Geometry Chapter 2 Study Guide
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1 Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies the statement: If. 3. (1 point) Name the Property of Congruence that justifies the statement: If. Use the given property to complete the statement. 4. (1 point) Addition Property of Equality If, then. 5. (1 point) Substitution Property of Equality If, then. 6. (1 point) Write the conditional statement that the Venn diagram illustrates.
2 Quadrilaterals Squares 7. (2 points) What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. 8. (2 points) Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample. If x = 2, then x 2 = (2 points) For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = -10, then x 3 = (2 points) Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. I will score well on the exam if I study for 1 hour each day. I can afford to buy a ticket. 11. (2 points) Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Driving is difficult if the weather is stormy. Driving is difficult.
3 12. (2 points) Use the Law of Syllogism to draw a conclusion from the two given statements. If you exercise regularly, you have a healthy body. If you have a healthy body, you have more energy. Fill in each missing reason. ( 1 Point for each blank) 13. (2 points) Given:,, and. Find x. P R Q S Drawing not to scale x x 7 = 100 2x 4 = 100 2x = 104 x = 52 a. b. Substitution Property c. Simplify d. e. Division Property of Equality 14. (5 points) Given: 4x 6x + 3 Drawing not to scale
4 15. (5 points) bisects = 11x. =. Find Write in two column proof style so that you can justify each step. 16. (6 points) Find the values of x and y. Write in two column proof style so that you can justify each step. 3y 6x Drawing not to scale 17. (3 points)
5 For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain. An acute angle has a measure greater than 0 and less than 90. is an acute angle. 18. (2 points) Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are complementary, then the sum of their measures is 90. and are complementary. 19. (4 points) Use two column proof format to prove: Given: are supplementary, and are supplementary. Prove: 1 2 3
6 Geometry Chapter 2 Study Guide Answer Section SHORT ANSWER 1. ANS: Addition Property PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra KEY: Properties of Equality 2. ANS: Symmetric Property PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra KEY: Properties of Congruence 3. ANS: Transitive Property PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra KEY: Properties of Congruence 4. ANS: PTS: 1 DIF: L3 REF: 2-4 Reasoning in Algebra KEY: Properties of Equality 5. ANS: PTS: 1 DIF: L3 REF: 2-4 Reasoning in Algebra KEY: Properties of Equality 6. ANS: If a figure is a square, then it is a quadrilateral. PTS: 1 DIF: L3 REF: 2-1 Conditional Statements OBJ: Conditional Statements TOP: 2-1 Example 4 KEY: Venn Diagram conditional statement 7. ANS: If the coordinates of a point are positive, then the point is in the first quadrant.
7 PTS: 2 DIF: L2 REF: 2-1 Conditional Statements OBJ: Converses STA: PA 2.4.B TOP: 2-1 Example 5 KEY: conditional statement coverse of a conditional 8. ANS: If x 2 = 4, then x = 2. False; if x 2 = 4, then x can be equal to 2. PTS: 2 DIF: L2 REF: 2-1 Conditional Statements OBJ: Converses TOP: 2-1 Example 6 KEY: conditional statement coverse of a conditional counterexample truth value 9. ANS: If x 2 = 9, then x = 3. False PTS: 2 DIF: L2 REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals NAT: NAEP 2005 G1c NAEP 2005 G5a ADP K.1.1 STA: PA 2.4.B TOP: 2-2 Example 1 KEY: conditional statement coverse of a conditional biconditional statement 10. ANS: not possible PTS: 2 DIF: L3 REF: 2-3 Deductive Reasoning OBJ: Using the Law of Detachment STA: PA 2.4.B TOP: 2-3 Example 3 KEY: deductive reasoning Law of Detachment 11. ANS: not possible PTS: 2 DIF: L3 REF: 2-3 Deductive Reasoning OBJ: Using the Law of Detachment STA: PA 2.4.B TOP: 2-3 Example 3 KEY: deductive reasoning Law of Detachment 12. ANS: If exercise regularly, you have more energy. PTS: 2 DIF: L2 REF: 2-3 Deductive Reasoning OBJ: Using the Law of Syllogism STA: PA 2.4.B TOP: 2-3 Example 4 KEY: deductive reasoning Law of Syllogism 13. ANS: Angle Addition Postulate; Addition Property of Equality PTS: 2 DIF: L2 REF: 2-4 Reasoning in Algebra NAT: NAEP 2005 A2e NAEP 2005 G5a ADP J.3.1 STA: PA 2.4.B TOP: 2-4 Example 1 KEY: Properties of Equality Angle Addition Postulate deductive reasoning 14. ANS: a. Segment Addition Postulate b. Substitution
8 c. Simplify d. Subtraction Property of Equality e. Division Property of Equality PTS: 5 DIF: L3 REF: 2-4 Reasoning in Algebra NAT: NAEP 2005 A2e NAEP 2005 G5a ADP J.3.1 TOP: 2-4 Example 2 KEY: deductive reasoning proof Properties of Equality 15. ANS: 56 PTS: 5 DIF: L4 REF: 2-4 Reasoning in Algebra NAT: NAEP 2005 A2e NAEP 2005 G5a ADP J.3.1 KEY: Properties of Congruence Properties of Equality deductive reasoning 16. ANS: x = 19, y = 23 PTS: 6 DIF: L2 REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles NAT: NAEP 2005 G3g ADP K.1.1 TOP: 2-5 Example 1 KEY: Vertical Angles Theorem vertical angles supplementary angles multi-part question 17. ANS: If an angle is acute, then its measure is greater than 0 and less than 90. Conclusion: is greater than 0 and less than 90. PTS: 3 DIF: L3 REF: 2-3 Deductive Reasoning OBJ: Using the Law of Detachment STA: PA 2.4.B KEY: conditional statement Law of Detachment writing in math 18. ANS: + = 90 PTS: 2 DIF: L2 REF: 2-3 Deductive Reasoning OBJ: Using the Law of Detachment TOP: 2-3 Example 2 KEY: deductive reasoning Law of Detachment ESSAY 19. ANS: [4] By the definition of complementary angles, and. By the Transitive Property of Equality (or Substitution Property),. By the Subtraction Property of Equality,, and by the definition of congruent angles. OR equivalent explanation [3] one step missing OR one incorrect justification [2] two steps missing OR two incorrect justifications [1] correct steps with no explanations PTS: 4 DIF: L4 REF: 2-5 Proving Angles Congruent
9 OBJ: Theorems About Angles NAT: NAEP 2005 G3g ADP K.1.1 STA: PA 2.4.B KEY: complementary angles Properties of Equality rubric-based question extended response proof
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