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Proportionality and structures (Proportionality between figures:…
Proportionality and structures
Proportionality between figures: Equality
Proportion means to compare two compositions, to calculate the ratio or the
ratio between them.
Equality is a relationship with a 1: 1 ratio. Two figures are equal when they overlap and coincide on all sides and angles, the figure matches in shape and size. When the shapes are the same length we call it congruents.
triangulation Triangulation is the division of a surface or plane polygon into a set of triangles
A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction
Any rotation is a motion of a certain space that preserves at least one point.
Proportionality between figures: Similarity and Symmetry
Reflection Symmetry is easy to see, because one half is the reflection of the other half
Symmetry A geometric object has symmetry if there is an "operation" or "transformation"
Line of Symmetry: The Line of Symmetry runs left-to-right. It is not perfect symmetry, as the image is changed a little by the lake surface
Rotational Symmetry The image is rotated (around a central point) so that it appears 2 or more times
Similarity Figures that are the same shape but not necessarily the same size are called similar figures.
How to tell if triangles are similar: AAA (angle angle angle) All three pairs of corresponding angles are the same. SSS in same proportion (side side side) All three pairs of corresponding sides are in the same proportion SAS (side angle side) Two pairs of sides in the same proportion and the included angle equal.
Similar Triangles can have shared parts Two triangles can be similar, even if they share some elements.
scale factor
Scale Factor The ratio of any two corresponding lengths in two similar geometric figures is called as Scale Factor
Representing scales The proportion between the drawing and the object can be represented by two ways as follows: a) Scale: - 1cm = 1m or 1cm=100cm or 1:100 b) Representative Fraction: - (RF) = 1/100 (less than one) i.e. the ratio between the size of the drawing and the object.
Reducing scale: When the dimensions on the drawing are smaller than the actual dimensions of the object. It is represented by the scale and RF 2. Full scale: Sometimes the actual dimensions of the object will be adopted on the drawing then in that case it is represented by the scale and RF . 3. Enlarging scale: In some cases when the objects are very small like inside parts of a wrist watch, the dimensions adopted on the drawing will be bigger than the actual dimensions of the objects then in that case it is represented by scale
Tessellations: A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.