Accident Leg Location:india

proportionality

Likeness is the product of a homothety by a stroke. Similarity of figures


Two figures are similar if their angles are equal and corresponding sides proportional. Reason


like similar figures in 2 similarity rate is the ratio of two homologous sides. Forman

group:
1 - internal operation: the product of 2 similarities is another similarity.
2 - is associative
3 - has neutral element is the similarity or equality unit figures.
4 - It has symmetrical element is the shift from A 'to A.

Properties
1 - Reflective: every figure is like unto itself
2 - Symmetric: If a figure is similar to another, it is to the 1 st
3 - Transitive: If a figure is similar to another, and this in a 3rd, what is the 1 st to 3 rd.



triangles A and B are homothetic and B is transformed into C by turning the center M. A rotation plus a dilation, ie the product of a homothety more a movement makes A and C are similar but not homothetic (as dilation must retain the alignment of homologous points of the triangles with the center N). So ABC are all similar to each other but only A and B are homothetic.


Here we see a homothety whose center is at point A. CD segment becomes the segment C'D 'expanded its scale to 8 / 5. Similarly, the segment BC becomes the segment B'C'a the same scale, 8 / 5. The fact that the segment becomes A'D AD 'in a ratio of 8 / 5 means that the two triangles ACD and AC'D' taking one side converted to 8 / 5, the others will become as themselves as they have is in this case the parallel sides and all sides are scaled proportionally.



To transform this regular polygon violet blue in the regular polygon given side is placed on one of the rays of the center and will align the blue side of the polygon, parallel to the violet side of the polygon.
Moves so that, as in the translations, is maintained parallel to the original segment until it intersects with another ray passing through the center and the vertex of the polygon violet. At the time that the blue shifted side of the polygon cut that beam we have placed the side of the polygon in the right place to build it so that the two polygons are concentric.


Here we see a triangle that transforms wide 5 / 8 from the center c. Following the scaling procedure, we do a segment from the center of the dilation and take eight units to join the eight-rule with A and the five until we make a parallel cut to the side at point T. By it. Make a line parallel to the line TD AM. We then have the sides of the triangles are parallel or overlapping and that all points are aligned with the center of projection.


A green circle three transforms radio from its center in one of five radio violet. We say that the two are homothetic to transform itself from a center O so that concentric circles are transformed in a ratio of 5 / 3.

An exercise that can be solved by dilation, it is possible to make the largest square in the triangle, so that the bases of both are collinear. Either construct a square with a vertex incident on one side of the triangle and matched at the base with it. On the lower left corner of the triangle becomes a straight line passing through the upper right corner of the square until it intersects the side of the triangle. From this point of intersection with the side of the triangle make the sides parallel to the original square and getting the blue square, the largest dimension whose vertices touch both sides triangle whose bases coincide.