DOCSLIB.ORG

Classifying Polygons Date ______

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Classifying Polygons Date ______ Name ________________________________ Classifying Polygons Date _________________________________ Form A For each polygon below, highlight or circle ALL the words that describe it mathematically. 1. 2. 3. quadrilateral hexagon quadrilateral hexagon quadrilateral hexagon triangle pentagon triangle pentagon triangle pentagon octagon decagon octagon decagon octagon decagon 4. 5. 6. quadrilateral hexagon quadrilateral trapezoid quadrilateral trapezoid triangle pentagon rectangle square rectangle square octagon decagon rhombus parallelogram rhombus parallelogram 7. 8. 9. quadrilateral trapezoid quadrilateral trapezoid quadrilateral trapezoid rectangle Preview square rectangle square rectangle square rhombus parallelogram rhombus parallelogram rhombus parallelogram 10. 11. 12. equilateral acute triangle equilateral acute triangle equilateral acute triangle scalene obtuse triangle scalene obtuse triangle scalene obtuse triangle isosceles right triangle isosceles right triangle isosceles right triangle Concept Created by Sue Maier ~ Activity by Laura Candler ~ Teaching Resources ~ www.lauracandler.com Classifying Polygons Answer Key Form A For each polygon below, highlight or circle ALL the words that describe it mathematically. 1. 2. 3. quadrilateral hexagon quadrilateral hexagon quadrilateral hexagon triangle pentagon triangle pentagon triangle pentagon octagon decagon octagon decagon octagon decagon 4. 5. 6. quadrilateral hexagon quadrilateral trapezoid quadrilateral trapezoid triangle pentagon rectangle square rectangle square octagon decagon rhombus parallelogram rhombus parallelogram 7. 8. 9. quadrilateral trapezoid quadrilateral trapezoid quadrilateral trapezoid rectangle Preview square rectangle square rectangle square rhombus parallelogram rhombus parallelogram rhombus parallelogram 10. 11. 12. equilateral acute triangle equilateral acute triangle equilateral acute triangle scalene obtuse triangle scalene obtuse triangle scalene obtuse triangle isosceles right triangle isosceles right triangle isosceles right triangle Concept Created by Sue Maier ~ Activity by Laura Candler ~ Teaching Resources ~ www.lauracandler.com Name ________________________________ Classifying Polygons Date _________________________________ Form B For each polygon below, highlight or circle ALL the words that describe it mathematically. 1. 2. 3. quadrilateral hexagon quadrilateral hexagon quadrilateral hexagon triangle pentagon triangle pentagon triangle pentagon octagon decagon octagon decagon octagon decagon 4. 5. 6. quadrilateral hexagon quadrilateral trapezoid quadrilateral trapezoid triangle pentagon rectangle square rectangle square octagon decagon rhombus parallelogram rhombus parallelogram 7. 8. 9. quadrilateral trapezoid quadrilateral trapezoid quadrilateral trapezoid rectangle Preview square rectangle square rectangle square rhombus parallelogram rhombus parallelogram rhombus parallelogram 10. 11. 12. equilateral acute triangle equilateral acute triangle equilateral acute triangle scalene obtuse triangle scalene obtuse triangle scalene obtuse triangle isosceles right triangle isosceles right triangle isosceles right triangle Concept Created by Sue Maier ~ Activity by Laura Candler ~ Teaching Resources ~ www.lauracandler.com Classifying Polygons Answer Key Form B For each polygon below, highlight or circle ALL the words that describe it mathematically. 1. 2. 3. quadrilateral hexagon quadrilateral hexagon quadrilateral hexagon triangle pentagon triangle pentagon triangle pentagon octagon decagon octagon decagon octagon decagon 4. 5. 6. quadrilateral hexagon quadrilateral trapezoid quadrilateral trapezoid triangle pentagon rectangle square rectangle square octagon decagon rhombus parallelogram rhombus parallelogram 7. 8. 9. quadrilateral trapezoid quadrilateral trapezoid quadrilateral trapezoid rectangle Preview square rectangle square rectangle square rhombus parallelogram rhombus parallelogram rhombus parallelogram 10. 11. 12. equilateral acute triangle equilateral acute triangle equilateral acute triangle scalene obtuse triangle scalene obtuse triangle scalene obtuse triangle isosceles right triangle isosceles right triangle isosceles right triangle Concept Created by Sue Maier ~ Activity by Laura Candler ~ Teaching Resources ~ www.lauracandler.com.
Load more

Recommended publications
  • How Can You Put Shapes Together to Make Other Shapes?
    Lesson 27 Understand Tiling in Rectangles Name: How can you put shapes together to make other shapes? Study the example showing how to put shapes together to make other shapes. Then solve Problems 1–4. Example How can you use smaller shapes to make a circle? Look at the shapes in the green box Draw lines to show how you could use the shapes Write how many of each shape you would need 2 4 1 Draw a line to show how you could use squares like the one in the green box to make a rectangle How many squares would you need? squares 2 Draw lines to show how you could use triangles like the one in the green box to make a rectangle How many triangles would you need? triangles ©Curriculum Associates, LLC Copying is not permitted. Lesson 27 Understand Tiling in Rectangles 283 Solve. 3 Draw lines to show how you could use hexagons to make the first shape below Then show how you could use trapezoids to make the second shape How many of each shape would you need? hexagons trapezoids 4 Draw lines to show how you could use triangles to make the first shape below Then show how you could use trapezoids to make the second shape Then show how you could use rhombuses to make the third shape How many of each shape would you need? triangles trapezoids rhombuses 284 Lesson 27 Understand Tiling in Rectangles ©Curriculum Associates, LLC Copying is not permitted. Lesson 27 Name: Draw and Count Squares Study the example showing how to draw and count squares.
    [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]
  • Quadrilateral Theorems
    Quadrilateral Theorems Properties of Quadrilaterals: If a quadrilateral is a TRAPEZOID then, 1. at least one pair of opposite sides are parallel(bases) If a quadrilateral is an ISOSCELES TRAPEZOID then, 1. At least one pair of opposite sides are parallel (bases) 2. the non-parallel sides are congruent 3. both pairs of base angles are congruent 4. diagonals are congruent If a quadrilateral is a PARALLELOGRAM then, 1. opposite sides are congruent 2. opposite sides are parallel 3. opposite angles are congruent 4. consecutive angles are supplementary 5. the diagonals bisect each other If a quadrilateral is a RECTANGLE then, 1. All properties of Parallelogram PLUS 2. All the angles are right angles 3. The diagonals are congruent If a quadrilateral is a RHOMBUS then, 1. All properties of Parallelogram PLUS 2. the diagonals bisect the vertices 3. the diagonals are perpendicular to each other 4. all four sides are congruent If a quadrilateral is a SQUARE then, 1. All properties of Parallelogram PLUS 2. All properties of Rhombus PLUS 3. All properties of Rectangle Proving a Trapezoid: If a QUADRILATERAL has at least one pair of parallel sides, then it is a trapezoid. Proving an Isosceles Trapezoid: 1st prove it’s a TRAPEZOID If a TRAPEZOID has ____(insert choice from below) ______then it is an isosceles trapezoid. 1. congruent non-parallel sides 2. congruent diagonals 3. congruent base angles Proving a Parallelogram: If a quadrilateral has ____(insert choice from below) ______then it is a parallelogram. 1. both pairs of opposite sides parallel 2. both pairs of opposite sides ≅ 3.
    [Show full text]
  • Cyclic Quadrilateral: Cyclic Quadrilateral Theorem and Properties of Cyclic Quadrilateral Theorem (For CBSE, ICSE, IAS, NET, NRA 2022)
    9/22/2021 Cyclic Quadrilateral: Cyclic Quadrilateral Theorem and Properties of Cyclic Quadrilateral Theorem- FlexiPrep FlexiPrep Cyclic Quadrilateral: Cyclic Quadrilateral Theorem and Properties of Cyclic Quadrilateral Theorem (For CBSE, ICSE, IAS, NET, NRA 2022) Get unlimited access to the best preparation resource for competitive exams : get questions, notes, tests, video lectures and more- for all subjects of your exam. A quadrilateral is a 4-sided polygon bounded by 4 finite line segments. The word ‘quadrilateral’ is composed of two Latin words, Quadric meaning ‘four’ and latus meaning ‘side’ . It is a two-dimensional figure having four sides (or edges) and four vertices. A circle is the locus of all points in a plane which are equidistant from a fixed point. If all the four vertices of a quadrilateral ABCD lie on the circumference of the circle, then ABCD is a cyclic quadrilateral. In other words, if any four points on the circumference of a circle are joined, they form vertices of a cyclic quadrilateral. It can be visualized as a quadrilateral which is inscribed in a circle, i.e.. all four vertices of the quadrilateral lie on the circumference of the circle. What is a Cyclic Quadrilateral? In the figure given below, the quadrilateral ABCD is cyclic. ©FlexiPrep. Report ©violations ＠https://tips.fbi.gov/ 1 of 5 9/22/2021 Cyclic Quadrilateral: Cyclic Quadrilateral Theorem and Properties of Cyclic Quadrilateral Theorem- FlexiPrep Let us do an activity. Take a circle and choose any 4 points on the circumference of the circle. Join these points to form a quadrilateral. Now measure the angles formed at the vertices of the cyclic quadrilateral.
    [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]
  • Properties of Equidiagonal Quadrilaterals (2014)
    Forum Geometricorum Volume 14 (2014) 129–144. FORUM GEOM ISSN 1534-1178 Properties of Equidiagonal Quadrilaterals Martin Josefsson Abstract. We prove eight necessary and sufficient conditions for a convex quadri- lateral to have congruent diagonals, and one dual connection between equidiag- onal and orthodiagonal quadrilaterals. Quadrilaterals with both congruent and perpendicular diagonals are also discussed, including a proposal for what they may be called and how to calculate their area in several ways. Finally we derive a cubic equation for calculating the lengths of the congruent diagonals. 1. Introduction One class of quadrilaterals that have received little interest in the geometrical literature are the equidiagonal quadrilaterals. They are defined to be quadrilat- erals with congruent diagonals. Three well known special cases of them are the isosceles trapezoid, the rectangle and the square, but there are other as well. Fur- thermore, there exists many equidiagonal quadrilaterals that besides congruent di- agonals have no special properties. Take any convex quadrilateral ABCD and move the vertex D along the line BD into a position D such that AC = BD. Then ABCD is an equidiagonal quadrilateral (see Figure 1). C D D A B Figure 1. An equidiagonal quadrilateral ABCD Before we begin to study equidiagonal quadrilaterals, let us define our notations. In a convex quadrilateral ABCD, the sides are labeled a = AB, b = BC, c = CD and d = DA, and the diagonals are p = AC and q = BD. We use θ for the angle between the diagonals. The line segments connecting the midpoints of opposite sides of a quadrilateral are called the bimedians and are denoted m and n, where m connects the midpoints of the sides a and c.
    [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]
  • 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]