Math Geom Ch 2 Midterm Review Solutions

Midterm Review Chapter 2 Geometry CP Name: Kay Describe the pattern and give the next 2 numbers in the sequence -3, 3, 9, 15... +6 21, 27 21, 12, 3... -9 -6, -15 1, 8, 27, 64... 1³, 2³, 3³, 4³ 125, 216, 343 The cube of a number is greater than the square False. 1³ = 1² If XY = YZ, then Y is the midpoint of XZ False. If two planes intersect, their intersection is a segment False. Intersection is a line Through any two points, there exists exactly 1 line True If two lines intersect, their intersection is a point True A line can be in more than one plane True Write the converse, inverse, and contrapositive of each statement. Tell whether each is true or false. If the measure of an angle is less than 90°, then the angle is acute Converse: If an angle is acute, then its measure is less than 90° True Inverse: If the measure of an angle is NOT acute, then its measure is NOT less than 90° True Contrapositive: If an angle is NOT acute, then its measure is NOT less than 90° True If two angles are supplementary, then they are adjacent Converse: If 2 angles are adjacent, then they are supplementary False Inverse: If 2 angles are NOT supplementary, then they are NOT adjacent True Contrapositive: If 2 angles are NOT adjacent, then they are NOT supplementary True If two rays share a vertex, then they are opposite rays Converse: If 2 rays are opposite, then they share a vertex True Inverse: If 2 rays DO NOT share a vertex, then they are NOT opposite rays True Contrapositive: If 2 rays are NOT opposite rays, then they do NOT share a vertex True Rewrite the conditional statement into If-Then form. Then write the statement as a biconditional statement. 13. All Grosse Pointe South students take three math courses. If-Then: If you are a GP South student, then you take 3 math courses. Biconditional: You are a GP South student IF AND ONLY IF you take 3 math courses. Decide whether each statement about the diagram is true. Explain your answer. 14. AD is perpendicular to BC. True (Symbol) 15. ∠ACD and ∠DCB are complementary. True comp. ∠s add to 90° 16. CD bisects ∠ACB. False. x = 2x. If they bisected, they would be = Use the Law of Detachment or the Law of Syllogism (Chain Rule) to make a valid conclusion. State the law that is used.   17. If it is a weekday, Natalie is at school. Today is Wednesday. Conclusion: Natalie is at school. Law: Detachment 18. If you like to study history, then you like to read books. If you like to read books, then you enjoy going to the library. Conclusion: If you like to study history, then you enjoy going to the library. Law: Chain Rule 19. If you can drive a car, then you must act responsibly. If you pass a driver's test, then you can drive a car. Conclusion: If you pass a driver's   test, then you must act responsibly. Law: Chain Rule 20. If a person is in the U.S., he or she is a U.S. citizen. Emily was born in Michigan. Conclusion: Emily is a U.S. citizen. Law: Detachment 21. If a triangle has a right angle, then it's a right triangle. If a polygon is a right triangle, then the two acute angles are complementary.   Conclusion: If a triangle has a right angle, then the two acute angles are complementary. Law: Chain Rule