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Scope Geometry Regular 2016-2017.xlsx
... Use coordinates to prove simple geometric theorems algebraically. Right Triangle • prove theorems about triangles, such as using triangle similarity to ...
... Use coordinates to prove simple geometric theorems algebraically. Right Triangle • prove theorems about triangles, such as using triangle similarity to ...
Example 2
... angles are equal and that all ratios of pairs of corresponding sides are equal, but with triangles, this is not necessary. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. It is however not essential to prove all 3 angles of one tr ...
... angles are equal and that all ratios of pairs of corresponding sides are equal, but with triangles, this is not necessary. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. It is however not essential to prove all 3 angles of one tr ...
Lesson 10:Areas
... To learn the formula of the area of parallelograms: rectangle, square, rhombus and rhomboid To learn the formula of the area of triangles and trapeziums. To learn the formula of the area of a regular polygon. To learn the formula of the area of a circle, of a circle sector and of an annulus. To appl ...
... To learn the formula of the area of parallelograms: rectangle, square, rhombus and rhomboid To learn the formula of the area of triangles and trapeziums. To learn the formula of the area of a regular polygon. To learn the formula of the area of a circle, of a circle sector and of an annulus. To appl ...
Investigation
... Polygons can be classified as concave and convex. Convex Polygon: A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note t ...
... Polygons can be classified as concave and convex. Convex Polygon: A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note t ...
Lesson 4.6 Isosceles
... SWBAT apply the isosceles triangle theorems and be able to identify the various points of concurrency. ...
... SWBAT apply the isosceles triangle theorems and be able to identify the various points of concurrency. ...
Triangle Tiling IV: A non-isosceles tile with a 120 degree angle
... case, involve linear algebra, elementary field theory and algebraic number theory, as well as geometrical arguments. Quite different methods are required when the sides of the tile are all integers. ...
... case, involve linear algebra, elementary field theory and algebraic number theory, as well as geometrical arguments. Quite different methods are required when the sides of the tile are all integers. ...
Tessellation
![](https://commons.wikimedia.org/wiki/Special:FilePath/Ceramic_Tile_Tessellations_in_Marrakech.jpg?width=300)
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semi-regular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called ""non-periodic"". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. In the geometry of higher dimensions, a space-filling or honeycomb is also called a tessellation of space.A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.