DOCSLIB.ORG

Parallelogram Rhombus Nonagon Hexagon Icosagon Tetrakaidecagon Hexakaidecagon Quadrilateral Ellipse Scalene T

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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 hexagon triangle Space triangle icosagon square parallelogram decagon hexakaidecagon right heptagon tetrakaidecagon triskaidecagon triangle circle Created using www.BingoCardPrinter.com B I N G O right icosagon tetrakaidecagon hendecagon heptagon triangle isosceles hexagon hexakaidecagon circle triangle ellipse scalene Free trapezium / parallelogram dodecagon triangle Space trapezoid equilateral quadrilateral octagon decagon rhombus triangle rectangle pentadecagon triskaidecagon square nonagon Created using www.BingoCardPrinter.com B I N G O trapezium / heptagon parallelogram trapezoid square ellipse dodecagon rhombus hendecagon pentagon hexagon isosceles Free scalene quadrilateral tetrakaidecagon triangle Space triangle rectangle decagon circle icosagon pentadecagon equilateral right nonagon triskaidecagon octagon triangle triangle Created using www.BingoCardPrinter.com B I N G O right triskaidecagon hendecagon hexakaidecagon triangle ellipse rectangle pentagon equilateral nonagon triangle circle trapezium / Free parallelogram pentadecagon octagon trapezoid Space dodecagon hexagon icosagon rhombus heptagon scalene isosceles tetrakaidecagon quadrilateral triangle square triangle Created using www.BingoCardPrinter.com B I N G O isosceles rhombus hendecagon parallelogram triskaidecagon triangle equilateral rectangle icosagon tetrakaidecagon triangle ellipse Free pentadecagon nonagon hexagon circle Space right scalene hexakaidecagon dodecagon quadrilateral triangle triangle trapezium / octagon heptagon decagon pentagon trapezoid Created using www.BingoCardPrinter.com.
Load more

Recommended publications
  • Islamic Geometric Ornaments in Istanbul
    ►SKETCH 2 CONSTRUCTIONS OF REGULAR POLYGONS Regular polygons are the base elements for constructing the majority of Islamic geometric ornaments. Of course, in Islamic art there are geometric ornaments that may have different genesis, but those that can be created from regular polygons are the most frequently seen in Istanbul. We can also notice that many of the Islamic geometric ornaments can be recreated using rectangular grids like the ornament in our first example. Sometimes methods using rectangular grids are much simpler than those based or regular polygons. Therefore, we should not omit these methods. However, because methods for constructing geometric ornaments based on regular polygons are the most popular, we will spend relatively more time explor- ing them. Before, we start developing some concrete constructions it would be worthwhile to look into a few issues of a general nature. As we have no- ticed while developing construction of the ornament from the floor in the Sultan Ahmed Mosque, these constructions are not always simple, and in order to create them we need some knowledge of elementary geometry. On the other hand, computer programs for geometry or for computer graphics can give us a number of simpler ways to develop geometric fig- ures. Some of them may not require any knowledge of geometry. For ex- ample, we can create a regular polygon with any number of sides by rotat- ing a point around another point by using rotations 360/n degrees. This is a very simple task if we use a computer program and the only knowledge of geometry we need here is that the full angle is 360 degrees.
    [Show full text]
  • Square Rectangle Triangle Diamond (Rhombus) Oval Cylinder Octagon Pentagon Cone Cube Hexagon Pyramid Sphere Star Circle
    SQUARE RECTANGLE TRIANGLE DIAMOND (RHOMBUS) OVAL CYLINDER OCTAGON PENTAGON CONE CUBE HEXAGON PYRAMID SPHERE STAR CIRCLE Powered by: www.mymathtables.com Page 1 what is Rectangle? • A rectangle is a four-sided flat shape where every angle is a right angle (90°). means "right angle" and show equal sides. what is Triangle? • A triangle is a polygon with three edges and three vertices. what is Octagon? • An octagon (eight angles) is an eight-sided polygon or eight-gon. what is Hexagon? • a hexagon is a six-sided polygon or six-gon. The total of the internal angles of any hexagon is 720°. what is Pentagon? • a plane figure with five straight sides and five angles. what is Square? • a plane figure with four equal straight sides and four right angles. • every angle is a right angle (90°) means "right ang le" show equal sides. what is Rhombus? • is a flat shape with four equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel, and opposite angles are equal what is Oval? • Many distinct curves are commonly called ovals or are said to have an "oval shape". • Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse. Powered by: www.mymathtables.com Page 2 What is Cube? • Six equal square faces.tweleve edges and eight vertices • the angle between two adjacent faces is ninety. what is Sphere? • no faces,sides,vertices • All points are located at the same distance from the center. what is Cylinder? • two circular faces that are congruent and parallel • faces connected by a curved surface.
    [Show full text]
  • Geometry Honors Mid-Year Exam Terms and Definitions Blue Class 1
    Geometry Honors Mid-Year Exam Terms and Definitions Blue Class 1. Acute angle: Angle whose measure is greater than 0° and less than 90°. 2. Adjacent angles: Two angles that have a common side and a common vertex. 3. Alternate interior angles: A pair of angles in the interior of a figure formed by two lines and a transversal, lying on alternate sides of the transversal and having different vertices. 4. Altitude: Perpendicular segment from a vertex of a triangle to the opposite side or the line containing the opposite side. 5. Angle: A figure formed by two rays with a common endpoint. 6. Angle bisector: Ray that divides an angle into two congruent angles and bisects the angle. 7. Base Angles: Two angles not included in the legs of an isosceles triangle. 8. Bisect: To divide a segment or an angle into two congruent parts. 9. Coincide: To lie on top of the other. A line can coincide another line. 10. Collinear: Lying on the same line. 11. Complimentary: Two angle’s whose sum is 90°. 12. Concave Polygon: Polygon in which at least one interior angle measures more than 180° (at least one segment connecting two vertices is outside the polygon). 13. Conclusion: A result of summary of all the work that has been completed. The part of a conditional statement that occurs after the word “then”. 14. Congruent parts: Two or more parts that only have the same measure. In CPCTC, the parts of the congruent triangles are congruent. 15. Congruent triangles: Two triangles are congruent if and only if all of their corresponding parts are congruent.
    [Show full text]
  • Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur Si Muove: Biomimetic Embedding of N-Tuple Helices in Spherical Polyhedra - /
    Alternative view of segmented documents via Kairos 23 October 2017 | Draft Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra - / - Introduction Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension? Dynamic bonding patterns in n-tuple helices engendering n-fold rotating symbols Embedding the triple helix in a spherical octahedron Embedding the quadruple helix in a spherical cube Embedding the quintuple helix in a spherical dodecahedron and a Pentagramma Mirificum Embedding six-fold, eight-fold and ten-fold helices in appropriately encircled polyhedra Embedding twelve-fold, eleven-fold, nine-fold and seven-fold helices in appropriately encircled polyhedra Neglected recognition of logical patterns -- especially of opposition Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity Symbol rotation as dynamic essential to engaging with value-inversion References Introduction The contrast to the geocentric model of the solar system was framed by the Italian mathematician, physicist and philosopher Galileo Galilei (1564-1642). His much-cited phrase, " And yet it moves" (E pur si muove or Eppur si muove) was allegedly pronounced in 1633 when he was forced to recant his claims that the Earth moves around the immovable Sun rather than the converse -- known as the Galileo affair. Such a shift in perspective might usefully inspire the recognition that the stasis attributed so widely to logos and other much-valued cultural and heraldic symbols obscures the manner in which they imply a fundamental cognitive dynamic. Cultural symbols fundamental to the identity of a group might then be understood as variously moving and transforming in ways which currently elude comprehension.
    [Show full text]
  • Applying the Polygon Angle
    POLYGONS 8.1.1 – 8.1.5 After studying triangles and quadrilaterals, students now extend their study to all polygons. A polygon is a closed, two-dimensional figure made of three or more non- intersecting straight line segments connected end-to-end. Using the fact that the sum of the measures of the angles in a triangle is 180°, students learn a method to determine the sum of the measures of the interior angles of any polygon. Next they explore the sum of the measures of the exterior angles of a polygon. Finally they use the information about the angles of polygons along with their Triangle Toolkits to find the areas of regular polygons. See the Math Notes boxes in Lessons 8.1.1, 8.1.5, and 8.3.1. Example 1 4x + 7 3x + 1 x + 1 The figure at right is a hexagon. What is the sum of the measures of the interior angles of a hexagon? Explain how you know. Then write an equation and solve for x. 2x 3x – 5 5x – 4 One way to find the sum of the interior angles of the 9 hexagon is to divide the figure into triangles. There are 11 several different ways to do this, but keep in mind that we 8 are trying to add the interior angles at the vertices. One 6 12 way to divide the hexagon into triangles is to draw in all of 10 the diagonals from a single vertex, as shown at right. 7 Doing this forms four triangles, each with angle measures 5 4 3 1 summing to 180°.
    [Show full text]
  • 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]
  • Folding the Regular Nonagon
    210 Folding the Regular Nonagon Robert Geretschlager, Bundesrealgymnasium, Graz, Austria Introduction In the March 1997 of Crux [1997: 81], I presented a theoretically precise method of folding a regular heptagon from a square of paper using origami methods in an article titled \Folding the Regular Heptagon". The method was derived from results established in \Euclidean Constructions and the Geometry of Origami" [2], where it is shown that all geometric problems that can be reduced algebraically to cubic equations can be solved by elementary methods of origami. Speci cally, the corners of the regular heptagon were thought of as the solutions of the equation 7 z 1=0 in the complex plane, and this equation was then found to lead to the cubic equation 3 2 + 2 1= 0; which was then discussed using methods of origami. Finally, a concrete method of folding the regular heptagon was presented, as derived from this discussion. In this article, I present a precise method of folding the regular nonagon from a square of paper, again as derived from results established in [2]. However, as we shall see, the sequence of foldings used is quite di erent from that used for the regular heptagon. As for the heptagon, the folding method is once again presented in standard origami notation, and the mathematical section cross-referenced to the appropriate diagrams. Angle Trisection For any regular n-gon, the angle under which each side appears as seen from 2 the mid-point is . Speci cally, for n =9, the sides of a regular nonagon n 2 are seen from its mid-point under the angle .
    [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]
  • Teach the Square…And the Rectangle
    f e a t u r e Teach the square…and the rectangle eaching these two geometric needs of ancient civilizations. familiar and trusted shapes, they Tshapes is like a line from an (Some believe the square symbol- represent order and stability. old song: “You can’t have one izes civilization.) Ancient peoples Because a square has four equal without the other.” needed to measure plots of land, sides, it can also be said to sym- The square and rectangle go build structures, collect taxes, bolize the seasons (spring, sum- hand in hand—maybe not like describe constellations, and create mer, fall, winter), cardinal direc- “love and marriage” or “horse calendars, all of which required tions (north, east, south, west), and carriage,” but perhaps best numbers, shapes, and calculations. and the elements (fire, water, air, understood in terms of the other. Of the basic geometric shapes in earth). Children have undoubtedly had today’s world, the rectangle is the In nature, we see no naturally experience with the two shapes in most common. The rectangle and formed squares or rectangles. objects all around them. They its square soul-mate form the Trees, branches, and leaves, for begin learning geometric shapes structure of most buildings. As example, are uneven, rounded, in a more formal way in preschool z T and are usually expected to know gae how to make and take apart N shapes by the time they finish kindergarten. by susa oto Texas Child Care has posted two ph previous articles on teaching geo- metric shapes: Go round: Teach the circle shape in Spring 2015 and Teach the triangle in Spring 2017.
    [Show full text]
  • Petrie Schemes
    Canad. J. Math. Vol. 57 (4), 2005 pp. 844–870 Petrie Schemes Gordon Williams Abstract. Petrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Grunbaum–Dress¨ polyhedra, pos- sess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes. 1 Introduction Historically, polyhedra have been conceived of either as closed surfaces (usually topo- logical spheres) made up of planar polygons joined edge to edge or as solids enclosed by such a surface. In recent times, mathematicians have considered polyhedra to be convex polytopes, simplicial spheres, or combinatorial structures such as abstract polytopes or incidence complexes. A Petrie polygon of a polyhedron is a sequence of edges of the polyhedron where any two consecutive elements of the sequence have a vertex and face in common, but no three consecutive edges share a commonface. For the regular polyhedra, the Petrie polygons form the equatorial skew polygons. Petrie polygons may be defined analogously for polytopes as well. Petrie polygons have been very useful in the study of polyhedra and polytopes, especially regular polytopes.
    [Show full text]