LOGIC - Home
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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N
C
H
U
L
A
T
M
1
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R
Q
P
M
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X
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O
M
T
H
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R
S
A
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C
D
E
R
N
9
8
F
R
O
G
G
D
E
F
R
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N
9
8
9
8
M
I
L
K
M
N
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l
1
2
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A
C
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D
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1
E
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1
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J
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1
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1
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1
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2
1
D
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A
A
2
1
C
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C
G
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A
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F
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A
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