Section 1 – 200pts Define convex.

Section 1 – 200pts A set in which every segment that connects two points in the set lies entirely in the set. Or A set with no “dents”.

Section 1 – 400pts Define non-convex. Give another term for non-convex.

Section 1 – 400pts A set where there exists a segment that connects two points in the set that does not lies entirely in the set. Or A set that contains at least one “dent”. Alternate term: Concave.

Section 1 – 600pts Categorize the following shape as convex or non- convex. If non-convex, prove it.

Section 1 – 600pts Convex

Section 1 – 800pts Categorize the following shape as convex or non- convex. If non-convex, prove it.

Section 1 – 800pts Non-convex

Section 1 – 1000pts Categorize the following shape as convex or non- convex. If non-convex, prove it. A B C

Section 1 – 1000pts Non-convex. An angle is the union of two rays and does NOT include the space between them. A B C

Section 2 – 200pts Another term for an “if-then” statement is...

Section 2 – 200pts A conditional

a.The statement that follows the “then” in a conditional is called... b.The statement that follows the “if” in a conditional is called... Section 2 – 400pts

a.The consequent. b.The antecedent.

Section 2 – 600pts Identify the antecedent and the consequent in the following statement. If a figure is a square, then it is a polygon.

Section 2 – 600pts If a figure is a square, then it is a polygon. antecedent consequent Notice that the “if’ and the “then” are NOT included in the antecedent or consequent.

Section 2 – 800pts Consider the statement: Every bird can fly. a.Rewrite it as a conditional. b.Is it true? If so give an example, if not give a counter example.

Section 2 – 800pts Consider the statement: Every bird can fly. a.If an animal is a bird, then it can fly. b.False. A counterexample would be an ostrich, dodo, penguin, kiwi,...

Section 2 – 1000pts p = a figure is a square q = If, then it is a polygon. a.Write p  q. b.Is it true? If so give an example, if not give a counter example. c.Write q  p. What is this called? d.Is it true? If so give an example, if not give a counter example.

Section 2 – 1000pts p = A figure is a square q = It is a polygon. a.“If a figure is a square, then it is a polygon.” b.True. An example would be a floor tile in the lab. c.“If a figure is a polygon, then it is a square.” This is called the converse. d.False. A counterexample would be a pentagon.

Section 3 – 200pts What do the following symbols mean? a.  b. 

Section 3 – 200pts What do the following symbols mean? a.If p, then q. p implies q. the conditional symbol b.p if and only if q. the bi-conditional sign

Section 3 – 400pts Consider the statement: A polygon has four sides, if it is a quadrilateral. Write the bi-conditional.

Section 3 – 400pts Consider the statement: A polygon has four sides, if it is a quadrilateral. The figure is a quadrilateral if and only if it is a polygon with four sides.

Section 3 – 600pts p = You can go to the movies. q = Your homework is done. a.Write p  q. b.Write q  p. What is this called? c.Write p  q. What is this called?

Section 3 – 600pts p = You can go to the movies. q = Your homework is done. a.If you can go to the movies, then your homework is done. b.If your homework is done, then you can go to the movies. This is the converse. c.You can go to the movies if and only if your homework is done. This is the bi-conditional.

Section 3 – 800pts p = x  9. q = x > 8. a.Write p  q. b.Is it true? If so give an example, if not give a counter example. c.Write q  p. What is this called? d.Is it true? If so give an example, if not give a counter example.

Section 3 – 800pts p = x  9. q = x > 8. a.If x  9, then x > 8. b.Yes, it is true. Some examples would be 9.2, 11, 15½ c. If x > 8, then x  9. This is the converse. d.This is false. Some counterexamples are 8.02, 8.5, 8¾. In fact all examples could be written as 8 < x < 9.

Section 3 – 1000pts p = x is positive. q = x > 0. a.Write p  q. b.Is it true? If so give an example, if not give a counter example. c.Write q  p. What is this called? d.Is it true? If so give an example, if not give a counter example. e.Write p  q.

Section 3 – 1000pts p = x is positive. q = x > 0. a.If x is positive, then x > 0. b.Yes it is true. Some examples are 1, 3, pi, 167.2,.... c.If x > 0, then x is positive. d.Yes it is true. Some examples are 1, 3, pi, 167.2,.... e.X is positive if and only if x > 0.

Section 4 – 200pts A good definition should be able to be written as a ______________ that is true.

Section 4 – 200pts Bi-conditional

Section 4 – 400pts The symbol  is read.

Section 4 – 400pts “if and only if”

Section 4 – 600pts Q is the midpoint of and QR = 8. a.Draw a sketch. b.RT = c.QT =

Section 4 – 600pts Q is the midpoint of and QR = 8. a. b.RT = 16 c.QT = 8 R T Q

Section 4 – 800pts A is the midpoint of. LA = 7x - 4 and AB = 4x + 5. a.Find x. b.Find LA & AB. c.Find LB.

Section 4 – 800pts A is the midpoint of. LA = 7x - 4 and AB = 4x + 5. a.7x - 4 = 4x x= 4x + 9-4x 3x=93 x=3 b.LA = 7x - 4 = 7(3) - 4 LA = 17 AB = 4x + 5 = 4(3) + 5 AB = 17 c.LB = 2LA = 2(17) LB = 34

Section 4 – 1000pts I is the midpoint of. ZI = 2x + 5 and ZP = 9x a.Find x. b.Find ZI. c.Find ZP.

Section 4 – 1000pts a.2x x + 5 = 9x x + 10 = 9x x+ 22 = 9x-4x 22 = 5x 4.4 = x I is the midpoint of. ZI = 2x + 5 and ZP = 9x b.ZI = 2x + 5 ZI = 2(4.4) + 5 ZI = 13.8 c.ZP = 9x - 12 ZP = 9(4.4) - 12 ZP = 27.6

Section 5 – 200pts a.What is the definition of the intersection? b.What is the symbol used?

Section 5 – 200pts a.The set of elements that are in both sets. b. 

Section 5 – 400pts a.What is the definition of the union? b.What is the symbol used?

Section 5 – 400pts a.The set of elements that are in either set or both sets. b. 

Section 5 – 600pts Let A = the set of numbers y with y  -1. Let B = the set of numbers with y < 7. In both cases, state answer as an inequality and on a number line. a.Find A  B. b.Find A  B.

Section 5 – 600pts Let A = the set of numbers y with y  -1. Let B = the set of numbers with y < 7. a.A  B : -1  y < 7 b.A  B : all reals 00

Section 5 – 800pts Let STIX be the quadrilateral and SIX be the triangle, as shown. a.Find STIX  SIX. b.Find STIX  SIX. S T I X

Section 5 – 800pts Let STIX be the quadrilateral and SIX be the triangle, as shown. a. b. S T I X

Let A = the set of numbers {1, 3, 4, 6, 7, 12} Let B = the set of numbers {1, 2, 5, 6, 8, 11, 13} Let C = the set of numbers {-2, 0, 1, 7, 12, 13, 17} a.Find A  B. b.Find B  C. c.Find A  C. d.Draw a venn diagram showing all the intersections and unions. Section 5 – 1000pts

a.A  B = {1, 6} b.A  B = {1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13} c.A  C = {1, 7, 12} d.venn diagram. 1 A B C

Section 6 – 200pts Define Polygon.

Section 6 – 200pts A polygon is the union of segments in the same plane such that each segment intersects exactly two others only at the endpoints.

Section 6 – 400pts Determine whether each is a polygon or not.

Section 6 – 400pts yes no yes no

Section 6 – 600pts Sketch a convex octagon.

Section 6 – 600pts

Section 6 – 800pts Identify each figure.

Section 6 – 800pts triangle Quadrilateral region Pentagon Hexagon 12-gon Heptagonal region

Section 6 – 1000pts Sketch the triangle hierarchy. Incorporate the following terms: scalene, figure, equilateral, polygon, triangle, isosceles. Draw the triangles with the appropriate markings to distinguish one type from another.

Section 6 – 1000pts Polygon Figure Triangle Scalene Isosceles Equilateral

Section 7 – 200pts State the triangle inequality postulate.

Section 7 – 200pts The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Section 7 – 400pts Tell whether the numbers given can be lengths of the three sides of a triangle. a.5, 5, 5 b.13, 16, 10 c.17, 4, 12 d.3, 4, 7

Section 7 – 400pts Tell whether the numbers given can be lengths of the three sides of a triangle. a.yes b.yes c.No since = 16 which is less than 17 d.No since = 7 which is equal to 7

Section 7 – 600pts Suppose two sides of a triangle have lengths 16inches and 11inches. What are the possible lengths of the remaining side? 11 16

Section 7 – 600pts 5 < x <

Section 7 – 800pts A hotel in Houston is 40 miles from the airport and 25 miles from the convention center. With that information, determine the possible range of distances between the airport and convention center.

Section 7 – 800pts 15 < distance < 65

Section 7 – 1000pts When you move point B off of line AC, a triangle is formed. Using the endpoints, state the triangle inequality postulate. A B C

Section 7 – 1000pts AB + BC > AC AC + BC > AB AC + AB > BC A B C

Section 8 – 200pts What is a conjecture?

Section 8 – 200pts A conjecture is an educated guess, a hypothesis, or an opinion.

Section 8 – 400pts What is needed to show that a conjecture is false?

Section 8 – 400pts Just one counterexample.

Section 8 – 600pts In mathematics, for a conjecture to be true, it must be ________.

Section 8 – 600pts PROVED!!!

Section 8 – 800pts Draw several instances of the following conjecture and conclude whether or not it is true. Use a straight edge. “If the midpoints of two sides of a triangle are joined the segment is parallel to the third side.”

Section 8 – 800pts This conjecture is true. Example.

Section 8 – 1000pts Draw several instances of the following conjecture and conclude whether or not it is true. Use a straight edge. “If the midpoints of the four sides of a rectangle are connected, the resulting figure is a rectangle.”

Section 8 – 1000pts This conjecture is not true. Example.