Download Worksheet 2.4

PROOF GEOMETRY
GWKSHT 2.4
CH. 2 SECTION 4
NAME___________________________________________ HR_____
DATE_____/_____/_____ Score:_________ Recorded ____/____/____
Complete the following chart
with symbolic
representations.
Law of Detachment:
Law of Syllogism:
DETERMINE WHETHER THE STATED CONCLUSION IS VALID BASED ON THE GIVEN INFORMATION. IF
NOT, WRITE INVALID. EXPLAIN YOUR REASONING.
1. Given: Right angles are congruent.
1 and 2 are right angles.
Conclusion: 1  2
2. Given: If a figure is a square, it has four right angles.
Figure ABCD has four right angles.
Conclusion: Figure ABCD is a square.
Valid? __________ If so, why? _______________
Valid? __________ If so why?: ______________________
__________________________________________
________________________________________________
3. Given: An angle bisector divides an angle into
two congruent angles.
⃗⃗⃗⃗⃗⃗⃗
𝐾𝑀 is an angle bisector of JKL.
Conclusion: JKM  MKL.
4. Given: If you leave your lights on while your car is off,
your battery will die.
Your battery is dead.
Conclusion: You left your lights on while your care was off.
Valid? __________ If so, why? _______________
Valid? __________ If so why?: ______________________
__________________________________________
________________________________________________
5. Given: If two angles are vertical angles,
6. Given: If two angles form a linear pair, then they are
then they are congruent.
A  C
Conclusion: A & C are vertical angles
adjacent.
1 and 2 form a linear pair
Conclusion: 1 and 2 are adjacent
Valid? __________ If so, why? _______________
Valid? __________ If so why?: ______________________
__________________________________________
________________________________________________
7. Given: If two angles are complementary to the
8. Given: If two angles are complementary to the
same angle, then they are congruent.
same angle, then they are congruent.
A & C are complementary to  B
A  C
Conclusion: A  C
Conclusion: A & C are complements of  B
Valid? __________ If so, why? _______________
Valid? __________ If so why?: ______________________
__________________________________________
________________________________________________
USE THE LAW OF SYLLOGISM OR LAW OF DETATCHMENT TO DETERMINE WHETHER A VALID
CONCLUSION CAN BE REACHED FROM EACH SET OF STATEMENTS. IF SO, WRITE IT. IF NOT, WRITE NO
CONCLUSION. STATE THE LAW USED.
9. If you spend money on it, then it is a business.
If you spend money on it, then it is fun.
10. If the measure of an angle is less than 90, then it is acute.
If an angle is acute, then it is not obtuse.
Conclusion: ______________________________
Conclusion: ______________________________
_________________________________________
_________________________________________
Law used: __________
Law used: __________
11. If a polygon is a triangle, then it has 3 sides.
Polygon ABC is a triangle.
12. If you are sixteen, then you can drive.
Jeff is sixteen.
Conclusion: ______________________________
Conclusion: ______________________________
_________________________________________
_________________________________________
Law used: __________
Law used: __________
13. If you are in Geometry, then you like math.
You like math.
14. If you are 18 years old, then you are in college.
If you are in college, then you go to LSSU.
Conclusion: ______________________________
Conclusion: ______________________________
_________________________________________
_________________________________________
Law used: ____________________
Law used: ____________________
DETERMINE WHETHER STATEMENT (3) FOLLOWS FROM STATEMENTS (1) AND (2) BY THE LAW OF
DETACHMENT OR THE LAW OF SYLLOGISM. IF IT DOES, STATE WHICH LAW WAS USED. IF IT DOES
NOT, WRITE INVALID.
15. (1) If the measure of an angle is greater than 90,
then it is obtuse.
(2) mABC  90
(3) ABC is obtuse.
16. (1) Vertical angles are congruent.
(2) 3  4
(3) 3 & 4 are vertical angles.
Valid? __________ If so, law used: ____________
Valid? __________ If so, law used: ____________
17. (1) If you drive safely, then you can avoid
accidents.
(2) Kelly drives safely.
(3) Kelly can avoid accidents.
18. (1) If you are a teenager, then you go to high school.
(2) If you go to high school, then you can drive.
(3) If you are a teenager, then you can drive.
Valid? __________ If so, law used: ____________
Valid? __________ If so, law used: ____________
USE THE LAW OF SYLLOGISM TO DRAW A VALID CONCLUSION FROM EACH SET OF STATEMENTS, IF
POSSIBLE. IF NO VALID CONCLUSION CAN BE DRAWN, WRITE NO VALID CONCLUSION AND EXPLAIN
YOUR REASONING.
19. If you interview for a job, then you wear a suit.
If you interview for a job, then you will update your resume.
Conclusion:__________________________________________________________________________________.
20. If Tina has a grade point average of 3.0 or greater, she will be on the honor roll.
If Tina is on the honor roll, then she will have her name in the school paper.
Conclusion: ___________________________________________________________________________________.
21. If the measure of an angle is between 90 and 180, then it is obtuse.
If an angle is obtuse, then it is not acute.
Conclusion: ____________________________________________________________________________________.
22. If two lines in a plane are not parallel, then they intersect.
If two lines intersect, then they intersect in a point.
Conclusion: ____________________________________________________________________________________.
23. If a number ends in 0, then it is divisible by 2.
If a number ends in 4, then it is divisible by 2.
Conclusion: ___________________________________________________________________________________.