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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) mABC 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: ___________________________________________________________________________________.