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Geometric Proofs

1) I can define, identify and illustrate the following terms

Conjecture

Inductive

Deductive

Conclusion

Proof

Postulate

Theorem

Prove

Given

Negation

Counterexample

Dates, assignments, and quizzes subject to change without advance notice.

|Monday |Tuesday |Block Day |Friday |

| | |3/4 |5 |

| | |Assumptions & | |

| | |Justifications; Making |Fill in the Blank and Plan|

| | |Conclusions |Proofs |

| | | | |

| | |Fill in the Blank Proofs | |

|8 |9 |10/11 |12 |

|Student Holiday |Writing Proofs |Practice Quiz |Test 4 |

| | |Review | |

Wednesday, 10/3 and Thursday, 10/4

|Assumptions and Justifications |

|Making conclusions |

|I can make correct assumptions from a picture, words, or statement. |

|I can justify a conclusion with a definition, theorem, or postulate. |

|I can make and justify the next logical conclusion from a given statement. |

|ASSIGNMENT: Assumptions, Justifications, and Conclusions Worksheet, |Completed: |

|pg. 113-114 (4, 7, 8) | |

Friday, 10/5

|Fill in the Blank and Plan Proofs |

|I can write a two column proof given a plan. |

|ASSIGNMENT: : pg. 113-114 (4, 7, 8) and Proofs Worksheet #1 |Completed: |

Tuesday, 10/9

|Writing Proofs |

|I can write a two column proof. |

|ASSIGNMENT: Proofs Worksheet #2 |Completed: |

Wednesday, 10/10 and Thursday, 10/11

|Review |

|*I can review for the test in class. |

|ASSIGNMENT: Review WS |Completed: |

Friday, 10/12

|Test 3 – Logic and Proofs |

|I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material. |

|ASSIGNMENT: Test #3 |Grade: |

Assumptions and Justifications

Use page 73 in your book to help complete the notes below…

Things You Can Assume From a Diagram Things You CAN’T Assume From a Diagram

I. For each picture list the facts you can assume from it.

II. Based on the picture alone, determine if each statement is true or false.

1. [pic] 5. [pic]

2. [pic]is a right angle. 6. [pic]

3. T is between E and H. 7. O and R are collinear.

4. M, O, S, and H are coplanar. 8. [pic] is a right angle.

1. [pic] is an acute angle. 6. [pic] are supplementary.

2. [pic] 7. [pic] are complementary.

3. [pic] 8. C is the midpoint of [pic].

4. [pic] 9. [pic] are a linear pair.

5. [pic] 10. [pic]are complementary.

III. For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification.

1. Given: [pic]

Conclusion: [pic]

Why: _________________________________

2. Given: E is the midpoint of [pic]

Conclusion: [pic]

Why: _________________________________

3. Given: A bisects [pic]

Conclusion: [pic]

Why: _________________________________

4. Given: CO = OL

Conclusion: [pic]

Why: _________________________________

5. Given: [pic]and [pic]are a linear pair.

Conclusion: [pic]&[pic]are supplementary

Why: _________________________________

6. Given: [pic]is the supplement of [pic]

Conclusion: [pic]

Why: _________________________________

7. Given: A and B lie in Plane JOG

Conclusion: A and B are collinear

Why: _________________________________

8. Given: A is in the interior of [pic]

Conclusion: [pic]

Why: _________________________________

9. Given: [pic]is the complement to [pic]

Conclusion: [pic]

Why: _________________________________

10. Given: [pic]is vertical to [pic]

Conclusion: [pic]

Why: _________________________________

11. Given: [pic]

Conclusion: U is the midpoint of [pic]

Why: _________________________________

12. Given: [pic]

Conclusion: [pic]and [pic]are vertical

Why: _________________________________

13. Given: [pic]

Conclusion:[pic]&[pic]are complementary

Why: _________________________________

14. Given: [pic]

Conclusion:[pic]

Why: _________________________________

15. Given: MA = TH

Conclusion: [pic]

Why: _________________________________

16. Given: [pic]

Conclusion: [pic]&[pic]are supplementary

Why: _________________________________

17. Given: [pic]

Conclusion: [pic]

Why: _________________________________

18. Given: [pic]

Conclusion: [pic]

Why: _________________________________

Name: ___________________________________ Period:_____

Making Conclusions

1. Given: [pic]

2. Conclusion:

Justification:

3. Given: E is the midpoint of [pic]

Conclusion:

Justification:

4. Given: A bisects [pic]

Conclusion:

Justification:

5. Given: CO = OL

Conclusion:

Justification:

6. Given: [pic]and [pic]are a linear pair

Conclusion:

Justification:

7. Given: [pic]is the supplement of [pic]

Conclusion:

Justification:

8. Given: [pic]

Conclusion:

Justification:

9. Given: [pic]

Conclusion:

Justification:

10. Given: [pic]

Conclusion:

Justification:

11. Given: [pic]

Conclusion:

Justification:

12. Given: [pic]

Conclusion:

Justification:

13. Given: [pic]and [pic]are vertical angles.

Conclusion:

Justification:

14. Given: [pic]

Conclusion:

Justification:

15. Given: A is in the interior of [pic]

Conclusion:

Justification:

16. Given: [pic]

Conclusion:

Justification:

17. Given: [pic]is vertical to [pic]

Conclusion:

Justification:

18. Given: [pic]

Conclusion:

Justification:

19. Given; [pic]

Conclusion:

Justification:

20. Given: [pic]

Conclusion:

Justification:

21. Given: [pic]bisects [pic]

Conclusion:

Justification:

22. Given: [pic]

Conclusion:

Justification:

23. Given: [pic]

Conclusion:

Justification:

24. Given: [pic]and[pic]are a linear pair

Conclusion:

Justification:

25. Given: [pic]and [pic]are complementary angles.

Conclusion:

Justification:

26. Given: [pic]

Conclusion:

Justification:

27. Given: A is between J and M

Conclusion:

Justification:

“Making Conclusions” Worksheet continues on the next page…

For #27 and 28, a two column proof is given but steps are missing. Fill in the missing steps and rewrite the whole proof correctly.

27.

Given:[pic]is supplementary to [pic]2, [pic]3 is supplementary

to [pic]4, and [pic]

Prove: [pic]

|Statements |Reasons |

|1. |[pic]&[pic]2 are supp. |Given |

| |[pic]3 &[pic]4 are supp. | |

|2. | [pic] |Def. of Supplement. |

| |[pic] | |

|3. |[pic] |Transitive Prop. |

|4. | | |

|5. | | |

|6. |[pic] |Substitution prop, |

| | |Steps __ and __ |

|7. |[pic] |Subtraction prop. |

|8. |[pic] |Def. of [pic] |

28.

Given: [pic]5 is complementary to [pic]7

Prove: [pic]

|Statements |Reasons |

|1. |[pic]&[pic]7 are comp. |Given |

|2. | [pic] |Def. of complement. |

|3. | | |

|4. |[pic] |Substitution, steps __ and __ |

|6. |[pic] |Definition of perpendicular |

P 113 (4, 7, 8)

Name: Period:

Proofs Worksheet #1

On a separate paper, write a two-column proof for each problem 1-5. Follow the plan provided for help.

1. Given: [pic]

Prove: RS = TU

Plan: Use the definition of congruent segments to write the given information in terms of lengths. Next use the Segment Addition Postulate to write RT in terms of RS + ST and SU as ST + TU. Substitute those into the given information and use the Subtraction Property of Equality to eliminate ST and leave RS = TU.

2. Given: [pic]

Prove: [pic]

Plan: Use the Linear Pair Theorem to show that [pic] and [pic] are supplementary. Then use the definition of supplementary angles to show that their measures add up to 180°. Finally use substitution and then subtraction to arrive at the “Prove” statement.

3. Given: AB = BC

BC = BD

Prove: B is the midpoint of [pic]

Plan: Write the “Given” information and use the transitive property to show that AB=BD. Then use the definition of congruence to show that the segments are congruent and the definition of midpoint to finish the proof.

4. Given: l bisects [pic] at P

Prove: MP = PN

Plan: Use the definition of bisect to show the two smaller segments are congruent. Then use the definition of congruence to show that their lengths are equal.

5. Given: [pic] and [pic] are supplementary;

[pic]

Prove: [pic] and [pic] are supplementary

Plan: Use the definition of supplementary angles and congruent angles to write the given information in terms of angle measures. Next use substitution to show that [pic]. Then use the definition of supplementary angles for the conclusion.

Proofs Worksheet #2

1. 2.

Given: O is the midpoint of [pic] Given: AB = CD

OM = OW Prove: AC = BD

Prove: OW = ON

3. 4.

Given: [pic] Given: [pic] and [pic] are complementary

Prove: [pic] [pic] and [pic] are complementary

Prove: [pic]

5. 6.

Given: [pic] Given: [pic]

Prove: [pic] Prove: [pic]

7. 8.

Given: [pic] Given: [pic]

Q is the midpoint of [pic] D is in the interior of [pic]

M is the midpoint of [pic] Prove: [pic] and [pic] are complementary

Prove: PQ = LM

9. 10.

Given: [pic] Given: [pic] and [pic] are supplementary

Prove: [pic] [pic]

Prove: [pic] and [pic] are right angles

11. 12.

Given: [pic] Given: [pic] and [pic] are complementary

Prove: [pic] and [pic] are right angles Prove: [pic] and [pic] are complementary

13. 14.

Given: [pic] Given: [pic] bisects [pic]

[pic]

Prove: [pic] Prove: [pic]

15. 16.

Given: [pic] is a right angle Given:[pic]

[pic]

Prove: [pic] and [pic] are complementary Prove: F is the midpoint of [pic]

17. 18.

Given: KU = HF Given: [pic] and [pic] are right angles

[pic]

Prove: [pic] Prove: [pic]

19. 20.

Given: [pic] Given: [pic]

Prove: [pic] is the angle bisector of [pic] Prove: [pic] and [pic] are complementary

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