om .
________ b. 4 60om .
________ c. If 1 120om , then 7 120om .
________ d. If 6 60om , then 5 120om .
________ e. If 4 60om , then 1 120om .
Conclusion: _____________________________________
Geometry: Unit 3 – Deductive Reasoning
Determine if each example is using deductive or inductive reasoning. 8. “If it is Friday, then Kendra’s family has pizza for dinner. Today is Friday, therefore, Kendra’s family will have pizza for dinner.”
INDUCTIVE DEDUCTIVE
9. For the past three Wednesdays the cafeteria has served macaroni and cheese for lunch. Julie concludes that the cafeteria will serve macaroni and cheese for lunch this Wednesday…hooray.
INDUCTIVE DEDUCTIVE
10. If you live in Texas and are 16, then you must take driver’s education to get your license. Marcus lives in Texas, is 16 years old, and has his driver’s license. Therefore, Marcus took driver’s education.
INDUCTIVE DEDUCTIVE
11. The Berkner Rams scored over 75 points for their first ten basketball games. The newspaper predicts that they will score more than 75 points tonight. Which form of reasoning is this conclusion based on?
(A) Deductive reasoning, because the conclusion is based on logic.
(B) Deductive reasoning, because the conclusion is based on a pattern.
(C) Inductive reasoning, because the conclusion is based on logic.
(D) Inductive reasoning, because the conclusion is based on a pattern.
When Alice meets the Pigeon in Wonderland, the Pigeon thinks she is a serpent. The Pigeon reasons that serpents eat eggs, and Alice confirms that she has eaten eggs.
12. Write “Serpents eat eggs” as a conditional statement. 13. Is the Pigeon’s conclusion that Alice is a serpent valid? Justify your reasoning.
14. If Cassie goes to the skate park, Hanna and Amy will go. If Hanna or Amy goes to the skate park, then Mark will go. If Marc goes to the skate park, then Dallas will go. If only two of the five people went to the skate park, who were they?
(A) Hanna and Amy
(B) Cassie and Dallas
(C) Dallas and Marc
(D) Amy and Marc
REVIEW: 15. Find the next 3 numbers in this sequence: 1, 5, 25, 125, _______, _______, _______.
Geometry: Unit 2 – Geometric Proof
Practice – Geometric Proof Pages 66-68, 71-78 Name ____________________________ Date ________________ Period _______
1. Given: 31
35
Prove: 51
2. Given: H is the midpoint of GI
JH HI
Prove: GH HJ
3. Given: V is the midpoint of SW
W is the midpoint of VT
Prove: SV WT
4. Given: NA AM
M is the midpoint of AB
Prove: NA MB
Statements Reasons
1. NA AM 1. ___________
2. M is midpt of AB 2.___________
3. AM MB 3.___________
4. NA MB 4.___________
5. Given: B is between A & C AB = 9 BC = 7
Prove: 16 = AC Statements Reasons
1. B is between A & C 1.____________
2. AB = 9 2.___________
3. BC = 7 3.___________
4. AB + BC = AC 4. ___________
5. 9 + 7 = AC 5.____________
6. 16 = AC 6. ___________
6. Given: 1 3 180om m
Prove: 1 4
Statements Reasons
1. 1 3 180om m 1. _____________
2. ______________ 2. Def. of supplementary
angles
3. 3 & 4 form a 3. ______________
Linear pair
4. 3 and 4 are 4.______________
supplementary 5. 1 4 5. ______________
A
N
B M
1 2 3 4
5
G
H
I J
W
V
T
S
4 2 1 3
H is the midpoint
of GI
JH HI
GH HI
GH HJ
V is the midpoint
of SW
W is the midpoint
of VT
SV VW
VW WT
SV WT
1 3
5 3
1 5
A B C • • •
Geometry: Unit 3 – Geometric Proof Day 2
Practice – Geometric Proof Day 2 Pages 66-68, 71 -78 Name ______________________________________ Date ________________ Period _______ 1. A ________________ is a statement you can prove. (postulate or theorem) 2. Vertical Angles Theorem - _________________________________________________________
3. If A and B are vertical angles, then ________________________ 4. Fill in the blanks for the proof of the Vertical Angles Theorem. Given: 1 and 3 are vertical angles
Prove: 1 3
Fill in the blanks to complete the following proofs. 5. Given: 2 3
Prove: 1 and 3 are supplementary
6. Given: 1 4 Prove: 2 3
Statements Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Statements Reasons
1. 2 3 1. Given
2. 2 3m m 2.
3. 1 and 2 form a linear pair 3.
4. 4. Linear Pair Theorem
5. 1 2 180m m 5. Def. of Supplementary Angles
6. 1 3 180m m 6.
7. 7. Def. of Supplementary Angles
Statements Reasons
1. 1 4 1.
2. 1 2 2.
3. 3 4 3.
4. 2 4 4.
5. 5.
3
2 1
4 1 2 3
Geometry: Unit 3 – Geometric Proof Day 2
7. Given: bisects BX ABC
45m ABX °
Prove: is a right angleABC
Statements Reasons
1. bisects BX ABC 1.
2. 2.
3. m ABX m XBC 3.
4. 45m ABX ° 4.
5. 45m XBC ° 5.
6. m ABX m XBC m ABC 6.
7. 45° + 45° = m ABC 7.
8. 90° = m ABC 8.
9. is a right angleABC 9.
8. Given: bisectsRV SRT
3 1
Prove: 3 2
Statements Reasons
1. 1.
2. 2.
3. 3.
4. 4.
9. Given: bisectsAH IAG
Prove: m GAH m HAI
Statements Reasons
1. 1.
2. 2.
3. 3.
State whether each statement is sometimes, always, or never true. 10. An angle and its complement are congruent. _____________________
11. A pair of right angles forms a linear pair. ______________________
12. An angle and its complement form a right angle. _________________
13. A linear pair of angles is complementary. _______ 14. Find 3m . 15. Find the value of x and then the measures of all 4 angles.
R
T V
S 3
1 2
A •
C
• X
B •
A
G
H
I
Geometry Name _________________________________ Review - Geometric Reasoning Date _______________ Period _______ For #1 – 4, identify the hypothesis and conclusion of the each given statement. 1. Underline the hypothesis: If two rays are opposite rays, then they form a line.
2. Circle the conclusion: If two rays are opposite rays, then they form a line. 3. Underline the hypothesis: Stacey will make an A if she does all of her homework.
4. Circle the conclusion: Stacey will make an A if she does all of her homework.
For #5 – 6, write the inverse, converse, and contrapositive for each statement. Then determine if each statement is true or false. 5. If two rays are opposite rays, then they form a line.
Converse: __________________________________________________________ True or False Inverse: ____________________________________________________________ True or False Contrapostive: _______________________________________________________ True or False
6. Stacey will make an A if she does all of her homework. Converse: __________________________________________________________ True or False Inverse: ____________________________________________________________ True or False Contrapostive: _______________________________________________________ True or False
For #7, determine the correct biconditional statement. 7. Which of the following is the biconditional for the statement below
“If two rays are opposite rays, then they form a line.”
A. If and only if two rays are opposite rays, then they form a line. B. If two rays are opposite rays, then they form a line. C. Two rays are opposite rays if and only if they form a line. D. If two rays form a line, then they are opposite rays.
For #8, determine which statement below is true! 8. Which of the following is the statements is true for the conditional statement below
“If two lines are parallel, then they have the same slope.”
A. Converse: If two lines are not parallel, then they have the same slope. B. Inverse: If two lines are not parallel, then they do not have the same slope. C. Contrapositive: If two lines have the same slope, then they are parallel. D. Biconditional: Parallel lines have the same slope if and only if.
For #9 - 10, what can you conclude from the following using the law of syllogism? 9. If I am hungry, then I eat ice cream.
If I eat ice cream, then I need a spoon.
Conclusion:____________________________________________________________
10. If two angles are a linear pair, then they add to 180o. Two angles are supplementary, if they add to 180o.
Conclusion:____________________________________________________________
For #11 – 14, determine whether each of the problem below uses Inductive or Deductive reasoning. 11. All jeans I own are blue. Inductive Deductive
All jeans must be blue.
12. The sum of A and B is 900. Inductive Deductive Complementary angles sum to 90o.
A and B are complementary.
13. All referees I have seen are men. Inductive Deductive Only men can be referees.
14. A triangle with two equal sides is isosceles. Inductive Deductive A triangle with three equal sides is equilateral. If a triangle does not have any equal sides, then it is not isosceles or equilateral.
For #15 – 16, determine the next two items for each pattern. 15. 4, 12, 36, 108, ________, _________
16. 5x6, 10x10, 15x14, 20x18, ________, _________
For #17 – 20, state the property being used. 17. , thenIf DEF GHI GHI DEF ____________________________________
18. If 3 90om A , then 30om A ____________________________________
19. COD COD ____________________________________
20. PQ + 4 = RS + 4
For #21 – 23, complete the following algebraic proofs. 21.
22. Use the diagram below to write an algebraic proof.
Statements Reasons
3 ( 2) 4 3( 2)x x x x Given
Statements Reasons
6x + 5)o
(5x - 12)o
For #22 – 25, complete the following geometric proofs.
23. Given: NA AM
M is the midpoint of AB
Prove: NA MB Statements Reasons
1. NA AM 1. _________________________________
2. M is midpoint of AB 2.__________________________________
3. AM MB 3.__________________________________
4. NA MB 4.__________________________________
24. Given: 2 3 Prove: 1 and 3 are supplementary
25. Given: bisectsRV SRT
3 1
Prove: 3 2 Statements Reasons
1. bisectsRV SRT
1.
2. 1 2 2. 3. 3 1 3. 4. 3 2 4.
Which of the following would be the correct for reason #4?
A. Definition of Angle Bisector
B. Transitive Property of Congruence
C. Substitution Property of Congruence
D. Segment addition Postulate
Statements Reasons
1. 2 3 1. Given
2. 2 3m m 2.
3. 1 and 2 form a linear pair 3.
4. 4. Linear Pair Theorem
5. 1 2 180m m 5.
6. 1 3 180m m 6.
7. 7. Def. of Supplementary Angles
A
N
BM
3 2 1
R
T V S 3
1 2