University:
Concordia University Texas
Course:
MTH 3101 | Problem Solving: Algebra, Geometry, and Trigonometry
Academic year:

2020
Views:

409

Pages:

2
Author:

Ruben Owens

Name: ______________________ Answers 1. Add 5; 14 2. Multiply by − 2; 6.25 3. Converse: If the angles are congruent, then they are right angles. Inverse: If the angles are not right angles, then they are not congruent. Contrapositive: If the angles are not congruent, then they are not right angles. 4. Converse: If it is an amphibian, then it is a frog. Inverse: If it is not a frog, then it is not an amphibian. Contrapositive: If it is not an amphibian, then it is not a frog. 5. If Margot goes to college, then she will need to buy a lab manual.; Law of Syllogism. 6. You will miss band practice.: Law of Detachment 7. Line; Plane 8. Two 9. Plane 1 10. Three 11. Point 12. Line 13. Two; Line 14. 9𝑥 + 31 = −23 9𝑥 = −54 𝑥 = −6 Given Subtraction Division 15. −7(−𝑥 + 2) = 42 −𝑥 + 2 = −6 −𝑥 = −8 𝑥=8 Given Division Subtraction Division 16. 26 + 2(3𝑥 + 11) = −18𝑥 26 + 6𝑥 + 22 = −18𝑥 48 + 6𝑥 = −18𝑥 48 = −24𝑥 −2 = 𝑥 𝑥 = −2 Given Distributive Property Simplify Subtraction Division Symmetric 17. Symmetric 18. Reflexive 19. Transitive 20. 54°, 54°, 126°, 126° 21. 1. 2. 3. 4. 5. 6. 𝐴𝑋 ≅ 𝐷𝑋, 𝑋𝐵 ≅ 𝑋𝐶 𝐴𝑋 = 𝐷𝑋, 𝑋𝐵 = 𝑋𝐶 𝐴𝑋 + 𝑋𝐶 = 𝐴𝐶, 𝐵𝑋 + 𝑋𝐷 = 𝐵𝐷 𝐷𝑋 + 𝑋𝐶 = 𝐴𝐶, 𝑋𝐶 + 𝑋𝐷 = 𝐵𝐷 𝐴𝐶 = 𝐵𝐷 𝐴𝐶 ≅ 𝐵𝐷 Given Definition of Congruent Segments Segment Addition Postulate Substitution Substitution (or Transitive) Definition of Congruent Segments Name: ______________________ Geometry Chapter 2 Review Describe the pattern in the numbers. Write the next number. 1. −6, −1, 4, 9, … 2. 100, −50, 25, −12.5, … Write the converse, the inverse, and the contrapositive for the given statement. 3. If they are right angles, then they are congruent. 4. If it is a frog, then it is an amphibian. Make a valid conclusion based on the information. Then state whether you used the Law of Detachment or the Law of Syllogism. 5. If Margot goes to college, then she will major in Chemistry. If Margot majors in Chemistry, then she will need to buy a lab manual. 6. If you decide to go to the football game, then you will miss band practice. Tonight, you are going the football game. Fill the blanks. 7. If two points lie in a plane, then the ____ containing them lies in the _____. 8. A line contains at least ___ points. 9. Through any three noncollinear points there exists exactly one _____. 10. A plane contains at least ______ noncollinear points. 11. If two lines intersect, then their intersection is exactly one _____. 12. If two planes intersect, then their intersection is a ___. 13. Through any ___ points there exists exactly one ____. Solve the equation. Write a reason for each step. 14. 9𝑥 + 31 = −23 15. −7(−𝑥 + 2) = 42 16. 26 + 2(3𝑥 + 11) = −18𝑥 Name the statement with the property that it illustrates. 17. If ∠𝑅𝑆𝑇 ≅ ∠𝑋𝑌𝑍, then ∠𝑋𝑌𝑍 ≅ ∠𝑅𝑆𝑇 18. 𝑃𝑄 ≅ 𝑃𝑄 19. If 𝐹𝐺 ≅ 𝐽𝐾 and 𝐽𝐾 ≅ 𝐿𝑀 , then 𝐹𝐺 ≅ 𝐿𝑀. 20. Find the measure of each angle in the diagram. 21. Write a two-column proof. Given: 𝐴𝑋 ≅ 𝐷𝑋, 𝑋𝐵 ≅ 𝑋𝐶 Prove: 𝐴𝐶 ≅ 𝐵𝐷