AMSCO'S Geometry. New York - Rye High School

26. Which is the converse of “If a rectangular prism is a cube, then its surface area is 6s 2 ”?(1) If a rectangular prism is not a cube, then its surface area is not 6s 2 .(2) If the surface area of a rectangular prism is 6s 2 , then it is a cube.(3) If the surface area of a rectangular prism is not 6s 2 , then it is not a cube.(4) If the surface area of a cube is 6s 2 , then it is a rectangular prism.27. Which is the inverse of “If z 4, then 2z 9”?(1) If 2z 9, then z 4. (3) If z 4, then 2z 9.(2) If 2z 9, then z 4. (4) If z 4, then 2z 9.28. Which is the contrapositive of “If y is greater than 3, then 2y 10y is not equal to 36”?(1) If 2y 10y is not equal to 36, then y is greater than 3.(2) If 2y 10y equals 36, then y is not greater than 3.(3) If 2y 10y is not equal to 36, then y is not greater than 3.(4) If 2y 10y equals 36, then y is greater than 3.Applying SkillsIn 29–34, assume that each conditional statement is true. Then:a. Write its converse in words and state whether the converse is always true, sometimestrue, or never true.b. Write its inverse in words and state whether the inverse is always true, sometimes true,or never true.c. Write its contrapositive in words and state whether the contrapositive is always true,sometimes true, or never true.29. If Derek lives in Las Vegas, then he lives in Nevada.30. If a bin contains 3 red marbles and 3 blue marbles, then the probability of picking a red1marble from the bin is 2.31. If a polygon has eight sides, then it is an octagon.32. If a garden grows carrots, then it grows vegetables.33. If the dimensions of a rectangle are 8 feet by 6 feet, then the area of the rectangle is 48square feet.34. If a number has 7 as a factor, then it is divisible by 7.Biconditionals 692-6 BICONDITIONALSA biconditional is the conjunction of a conditional and its converse. For theconditional (p → q), the converse is (q → p). The biconditional can be written as(p → q) ∧ (q → p) or in the shorter form p ↔ q, which is read p if and only if q.