AMSCO'S Geometry. New York - Rye High School

92 Logic11. The first two sentences below are true. Determine whether the third sentenceis true, is false, or cannot be found to be true or false. Justify youranswer.I win the ring toss game.If I win the ring toss game, then I get a goldfish.I get a goldfish.12. On the number line, the coordinate of R is 5 and the coordinate of S is1. What is the coordinate of T if S is the midpoint of RT?Part IIIAnswer all questions in this part. Each correct answer will receive 4 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.13. Let A and B be two points in a plane. Explain the meanings of the symbolsAB g, AB h, AB, and AB.14. The ray BD his the bisector of ABC, a straight angle. Explain why BD hisgperpendicular to ABC. Use definitions to justify your explanation.Part IVAnswer all questions in this part. Each correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.15. The steps used to simplify an algebraic expression are shown below. Namethe property that justifies each of the steps.a(2b 1) a(2b) a(1) (a 2) b a(1) (2 a) b a(1) 2ab a16. The statement “If x is divisible by 12, then x is divisible by 4” is always true.a. Write the converse of the statement.b. Write the inverse of the statement.c. Are the converse and inverse true for all positive integers x? Justifyyour answer.d. Write another statement using “x is divisible by 12” and “x is divisibleby 4” or the negations of these statements that is true for all positiveintegers x.