DOCSLIB.ORG

No Slide Title

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
No Slide Title 9.2 Polygons Copyright © 2005 Pearson Education, Inc. Polygons Polygons are names according to their number of sides. Number of Name Number of Name Sides Sides 3 Triangle 8 Octagon 4 Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Hexagon 12 Dodecagon 7 Heptagon 20 Icosagon Copyright © 2005 Pearson Education, Inc. Slide 9-2 Triangles The sum of the measures of the interior angles of an n-sided polygon is (n − 2)180°. Example: A certain brick paver is in the shape of a regular octagon. Determine the measure of an interior angle and the measure of one exterior angle. Copyright © 2005 Pearson Education, Inc. Slide 9-3 Triangles continued Determine the sum of the The measure of one interior angles. interior angle is o 1080 o o = 135 Sn=−(2)180 8 o =−(8 2)(180 ) The exterior angle is = 6(180o ) supplementary to the interior angle, so = 1080o 180°−135° = 45° Copyright © 2005 Pearson Education, Inc. Slide 9-4 Types of Triangles Copyright © 2005 Pearson Education, Inc. Slide 9-5 Similar Figures Two polygons are similar if their corresponding angles have the same measure and their corresponding sides are in proportion. 9 6 4 4 66 3 4.5 Copyright © 2005 Pearson Education, Inc. Slide 9-6 Example Catherine Johnson wants to measure the height of a lighthouse. Catherine is 5 feet tall and determines that when her shadow is 12 feet long, the shadow of the lighthouse is 75 feet long. How tall is the lighthouse? x 5 12 75 Copyright © 2005 Pearson Education, Inc. Slide 9-7 Example continued ht. lighthouse lighthouse's shadow = ht. Catherine Catherine's shadow x75 = 512 12x = 375 x = 31.25 x 5 12 75 Therefore, the lighthouse is 31.25 feet tall. Copyright © 2005 Pearson Education, Inc. Slide 9-8 Congruent Figures If corresponding sides of two similar figures are the same length, the figures are congruent. Corresponding angles of congruent figures have the same measure. Copyright © 2005 Pearson Education, Inc. Slide 9-9 Quadrilaterals Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360°. Quadrilaterals may be classified according to their characteristics. Copyright © 2005 Pearson Education, Inc. Slide 9-10 Classifications Trapezoid Parallelogram Both pairs of opposite Two sides are parallel. sides are parallel. Both pairs of opposite sides are equal in length. Copyright © 2005 Pearson Education, Inc. Slide 9-11 Classifications continued Rhombus Rectangle Both pairs of opposite sides Both pairs of opposite sides are parallel. The four sides are are parallel. Both pairs of equal in length. opposite sides are equal in length. The angles are right angles. Copyright © 2005 Pearson Education, Inc. Slide 9-12 Classifications continued Square Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles. Copyright © 2005 Pearson Education, Inc. Slide 9-13 9.3 Perimeter and Area Copyright © 2005 Pearson Education, Inc. Formulas Figure Perimeter Area Rectangle P = 2l + 2w A = lw Square P = 4s A = s2 Parallelogram P = 2b + 2w A = bh Triangle P = s + s + s 1 1 2 3 A = 2 bh P = s + s + b + b 1 Trapezoid 1 2 1 2 Ah= 2 ()b12+ b Copyright © 2005 Pearson Education, Inc. Slide 9-15 Example Marcus Sanderson needs to put a new roof on his barn. One square of roofing covers 100 ft2 and costs $32.00 per square. If one side of the barn roof measures 50 feet by 30 feet, determine a) the area of the entire roof. b) how many squares of roofing he needs. c) the cost of putting on the roof. Copyright © 2005 Pearson Education, Inc. Slide 9-16 Example continued a) The area of the roof is A = lw A = 30(50) A = 1500 ft2 1500(2 both sides of the roof) = 3000 ft2 b) Determine the number of squares area of roof 3000 ==30 area of one square 100 Copyright © 2005 Pearson Education, Inc. Slide 9-17 Example continued c) Determine the cost 30 squares × $32 per square $960 It will cost a total of $960 to roof the barn. Copyright © 2005 Pearson Education, Inc. Slide 9-18 Pythagorean Theorem Copyright © 2005 Pearson Education, Inc. Slide 9-19 Example Tomas is bringing his boat into a dock that is 12 feet above the water level. If a 38 foot rope is attached to the dock on one side and to the boat on the other side, determine the horizontal distance from the dock to the boat. 38 ft rope 12 ft Copyright © 2005 Pearson Education, Inc. Slide 9-20 Example continued abc22+= 2 1222+=b 38 3 144+=b2 1444 b2 = 1300 b2 = 1300 b ≈ 36.06 The distance is approximately 36.06 feet. Copyright © 2005 Pearson Education, Inc. Slide 9-21 Circles A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. Copyright © 2005 Pearson Education, Inc. Slide 9-22 Example Terri is installing a new circular swimming pool in her backyard. The pool has a diameter of 27 feet. How much area will the pool take up in her yard? Ar= π 2 The radius of the pool is 13.5 feet. A = π(13.5)2 The pool will take up about A = 572.54 573 square feet. Copyright © 2005 Pearson Education, Inc. Slide 9-23 Next Steps Study Examples 1,3,4 in 9.2 Study Examples 1-6 in 9.3 Do Online homework Do Online quiz once you’ve studied both sections Copyright © 2005 Pearson Education, Inc. Slide 9-24.
Load more

Recommended publications
  • Polygon Review and Puzzlers in the Above, Those Are Names to the Polygons: Fill in the Blank Parts. Names: Number of Sides
    Polygon review and puzzlers ÆReview to the classification of polygons: Is it a Polygon? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon Not a Polygon Not a Polygon (straight sides) (has a curve) (open, not closed) Regular polygons have equal length sides and equal interior angles. Polygons are named according to their number of sides. Name of Degree of Degree of triangle total angles regular angles Triangle 180 60 In the above, those are names to the polygons: Quadrilateral 360 90 fill in the blank parts. Pentagon Hexagon Heptagon 900 129 Names: number of sides: Octagon Nonagon hendecagon, 11 dodecagon, _____________ Decagon 1440 144 tetradecagon, 13 hexadecagon, 15 Do you see a pattern in the calculation of the heptadecagon, _____________ total degree of angles of the polygon? octadecagon, _____________ --- (n -2) x 180° enneadecagon, _____________ icosagon 20 pentadecagon, _____________ These summation of angles rules, also apply to the irregular polygons, try it out yourself !!! A point where two or more straight lines meet. Corner. Example: a corner of a polygon (2D) or of a polyhedron (3D) as shown. The plural of vertex is "vertices” Test them out yourself, by drawing diagonals on the polygons. Here are some fun polygon riddles; could you come up with the answer? Geometry polygon riddles I: My first is in shape and also in space; My second is in line and also in place; My third is in point and also in line; My fourth in operation but not in sign; My fifth is in angle but not in degree; My sixth is in glide but not symmetry; Geometry polygon riddles II: I am a polygon all my angles have the same measure all my five sides have the same measure, what general shape am I? Geometry polygon riddles III: I am a polygon.
    [Show full text]
  • Properties of N-Sided Regular Polygons
    PROPERTIES OF N-SIDED REGULAR POLYGONS When students are first exposed to regular polygons in middle school, they learn their properties by looking at individual examples such as the equilateral triangles(n=3), squares(n=4), and hexagons(n=6). A generalization is usually not given, although it would be straight forward to do so with just a min imum of trigonometry and algebra. It also would help students by showing how one obtains generalization in mathematics. We show here how to carry out such a generalization for regular polynomials of side length s. Our starting point is the following schematic of an n sided polygon- We see from the figure that any regular n sided polygon can be constructed by looking at n isosceles triangles whose base angles are θ=(1-2/n)(π/2) since the vertex angle of the triangle is just ψ=2π/n, when expressed in radians. The area of the grey triangle in the above figure is- 2 2 ATr=sh/2=(s/2) tan(θ)=(s/2) tan[(1-2/n)(π/2)] so that the total area of any n sided regular convex polygon will be nATr, , with s again being the side-length. With this generalized form we can construct the following table for some of the better known regular polygons- Name Number of Base Angle, Non-Dimensional 2 sides, n θ=(π/2)(1-2/n) Area, 4nATr/s =tan(θ) Triangle 3 π/6=30º 1/sqrt(3) Square 4 π/4=45º 1 Pentagon 5 3π/10=54º sqrt(15+20φ) Hexagon 6 π/3=60º sqrt(3) Octagon 8 3π/8=67.5º 1+sqrt(2) Decagon 10 2π/5=72º 10sqrt(3+4φ) Dodecagon 12 5π/12=75º 144[2+sqrt(3)] Icosagon 20 9π/20=81º 20[2φ+sqrt(3+4φ)] Here φ=[1+sqrt(5)]/2=1.618033989… is the well known Golden Ratio.
    [Show full text]
  • Formulas Involving Polygons - Lesson 7-3
    you are here > Class Notes – Chapter 7 – Lesson 7-3 Formulas Involving Polygons - Lesson 7-3 Here’s today’s warmup…don’t forget to “phone home!” B Given: BD bisects ∠PBQ PD ⊥ PB QD ⊥ QB M Prove: BD is ⊥ bis. of PQ P Q D Statements Reasons Honors Geometry Notes Today, we started by learning how polygons are classified by their number of sides...you should already know a lot of these - just make sure to memorize the ones you don't know!! Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon 12 Dodecagon 13 Tridecagon 14 Tetradecagon 15 Pentadecagon 16 Hexadecagon 17 Heptadecagon 18 Octadecagon 19 Enneadecagon 20 Icosagon n n-gon Baroody Page 2 of 6 Honors Geometry Notes Next, let’s look at the diagonals of polygons with different numbers of sides. By drawing as many diagonals as we could from one diagonal, you should be able to see a pattern...we can make n-2 triangles in a n-sided polygon. Given this information and the fact that the sum of the interior angles of a polygon is 180°, we can come up with a theorem that helps us to figure out the sum of the measures of the interior angles of any n-sided polygon! Baroody Page 3 of 6 Honors Geometry Notes Next, let’s look at exterior angles in a polygon. First, consider the exterior angles of a pentagon as shown below: Note that the sum of the exterior angles is 360°.
    [Show full text]
  • Geometric Constructions of Regular Polygons and Applications to Trigonometry Introduction
    Geometric Constructions of Regular Polygons and Applications to Trigonometry José Gilvan de Oliveira, Moacir Rosado Filho, Domingos Sávio Valério Silva Abstract: In this paper, constructions of regular pentagon and decagon, and the calculation of the main trigonometric ratios of the corresponding central angles are approached. In this way, for didactic purposes, it is intended to show the reader that it is possible to broaden the study of Trigonometry by addressing new applications and exercises, for example, with angles 18°, 36° and 72°. It is also considered constructions of other regular polygons and a relation to a construction of the regular icosahedron. Introduction The main objective of this paper is to approach regular pentagon and decagon constructions, together with the calculation of the main trigonometric ratios of the corresponding central angles. In textbooks, examples and exercises involving trigonometric ratios are usually restricted to so-called notable arcs of angles 30°, 45° and 60°. Although these angles are not the main purpose of this article, they will be addressed because the ingredients used in these cases are exactly the same as those we will use to build the regular pentagon and decagon. The difference to the construction of these last two is restricted only to the number of steps required throughout the construction process. By doing so, we intend to show the reader that it is possible to broaden the study of Trigonometry by addressing new applications and exercises, for example, with angles 18°, 36° and 72°. The ingredients used in the text are those found in Plane Geometry and are very few, restricted to intersections of lines and circumferences, properties of triangles, and Pythagorean Theorem.
    [Show full text]
  • Parallelogram Rhombus Nonagon Hexagon Icosagon Tetrakaidecagon Hexakaidecagon Quadrilateral Ellipse Scalene T
    Call List parallelogram rhombus nonagon hexagon icosagon tetrakaidecagon hexakaidecagon quadrilateral ellipse scalene triangle square rectangle hendecagon pentagon dodecagon decagon trapezium / trapezoid right triangle equilateral triangle circle octagon heptagon isosceles triangle pentadecagon triskaidecagon Created using www.BingoCardPrinter.com B I N G O parallelogram tetrakaidecagon square dodecagon circle rhombus hexakaidecagon rectangle decagon octagon Free trapezium / nonagon quadrilateral heptagon Space trapezoid right isosceles hexagon hendecagon ellipse triangle triangle scalene equilateral icosagon pentagon pentadecagon triangle triangle Created using www.BingoCardPrinter.com B I N G O pentagon rectangle pentadecagon triskaidecagon hexakaidecagon equilateral scalene nonagon parallelogram circle triangle triangle isosceles Free trapezium / octagon triangle Space square trapezoid ellipse heptagon rhombus tetrakaidecagon icosagon right decagon hendecagon dodecagon hexagon triangle Created using www.BingoCardPrinter.com B I N G O right decagon triskaidecagon hendecagon dodecagon triangle trapezium / scalene pentagon square trapezoid triangle circle Free tetrakaidecagon octagon quadrilateral ellipse Space isosceles parallelogram hexagon hexakaidecagon nonagon triangle equilateral pentadecagon rectangle icosagon heptagon triangle Created using www.BingoCardPrinter.com B I N G O equilateral trapezium / pentagon pentadecagon dodecagon triangle trapezoid rectangle rhombus quadrilateral nonagon octagon isosceles Free scalene hendecagon
    [Show full text]
  • From One Polygon to Another: a Distinctive Feature of Some Ottoman Minarets
    Bernard Parzysz Research Université d’Orléans (France) From One Polygon to Another: Laboratoire André-Revuz Université Paris-Diderot A Distinctive Feature of Some 22 avenue du Général Leclerc Ottoman Minarets 92260 Fontenay-aux-Roses FRANCE Abstract. This article is a geometer’s reflection on a specificity [email protected] presented by some Turkish minarets erected during the Ottoman period which gives them a recognisable appearance. Keywords: Ottoman The intermediate zone (pabuç) between the shaft and the architecture, minarets, base of these minarets, which has both a functional and an polyhedra, Turkish triangles aesthetic function, is also an answer to the problem of connecting two prismatic solids having an unequal number of lateral sides (namely, two different multiples of 4). In the present case this connection was achieved by creating a polyhedron, the lateral sides of which are triangles placed head to tail. The multiple variables of the problem allowed the Ottoman architects to produce various solutions. 1 Introduction Each religion developed specific places for worship: synagogues, temples, churches, mosques, and so forth, and the rites and ceremonies for which they were designed conditioned their architecture. Mosques are associated with Islam, and are most certainly perceived throughout the world as its most typical monuments. They accompanied very early the history of this religion, but one of their most emblematic features, the minaret, did not appear immediately and when they did, specificities occurred depending on the period and geographic and cultural area they were built in. As Auguste Choisy writes in his Histoire de l’architecture: “Minarets have their own geography, just as steeples have theirs”.
    [Show full text]
  • Wythoffian Skeletal Polyhedra
    Wythoffian Skeletal Polyhedra by Abigail Williams B.S. in Mathematics, Bates College M.S. in Mathematics, Northeastern University A dissertation submitted to The Faculty of the College of Science of Northeastern University in partial fulfillment of the requirements for the degree of Doctor of Philosophy April 14, 2015 Dissertation directed by Egon Schulte Professor of Mathematics Dedication I would like to dedicate this dissertation to my Meme. She has always been my loudest cheerleader and has supported me in all that I have done. Thank you, Meme. ii Abstract of Dissertation Wythoff's construction can be used to generate new polyhedra from the symmetry groups of the regular polyhedra. In this dissertation we examine all polyhedra that can be generated through this construction from the 48 regular polyhedra. We also examine when the construction produces uniform polyhedra and then discuss other methods for finding uniform polyhedra. iii Acknowledgements I would like to start by thanking Professor Schulte for all of the guidance he has provided me over the last few years. He has given me interesting articles to read, provided invaluable commentary on this thesis, had many helpful and insightful discussions with me about my work, and invited me to wonderful conferences. I truly cannot thank him enough for all of his help. I am also very thankful to my committee members for their time and attention. Additionally, I want to thank my family and friends who, for years, have supported me and pretended to care everytime I start talking about math. Finally, I want to thank my husband, Keith.
    [Show full text]
  • Handling Handles. Part II. Stratification and Data Analysis
    Handling Handles. Part II. Stratification and Data Analysis T. Bargheera,b,c, J. Caetanod, T. Fleuryd,e, S. Komatsuf , P. Vieirag,h aInstitut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany bDESY Theory Group, DESY Hamburg, Notkestraße 85, D-22603 Hamburg, Germany cKavli Institute for Theoretical Physics, University of California Santa Barbara, CA 93106, USA dLaboratoire de Physique Théorique de l’École Normale Supérieure de Paris, CNRS, ENS & PSL Research University, UPMC & Sorbonne Universités, 75005 Paris, France. eInternational Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario, Lagoa Nova, Natal-RN 59078-970, Brazil f School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA gPerimeter Institute for Theoretical Physics, 31 Caroline St N Waterloo, Ontario N2L 2Y5, Canada hInstituto de Física Teórica, UNESP - Univ. Estadual Paulista, ICTP South American Institute for Fundamental Research, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP, Brasil [email protected], [email protected], [email protected], [email protected], [email protected] Abstract In a previous work [1], we proposed an integrability setup for computing non-planar corrections to correlation functions in N = 4 super Yang– Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over arXiv:1809.09145v2 [hep-th] 4 Jun 2019 graphs can be interpreted as a quantization of the string moduli space integration.
    [Show full text]
  • REVIEW—Polygons This Is the Worksheet We Were Doing During the Basketball Tournaments
    REVIEW—Polygons This is the worksheet we were doing during the basketball tournaments. YES or NO: Is each of these shapes a polygon? 7. YES or NO: Is the polygon at right ____________a. equilateral ____________b. equiangular ____________c. regular 8. YES or NO: Is the polygon at right ____________a. equilateral ____________b. equiangular ____________c. regular 9. YES or NO: Is the polygon at right ____________a. equilateral ____________b. equiangular ____________c. regular 10. YES or NO: Is the polygon at right ____________a. equilateral ____________b. equiangular ____________c. regular 11. ____________12. What is the sum of the angles in a nonagon? ____________13. What is the sum of the angles in a 22-gon? ____________14. What is the sum of the angles in a hexagon? ____________15. What is the sum of the angles in a 53-gon? Find the measure of one interior angle of each of these regular polygons. ____________16. ____________17. ____________18. ____________19. A regular 15-gon ____________22. A regular dodecagon ____________20. A regular 60-gon ____________23. A regular triangle ____________21. A regular quadrilateral ____________24. A regular triangle Find the missing angles. ____________25. ____________27. ____________26. ____________28. Find the measure of an exterior angle of each of these regular polygons. ____________29. Regular hexagon ____________33. Regular quadrilateral ____________30. Regular hectogon (100-gon) ____________34. Regular octagon ____________31. Regular pentagon ____________35. Regular 182-gon ____________32. Regular icosagon (20-gon) Regular polygons are shown in the pictures below. Find the values of the angles shown. 36. 37. 38. x = ____________ n = ____________ a = ____________ y = ____________ b = ____________ Match the pictures below to the most specific name for each shape. A.
    [Show full text]
  • Applied Mathematics, Fourth Edition II Contents
    Applied Mathematics FOURTH EDITION For MATH 104B at the College of Southern Nevada Written by Jim Matovina and Ronald Yates, with input and assistance from several members of the CSN Math Department. APPLIED MATHEMATICS FOURTH EDITION Jim Matovina Math Professor College of Southern Nevada [email protected] Ronald Yates, PhD Math Professor College of Southern Nevada [email protected] Copyright 2011-2021 by Jim Matovina and Ronald Yates, All Rights Reserved Version 1: April 13, 2020 Version 2: September 1, 2020 Version 3: July 18, 2021 Contents I TABLE OF CONTENTS PREFACE VII MATH 104B COURSE DESCRIPTION & OUTCOMES VII COURSE DESCRIPTION VII COURSE OUTCOMES VII TO THE INSTRUCTOR VII TO THE STUDENT VIII NEW TO THE FOURTH EDITION VIII ACKNOWLEDGEMENTS IX CHAPTER 1: ARITHMETIC & PREALGEBRA 1 CHAPTER OUTLINE AND OBJECTIVES 1 1.1: ROUNDING, DECIMALS & ORDER OF OPERATIONS 2 PLACE VALUES 2 ESTIMATION VS. ROUNDING 3 ESTIMATION 3 ROUNDING 3 DON’T GET TRAPPED MEMORIZING INSTRUCTIONS 5 WHEN TO ROUND AND WHEN NOT TO ROUND 6 ADDING AND SUBTRACTING DECIMALS 7 MULTIPLYING DECIMALS 7 DIVIDING DECIMALS 7 ORDER OF OPERATIONS 8 ROUND ONLY AS THE LAST STEP 11 USING YOUR CALCULATOR 11 SECTION 1.1 EXERCISES 13 SECTION 1.1 EXERCISE SOLUTIONS 17 1.2: BINARY & HEXADECIMAL NUMBERS 19 BINARY NUMBERS 19 CONVERTING BINARY NUMBERS TO DECIMAL NUMBERS 19 CONVERTING DECIMAL NUMBERS TO BINARY NUMBERS 21 HEXADECIMAL NUMBERS 23 CONVERTING HEXADECIMAL NUMBERS TO DECIMAL NUMBERS 23 CONVERTING DECIMALS NUMBERS TO HEXADECIMAL NUMBERS 24 USING YOUR CALCULATOR 25 SECTION
    [Show full text]
  • Summary of Introductory Geometry Terminology
    MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary Section 11-1: Basic Notions Undefined Terms: Point; Line; Plane Collinear Points: points that lie on the same line Between[-ness]: exactly what the term implies with regard to points [Line] Segment: part of a line consisting of (and named by) two endpoints and all points between them Closed Segment: segment with two included endpoints Half-Open Segment: segment with one included endpoint (also called Half-Closed Segment) Open Segment: segment with no included endpoints Ray: part of a line consisting of one endpoint, a second unique point on the line, all points between them, and all points that have the aforementioned second point between them and the endpoint Half-Line: part of a line on one side of a point on the line (does not include the point) Coplanar: lying on the same plane (points, lines, or parts of lines) Noncoplanar: not coplanar Intersecting Lines: lines with exactly one point in common Skew Lines: lines that cannot be contained in a single plane Concurrent Lines: three or more lines that intersect in the same point Coinciding Lines: identical lines; lines intersecting at every point Parallel Lines: either: a) nonintersecting coplanar lines; or b) two lines that are actually the same line (any line is parallel to itself; coinciding lines as defined above); symbol is Intersecting Planes: planes with exactly one line in common Coinciding Planes: identical planes; planes intersecting at every line Parallel Planes: either: a) nonintersecting planes; or b) two planes that are actually the same plane (any plane is parallel to itself; coinciding planes as defined above) Parallel Line and Plane: a line and plane that either: a) do not intersect in any point; or b) intersect in every point on the line Half-Plane: part of a plane on one side of a line in the plane (does not include the line) Prof.
    [Show full text]
  • Chapter Nine Geometry
    CHAPTER NINE GEOMETRY Exercise Set 9.1 1. a) Undefined terms, definitions, postulates (axioms), and theorems b) First, Euclid introduced undefined terms. Second, he introduced certain definitions. Third, he stated primitive propositions called postulates (axioms) about the undefined terms and definitions. Fourth, he proved, using deductive reasoning, other propositions called theorems. 2. An axiom (postulate) is a statement that is accepted as being true on the basis of its "obviousness" and its relation to the physical world. A theorem is a statement that has been proven using undefined terms, definitions, and axioms. 3. Two lines in the same plane that do not intersect are parallel lines. 4. Two lines that do not lie in the same plane and do not intersect are called skewed lines. 5. Two angles in the same plane are adjacent angles when they have a common vertex and a common side but no common interior points. 6. Two angles the sum of whose measure is 180° are called supplementary angles. 7. Two angles the sum of whose measure is 90° are called complementary angles. 8. An angle whose measure is 180° is a straight angle. 9. An angle whose measure is greater than 90° but less than 180° is an obtuse angle. 10. An angle whose measure is less than 90° is an acute angle. 11. An angle whose measure is 90° is a right angle. 12. In the pair of intersecting lines below, ( 1 and ( 3 are vertical angles as are ( 2 and ( 4. 2 1 3 4 JJJG 13. Half line, 14. Half open line 15.
    [Show full text]