A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 11.2B, Problem 14A
To determine
(a)
To find:
Line of symmetry for the given numbers
To determine
(b)
To find:
Point symmetry for the given numbers
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Complete parts a and b below.
a. How many reflection symmetries does a
five-pointed star have? How many rotational
symmetries does a five-pointed star have?
b. How many reflection symmetries does a
fourteen-pointed star have? How many
rotational symmetries does a fourteen-pointed
star have?
a.
☆
b.
The five-pointed star has reflection symmetries and rotational symmetries.
5) How many symmetries (number of each type line, rotation ..) does a regular hexagon have?
Explain.
The operation between two symmetries can be thought of as a composition,with the result of the first symmetry being the starting point for thesecond symmetry. The composition symbol, °, will denote the operation between two symmetries. For example, the operation R180 ° MH would mean that, starting from the rightmost operation, the symmetry MH would be applied to the original figure first, with the result then being followed by R180, a counterclockwise rotation by 180 degrees.
The result of the composition is equivalent to symmetry MV applied to the original figure (Figure 5), so we can express the final result as R180 ° MH = MV.
Complete the following Cayley table:
°
Apply First
Apply Second
°
1
R180
MH
MV
1
R180
MV
MH
MV
The symmetries will be denoted by S, i.e., S = {1, R180, MH, MV}.ii. Explain why the system (S, °) is closed.iii. Provide at least three examples that can be used to conjecture that the system (S, °) is associative.
iv.…
Chapter 11 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Ch. 11.1 - Answer each of the following and explain your...Ch. 11.1 - Given a line and a point not on the line, explain...Ch. 11.1 - How are pairs of parallel lines and skew lines a....Ch. 11.1 - Is it possible for ABC to have vertex C? Why?Ch. 11.1 - If planes and are distinct planes having points...Ch. 11.1 - Prob. 7MCCh. 11.1 - MATHEMATICAL CONNECTIONS A line n is perpendicular...Ch. 11.1 - MATHEMATICAL CONNECTIONS a. Sketch three rays that...Ch. 11.1 - Identify a physical object within the classroom to...Ch. 11.1 - Prob. 12MC
Ch. 11.1 - Let each member of your group use a protractor to...Ch. 11.1 - Allie says that AB and CD are parallel because...Ch. 11.1 - Prob. 15MCCh. 11.1 - A student says that ABBA because AB starts at A...Ch. 11.1 - Prob. 17MCCh. 11.1 - A student claims that if any two planes that do...Ch. 11.1 - A student says that it is actually impossible to...Ch. 11.1 - Prob. 20MCCh. 11.1 - A student says there can be only 360 different...Ch. 11.1 - What is the intersection of rays PQ and QP in the...Ch. 11.1 - Lines a and b are parallel to each other. Lines c...Ch. 11.1 - Prob. 3NAEPCh. 11.1A - Name two rays that contain a. BC. b. EG.Ch. 11.1A - Let S be the set of lines, skew to a given line,...Ch. 11.1A - Label each of the following as true or false. If...Ch. 11.1A - a. Points A,B,C and D are collinear. In how many...Ch. 11.1A - The following figure is a rectangular box in which...Ch. 11.1A - Assessment Use the following drawing of one of the...Ch. 11.1A - ASSESSMENT Determine how many acute angles are...Ch. 11.1A - Identify a physical model for each of the...Ch. 11.1A - Find the measure of each of the following angles....Ch. 11.1A - Assessment a. Perform each of the following...Ch. 11.1A - Assessment Consider a correctly set clock that...Ch. 11.1A - In parts a and b of the following figures,...Ch. 11.1A - Given three collinear points A,B,C with B between...Ch. 11.1A - Prob. 14ACh. 11.1A - ASSESSMENT Trace each of the following drawings....Ch. 11.1A - Prob. 17ACh. 11.1A - Prob. 18ACh. 11.1B - ASSESSMENT Name three points that are not...Ch. 11.1B - Let C be the set of coplanar lines with a given...Ch. 11.1B - Prob. 4ACh. 11.1B - ASSESSMENT The following figure is a box in which...Ch. 11.1B - Prob. 6ACh. 11.1B - ASSESSMENT Determine the number of obtuse angles...Ch. 11.1B - Identify a physical model for each of the...Ch. 11.1B - ASSESSMENT Find the measures of each of the...Ch. 11.1B - a. Perform a following operations. Leave your...Ch. 11.1B - Prob. 11ACh. 11.1B - Assessment In each of the following figures,...Ch. 11.1B - ASSESSMENT In each of the following pairs,...Ch. 11.1B - Prob. 15ACh. 11.1B - ASSESSMENT On the dot paper below, draw all...Ch. 11.1B - ASSESSMENT In the figure below, O is the center of...Ch. 11.1B - If the measure of A is 30 more than twice the...Ch. 11.1B - ASSESSMENT Describe each of the following sets of...Ch. 11.2 - Prob. 1MCCh. 11.2 - Can a regular polygon be concave? Explain.Ch. 11.2 - Prob. 3MCCh. 11.2 - Classify each of the following as true or false....Ch. 11.2 - MATHEMATICAL CONNECTIONS Copy and complete...Ch. 11.2 - MATHEMATICAL CONNECTIONS On a geoboard or dot...Ch. 11.2 - Work with partners to create a Venn diagram with...Ch. 11.2 - Work with partners to create a Venn diagram...Ch. 11.2 - The six pattern blocks shown below are...Ch. 11.2 - Prob. 12MCCh. 11.2 - Prob. 13MCCh. 11.2 - Millie claims that a rhombus is regular because...Ch. 11.2 - Jane heard a student say that all squares are...Ch. 11.2 - A student asks if ABCD is a valid name for the...Ch. 11.2 - MATHEMATICAL CONNECTIONS A student claims that all...Ch. 11.2 - MATHEMATICAL CONNECTIONS Two students are thinking...Ch. 11.2 - Use GeoGebra Lab-2 to construct quadrilaterals.Ch. 11.2 - If three distinct rays with the same vertex are...Ch. 11.2 - Prob. 21MCCh. 11.2 - Prob. 22MCCh. 11.2 - Prob. 1NAEPCh. 11.2 - NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS NAEP...Ch. 11.2A - Determine which of the following figures labeled 1...Ch. 11.2A - What is the maximum number of intersection points...Ch. 11.2A - What type of polygon must have a diagonal such...Ch. 11.2A - Describe the shaded region as simply as possible.Ch. 11.2A - If possible, draw the following triangles. If it...Ch. 11.2A - Determine how many diagonals each of the following...Ch. 11.2A - Draw all lines of symmetry if any exist for each...Ch. 11.2A - Identify each of the following triangles as...Ch. 11.2A - Various international signs have symmetries....Ch. 11.2A - Prob. 11ACh. 11.2A - Design symbols that have each of the following...Ch. 11.2A - In each of the following figures, complete the...Ch. 11.2A - Prob. 14ACh. 11.2A - Prob. 15ACh. 11.2A - Complete the following figures so that they have...Ch. 11.2A - Prob. 17ACh. 11.2B - ASSESSMENT Determine which of the following...Ch. 11.2B - ASSESSMENT What is the maximum number of...Ch. 11.2B - ASSESSMENT A pentagon has only two diagonals that...Ch. 11.2B - ASSESSMENT Which of the following figures are...Ch. 11.2B - ASSESSMENT Describe the shaded region as simply as...Ch. 11.2B - Prob. 6ACh. 11.2B - Prob. 7ACh. 11.2B - Prob. 8ACh. 11.2B - ASSESSMENT Identify each of the following...Ch. 11.2B - Prob. 10ACh. 11.2B - Prob. 11ACh. 11.2B - Prob. 12ACh. 11.2B - Prob. 13ACh. 11.2B - Prob. 14ACh. 11.2B - Prob. 15ACh. 11.2B - Prob. 16ACh. 11.2B - Prob. 17ACh. 11.3 - Prob. 1MCCh. 11.3 - Prob. 2MCCh. 11.3 - Prob. 3MCCh. 11.3 - Prob. 4MCCh. 11.3 - Prob. 5MCCh. 11.3 - Prob. 6MCCh. 11.3 - Prob. 7MCCh. 11.3 - Prob. 8MCCh. 11.3 - Regular hexagons have been used to tile floors....Ch. 11.3 - Lines a and b are cut by transversals c and d. If...Ch. 11.3 - A beam of light from A hits the surface of a...Ch. 11.3 - Find a possible set of measures of the interior...Ch. 11.3 - Draw three different concave polygons. When you...Ch. 11.3 - Draw three concave polygons. Measure all the...Ch. 11.3 - Prob. 15MCCh. 11.3 - Prob. 16MCCh. 11.3 - Jan wants to make tiles in the shape of a convex...Ch. 11.3 - A student wonders if there exists a convex decagon...Ch. 11.3 - A student wants to know if a triangle can have two...Ch. 11.3 - In each of the following, name the required...Ch. 11.3 - Prob. 21MCCh. 11.3 - Prob. 22MCCh. 11.3 - Design symbols that have each of the following...Ch. 11.3 - Prob. 24MCCh. 11.3 - Explain whether the following quilt patterns have...Ch. 11.3 - Find the lines of symmetry, if any, for each of...Ch. 11.3 - Prob. 1NAEPCh. 11.3 - In the given figure, what is the measure of angle...Ch. 11.3 - Prob. 3NAEPCh. 11.3A - If three lines all meet in a single point, how...Ch. 11.3A - Prob. 2ACh. 11.3A - Find the measure of a complementary angle, a...Ch. 11.3A - Assessment In ABC, the measure of B is three times...Ch. 11.3A - Prob. 5ACh. 11.3A - Prob. 6ACh. 11.3A - Prob. 7ACh. 11.3A - Prob. 8ACh. 11.3A - Prob. 9ACh. 11.3A - Prob. 10ACh. 11.3A - Find the sum of the measures of the numbered...Ch. 11.3A - Prob. 12ACh. 11.3A - Prob. 13ACh. 11.3A - Prob. 14ACh. 11.3A - Prob. 15ACh. 11.3A - Prob. 16ACh. 11.3A - Prob. 17ACh. 11.3A - Find the measures of ange 1, 2, and 3 given that...Ch. 11.3A - Prob. 19ACh. 11.3A - Prob. 20ACh. 11.3A - Prob. 21ACh. 11.3A - Assessment 11-3A If m(2)=m(3), prove m(1)=m(4).Ch. 11.3B - If two planes intersect in a single line forming...Ch. 11.3B - Assessment 11-3B Find the measures of angle marked...Ch. 11.3B - Prob. 3ACh. 11.3B - Assessment 11-3B An angle measures 15 more than 4...Ch. 11.3B - Prob. 5ACh. 11.3B - Prob. 6ACh. 11.3B - Prob. 7ACh. 11.3B - In part (a), prove that kl .In parts (b)and(c),...Ch. 11.3B - Prob. 9ACh. 11.3B - Prob. 10ACh. 11.3B - Prob. 11ACh. 11.3B - Calculate the measure of each angle of a pentagon,...Ch. 11.3B - The sides of DEF are parallel to the sides of BCA....Ch. 11.3B - In each of the following figures, find the...Ch. 11.3B - Prob. 15ACh. 11.3B - Prob. 16ACh. 11.3B - Prob. 17ACh. 11.3B - Find the measure of x in the figure below.Ch. 11.3B - Prob. 19ACh. 11.3B - Prob. 20ACh. 11.3B - Given the figure shown with AXDY, find the...Ch. 11.3B - Prob. 22ACh. 11.4 - How many possible pairs of bases does a right...Ch. 11.4 - Prob. 2MCCh. 11.4 - Prob. 3MCCh. 11.4 - What is the name of a pyramid that has 9 vertices?Ch. 11.4 - Prob. 5MCCh. 11.4 - What is the minimum number of faces that intersect...Ch. 11.4 - Sketch at least 2 nets for the prism shown below.Ch. 11.4 - Prob. 11MCCh. 11.4 - Prob. 12MCCh. 11.4 - Prob. 13MCCh. 11.4 - Prob. 14MCCh. 11.4 - Prob. 15MCCh. 11.4 - Prob. 17MCCh. 11.4 - Prob. 18MCCh. 11.4 - Prob. 19MCCh. 11.4 - Find the supplement of 181342.Ch. 11.4 - Prob. 21MCCh. 11.4 - Can two adjacent angles be vertical angles?...Ch. 11.4 - How many diagonals are there in a decagon?Ch. 11.4 - In a regular 20-gon, what is the measure of each...Ch. 11.4 - If mn find m(1).Ch. 11.4 - Which of the following can be folded to form the...Ch. 11.4 - Kyle makes a 3-dimensional shape using 3...Ch. 11.4 - Prob. 3NAEPCh. 11.4 - The figure above shown a pyramid with a square...Ch. 11.4A - Identify each of the following polyhedral. If a...Ch. 11.4A - Prob. 2ACh. 11.4A - Given the tetrahedron shown, name the following....Ch. 11.4A - Prob. 4ACh. 11.4A - Prob. 5ACh. 11.4A - Prob. 6ACh. 11.4A - Classify each of the following statements as true...Ch. 11.4A - Prob. 8ACh. 11.4A - Prob. 9ACh. 11.4A - Sketch a pyramid that is hexahedron six facesCh. 11.4A - Prob. 11ACh. 11.4A - Prob. 12ACh. 11.4A - Prob. 13ACh. 11.4A - Prob. 14ACh. 11.4A - Prob. 15ACh. 11.4A - Prob. 16ACh. 11.4A - Name the intersection of each of the following...Ch. 11.4A - Prob. 18ACh. 11.4A - Prob. 19ACh. 11.4A - Prob. 20ACh. 11.4B - Identify each of the following three-dimensional...Ch. 11.4B - The following are pictures of solid cubes lying on...Ch. 11.4B - Prob. 4ACh. 11.4B - Prob. 5ACh. 11.4B - Determine the minimum number of edges possible for...Ch. 11.4B - Prob. 8ACh. 11.4B - Prob. 9ACh. 11.4B - Prob. 10ACh. 11.4B - Name the polyhedron that can be constructed using...Ch. 11.4B - Prob. 13ACh. 11.4B - Prob. 14ACh. 11.4B - Prob. 15ACh. 11.4B - On the left of each of the following figure is a...Ch. 11.4B - Prob. 17ACh. 11.4B - Prob. 18ACh. 11.4B - Answer each of the following questions about a...Ch. 11.4B - A diagonal of a prism is any segment determined by...Ch. 11.4B - A soccer ball resembles a polyhedron with 32 faces...Ch. 11.CR - Prob. 1CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - a. Can a triangle have two obtuse angles? Justify...Ch. 11.CR - In a certain triangle, the measure of one angle is...Ch. 11.CR - If ABC is a right angles triangle and m(A)=42,...Ch. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - In each of the following figures, determine the...Ch. 11.CR - Prob. 26CRCh. 11.CR - Prob. 28CRCh. 11.CR - In the figure below, ab. Find the following...Ch. 11.CR - Prob. 30CRCh. 11.CR - Carefully draw nets that can be folded into each...Ch. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11 - Just as a point separates a line into three parts,...Ch. 11 - a. Can skew lines have a point in common? Why? b....Ch. 11 - Now try this Convert 8.42 to degrees, minutes and...Ch. 11 - Prob. 6NTCh. 11 - Prob. 7NTCh. 11 - Prob. 8NTCh. 11 - Use the definitions in Table 8 and several...Ch. 11 - Prob. 11NTCh. 11 - Prob. 12NTCh. 11 - Prob. 13NT
Knowledge Booster
Similar questions
- a Does the similarity relationship have a reflexive property for triangles and polygons in general? b Is there a symmetric property for the similarity of triangles and polygons? c Is there a transitive property for the similarity of triangles and polygons?arrow_forwardMust two different points be collinear? Must three or more points be collinear? Can three or more points be collinear?arrow_forwardThree groups of triangles are given here. Each group consists of four triangles. Within each group, name the triangles-a, b, c, or d-in which the angles A are equal.arrow_forward
- Which John Conway's scheme best describes the patter? O a. spinning jump O b. jump O c. spinning sidle d. sidlearrow_forwardForming triangles from 6 distinct points in which no 3 points are collinear. Combination Permutationarrow_forwardTOPIC: Combination / Permutation. show the solutions How many triangles can be drawn on a plane using 8 noncollinear points? There are 12 Math teachers in the Math department. How many ways can one or more of them be invited to dinner? How many groups can be formed from 8 students taking at least 2 at a time?arrow_forward
- How many symmetries does a regular n-gon have? (This means an n-sided polygon, all of whose sides are equal and all of whose angles are equal.)arrow_forwardGive adequate explanationarrow_forwardProvide three examples of Frieze Pattern you encounter daily (include photo of those) and determine which symmetries are present in the examples.arrow_forward
- 2. Which situation does NOT illustrate combination? * A. assembling a jigsaw puzzle B. forming a team of 4 from 10 eligible members C. choosing three of your classmates to attend the party D. forming triangles from seven points with no three of which are collineararrow_forwardHow many triangles can be made if the vertices are from three of the six points on the circle? One such triangle is shown in the figure. Barrow_forward16. Each vertex of convex pentagon ABCDE is to be assigned a color. There are 6 colors to choose from, and the ends of cach diagonal must have different colors. How many different colorings are possible? (A) 2520 (B) 2880 (C) 3120 (D) 3250 (E) 3750arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL