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Geometry A Unit 2 Review Name 1. Geoff is really excited to learn about triangles next week. Over the weekend, he is exploring different triangles and their angle measures. After exploring many triangles, he notices a pattern. All of the measures of the angles inside the triangle seem to sum to 180 degrees. Using reasoning, he makes a that the angles in a triangle always sum to 180 degrees. Using reasoning and Mrs. Gerrish’s help, he proves the conjecture to be true. 2. Write the converse, inverse, and contrapositive of the following conditional. Then, determine their truth value. “If we have a snow day, then school is closed.” T/F: Hypothesis: Conclusion: Converse: T/F: Inverse: T/F: Contrapositive: T/F: 3. Determine if each statement is true or false. If the statement is false, give a counterexample. a. If the month is February, then there are 28 days in the month. b. If x 6 , then x 2 36 . c. If x 2 36 , then x 6 . d. If 2+2=5, then it rains cats and dogs. e. If it is a flower, then it is a daisy. f. If Zach wins the lottery, then he will give everyone in Geometry class $1000. (he didn’t) 4. Write the definition as a biconditional. “An idiot is an utterly foolish or senseless person.” (dictionary.reference.com) T 5. Determine if the biconditional statement is true or false. If it is true, explain why. If it is not, explain why not. “Angles are congruent if and only if they are vertical angles. “ 6. Determine if the conclusion is valid using the Law of Detachment. If you mow the neighbor’s yard, then you will earn $20. Jared has $20. Conclusion: Jared mowed the neighbor’s yard. Given: Valid Invalid 7. Complete the conclusion based on the Law of Syllogism. If you mow the neighbor’s yard, then you earn $20. If you earn $20, then you will go to the movies. Conclusion: If you mow the neighbor’s yard, then Given: 8. Write the algebra proof. Given: 2( x 4) 4 x 5 x 10 Prove: x 6 Statement 1. 2. 3. 4. 5. 6. 7. 8. 9. Reason . 9. Complete the proof. Given: SR bisects QST mQSR 3 x 5 , mRST 2 x 9 Prove: mQST 74 Statement Reason 1. SR bisects QST 2. mQSR 3 x 5 , mRST 2x 9 3. QSR RST 4. mQSR mRST 5. 3x 5 2x 9 6. 3 x 2x 5 2x 2x 9 7. x 5 9 8. x 5 5 9 5 9. x 14 10. mQSR 3 14 5 , mRST 2 14 9 11. mQSR 37 , mRST 37 12. mQSR mRST mQST 13. 37 37 mQST 14. 74 mQST 15. mQST 74 10. Write the proof of the Right Angle Congruence Theorem. Given: Prove: Statement 1. 2. 3. 4. Reason 11. Write the proof of the Linear Pair Theorem. Given: Prove: Statement Reason 1. 2. 3. 4. 5. 6. 7. 8. 9. 12. Complete the proof of the Congruent Complements Theorem. Given: 1 and 2 are complementary 2 and 3 are complementary Prove: 1 3 Statement 1. 2. 3. 4. 5. 6. 7. 8. 9. Reason Given Definition of complementary angles Given Transitive Property of Equality m2 m2 m1 m2 m2 m2 m2 m3 Simplify 13. Given the diagram below, find all the pairs of… a. corresponding angles b. vertical angles c. linear pairs d. alternate interior angles e. alternate exterior angles f. same-side interior angles 14. Use the parallel line theorems to find the missing angle. Be sure to state which theorem/postulate you used. a. Find mKLM . b. Find mDEF c. Find mQRS . d. Find the value of x that would make m n . (6x + 5)º m (5x - 12)º n 15. Determine if the following relationships prove that the lines are parallel. If so, you should have a theorem/postulate that supports it. If not, determine if there is “not enough info” or “not parallel”. 1. m3 150 , m6 30 2. m4 90 , m5 90 3. 4 8 4. 1 3 5. m4 50 , m6 50 6. m2 80 , m8 80 7. m6 40 , m3 120 8. m5 115 , m6 65 9. 4 7