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DEFINITION: TILES AND TILING13.3 DEFINITION: TILES AND TILING A simple closed curve, together with its interior, is a tile. A set of tiles forms a tiling of a figure if the figure is completely covered by the tiles without overlapping any interior points of the tiles. In a tiling of a figure, there can be no gaps between tiles. Tilings are also known as tessellations. Copyright © 2008 Pearson Education, Inc.
TILING WITH REGULAR POLYGONS13.3 TILING WITH REGULAR POLYGONS Any arrangement of nonoverlapping polygonal tiles surrounding a common vertex is called a vertex figure. Equilateral triangles form a regular tiling because the measures of the interior angles meeting at a vertex figure add to 360. Copyright © 2008 Pearson Education, Inc.
TILING WITH EQUILATERAL TRIANGLES13.3 TILING WITH EQUILATERAL TRIANGLES One interior angle of an equilateral triangle has measure 60. At a vertex angle: Copyright © 2008 Pearson Education, Inc.
One interior angle of a square has measure 90.13.3 TILING WITH SQUARES One interior angle of a square has measure 90. At a vertex angle: Copyright © 2008 Pearson Education, Inc.
TILING WITH REGULAR HEXAGONS13.3 TILING WITH REGULAR HEXAGONS One interior angle of a regular hexagon has measure At a vertex angle: Copyright © 2008 Pearson Education, Inc.
TILING WITH REGULAR PENTAGONS?13.3 TILING WITH REGULAR PENTAGONS? One interior angle of a regular pentagon has measure At a vertex angle: Copyright © 2008 Pearson Education, Inc.
THE REGULAR TILINGS OF THE PLANE13.3 THE REGULAR TILINGS OF THE PLANE There are exactly three regular tilings of the plane: by equilateral triangles, by squares, and by regular hexagons. Copyright © 2008 Pearson Education, Inc.
TILING THE PLANE WITH CONGRUENT POLYGONAL TILES13.3 TILING THE PLANE WITH CONGRUENT POLYGONAL TILES The plane can be tiled by: any triangular tile; any quadrilateral tile, convex or not; certain pentagonal tiles (for example, those with two parallel sides); certain hexagonal tiles (for example, those with two opposite parallel sides of the same length). Copyright © 2008 Pearson Education, Inc.
SEMIREGULAR TILINGS OF THE PLANE13.3 SEMIREGULAR TILINGS OF THE PLANE An edge-to-edge tiling of the plane with more than one type of regular polygon and with identical vertex figures is called a semiregular tiling. Copyright © 2008 Pearson Education, Inc.
ITS GRID OF PARALLELOGRAMS13.3 TILINGS OF ESCHER TYPE Dutch artist Escher created a large number of artistic tilings. ESCHER’S BIRDS ITS GRID OF PARALLELOGRAMS Copyright © 2008 Pearson Education, Inc.
MODIFYING A REGULAR HEXAGON WITH ROTATIONS13.3 TILINGS OF ESCHER TYPE MODIFYING A REGULAR HEXAGON WITH ROTATIONS CREATES: Copyright © 2008 Pearson Education, Inc.
Transformations, Symmetries, and Tilings 11.1 Rigid Motions and Similarity Transformations 11.2 Patterns and Symmetries 11.3 Tilings and Escher-like Designs.
Here are the eight semi-regular tessellations:
Lesson 10-4: Tessellation 1 Tessellations Lesson 10-4 Images from ygons/regular.1.html
Tessellations 1 G.10b Images from ygons/regular.1.html
Tessellations 5.9 Pre-Algebra.
Chapter Congruence and Similarity with Transformations 13 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Tessellations *Regular polygon: all sides are the same length (equilateral) and all angles have the same measure (equiangular)
Pre-Algebra 5-9 Tessellations 5-9 Tessellations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Lesson 10-4: Tessellation 1 Tessellations Lesson 10-4.
A tessellation (or tiling) is a special type of pattern that consists of geometric figures that fit without gaps or overlaps to cover the plane.
Geometry 5 Level 1. Interior angles in a triangle.
10.3 Polygons, Perimeters, and Tessalatiolns. Polygon- -Any closed shape in the plane formed by three or more line segments that intersect only at their.
Tessellations. What is a Tessellation? A tessellation is a tiling, kind of like the floor, except it goes on forever. There must be no overlapping.
7-9 Tessellations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
CHAPTER 24 Polygons. Polygon Names A POLYGON is a shape made up of only STRAIGHT LINES.
TESSELLATIONS A Tessellation (or Tiling) is a repeating pattern of figures that covers a plane without any gaps or overlaps.
© T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not.
Chapter 20: Tilings Lesson Plan
Geometry Review. What is a six sided polygon called?
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.
6.1 Polygons 6.2 Properties of Parallelograms Essential Question: How would you describe a polygon?
Tessellations with Regular Polygons. Many regular polygons or combinations of regular polygons appear in nature and architecture. Floor Designs
Tessellations. Patterns covering the plane by fitting together replicas of the same basic shape have been created by Nature and Man either by accident.
Tessellations 12-6 Warm Up Lesson Presentation Lesson Quiz
Are patterns of shapes that fit together without any gaps Way to tile a floor that goes on forever Puzzles are irregular tessellations Artists.
Polygons Lesson What is a polygon? A polygon is a simple, closed, two-dimensional figure formed by three or more line segments (sides). Closed?
Tessellations Warm Up Lesson Presentation Lesson Quiz
Polygons and Area (Chapter 10). Polygons (10.1) polygon = a closed figure convex polygon = a polygon such that no line containing a side goes through.
G Stevenson What Are Tessellations? Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping.
Holt Geometry 12-6 Tessellations 12-6 Tessellations Holt Geometry Make a Thinking Map Make a Thinking Map to summarize this presentation to summarize this.
© 2010 Pearson Education, Inc. All rights reserved Motion Geometry and Tessellations Chapter 14.
10-7: Tessellations T ESSELLATION : A tiled pattern formed by repeating figures to fill a plane without gaps or overlaps. Regular Tessellation: When a.
Using Transformations to Create Fantastic Tessellations! Dr. Maria Mitchell 1.
TESSELLATIONS Oleh : Sulistyana SMP N 1 Wonosari.
Plane figure A two dimensional figure. Chapter 10.
Chapter Introductory Geometry 11 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Students will name two dimensional figures (9-4).
1. Prove that the sum of the interior angles of a polygon of n sides is 180 (n – 2). § 8.1 C B E D P F A Note that a polygon of n sides may be dissected.
A tessellation or a tiling is a way to cover a floor with shapes so that there is no overlapping or gaps. Tessellation Remember the last jigsaw puzzle.
POLYGONS & QUADRILATERALS. POLYGON A polygon is a flat, closed plane figure made up of three or more line segments. polygons Not polygons.
Becca Stockford Lehman. Tessellate: to form or arrange small squares or blocks in a checkered or mosaic pattern Tessellate: to form or arrange small squares.
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A tessellation or a tiling is a way to cover a floor with shapes so that there is no overlapping or gaps. Tessellations Remember the last jigsaw puzzle.
Classifications Bowen’s Class. Quadrilateral Any four sided polygon Any four sided polygon.
§8.1 Polygons The student will learn: the definition of polygons, 1 The terms associated with polygons, and how to tessellate a surface.
All about Shapes Ask Boffin!.
Two - Dimensional Shapes
Let’s review our shapes….
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