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Test 2 Review Geometry Pre-AP Due Test Day! Name __________________________ Section: 2.1 – 2.3, 2.5 – 2.7 Determine if the following conjectures are True or False. If False, give a counterexample. _____1. The sum of any three consecutive integers is three times the second number. _____2. All prime numbers are odd. _____3. If the product of two numbers is positive, then the two numbers must both be positive. _____4. A number is divisible by four if the last two digits of that number are divisible by four. _____5. For all x values greater than or equal to zero, 2 x is even. _____6. If x is a prime number, then x + 1 is not prime. _____7. If X, Y, and Z are collinear points, then XY + YZ = XZ. 8. Identify the hypothesis and conclusion of the following conditional statement: “The show is cancelled if it rains”. 9. Write a conditional statement from the sentence “Parallel lines do not intersect”. _________________________________________________________________________________. Now, write the a. converse, b. inverse, and c. contrapositive of that statement, then determine the truth value of each one. a. b. c. 10. If the hypothesis of a conditional statement is true, and the conclusion is false, then the statement is ___? 11. If the hypothesis of a conditional statement is false, and the conclusion is true, then the statement is ___? 12. If the hypothesis of a conditional statement is false, and the conclusion is false, then the statement is ___? 13. Which statement is always logically equivalent to the conditional? ________________________________ 14. Which statement is always logically equivalent to the inverse? __________________________________ Write the conditional and converse statements that make up each biconditional statement. Then determine the truth value of the biconditional statement. 15. An angle is a right angle if and only if its measure is 90 degrees. True / False Conditional: _________________________________________________________________ Converse: ___________________________________________________________________ 16. A parallelogram is a rectangle if and only if it has four right angles. True / False Conditional: _________________________________________________________________ Converse: ___________________________________________________________________ 17. Write FOUR conditional statements that describe the relationship between the various groups of musicians as shown in the Venn Diagram. Musicians Band Chorus 1. 2. 3. 4. Jazz Band 18. Using a two–column proof, solve the following equations and justify each step! a. 5 – x = -3(2x + 4) 4x 6 2 4 3 b. 19. Fillin the blanks to complete the two-column proof. 2 3 Prove: 1 and 3 are supplementary Given: 1 1 Statements 1. 2 3 2 Justifications 1. Given 2. m 2 = m 3 2. 3. 3. Linear Pair Theorem 4. m 1 + m 2 = 180 4. Def. of ___________ angles 5. m 1 + m 2 = 180 5. 6. 6. Def. of Supplementary 3 Complete the following two-column proof. NUMBER EACH STEP! 20. Given: X is the midpoint of segment AY, and Y is the midpoint of segment XB. A X Y B Prove: AX YB Identify the property that justifies each statement. ST XY , then XY ST 21. If 18 = 9x, then x = 2 25. If 22. If 2x = y and y = 7, then 2x = 7 26. If x = z, then xy = yz 23. m DEF = m DEF 27. If mn + mp, then m(n + p) 24. X P, P D. So X D. 28. If AB + CD = EF + GH and AB + CD = MN and EF + GH = OP, then MN = OP 29. Which theorem correctly justifies the conclusion that 1 4? _____________________________________________