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