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Geometry 2.1.2 Class Exploration #13 Examine the diagrams below
... relationships when he happened to notice a pattern of parallelogram tiles on the wall of a building. Marcos saw lots of special angle relationships in this pattern, so he decided to copy the pattern into his notebook. The beginning of Marco’s diagram is shown below. This pattern is sometimes called ...
... relationships when he happened to notice a pattern of parallelogram tiles on the wall of a building. Marcos saw lots of special angle relationships in this pattern, so he decided to copy the pattern into his notebook. The beginning of Marco’s diagram is shown below. This pattern is sometimes called ...
Ratios Proportions and Geometric Means a) ratio b) simplify ratio
... 8. Two triangles are similar. The sides of the first triangle are 7, 9, and 11, the smallest side of the second triangle is 21. Find the perimeter of the second triangle. 9. Two polygons are similar. If the ratio of the perimeters is 7:4, find the ratio corresponding sides. ...
... 8. Two triangles are similar. The sides of the first triangle are 7, 9, and 11, the smallest side of the second triangle is 21. Find the perimeter of the second triangle. 9. Two polygons are similar. If the ratio of the perimeters is 7:4, find the ratio corresponding sides. ...
Geometry Statements
... passes through the other two sides, then it divides the other two sides______________. Conversely, if a line cuts two sides of a triangle proportionally, then it is ___________________to the third side. ...
... passes through the other two sides, then it divides the other two sides______________. Conversely, if a line cuts two sides of a triangle proportionally, then it is ___________________to the third side. ...
Postulate 22: Angle-Angle (AA) Similarity Postulate If two angles of
... If the corresponding side lengths of two triangles are proportional, then the triangles are similar. R A ...
... If the corresponding side lengths of two triangles are proportional, then the triangles are similar. R A ...
0035_hsm11gmtr_0904.indd
... sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation. 1. To start, look for the ways that the figure will reflect ...
... sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation. 1. To start, look for the ways that the figure will reflect ...
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many remarkable properties, most notably:It is non-periodic, which means that it lacks any translational symmetry. It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through ""inflation"" (or ""deflation"") and any finite patch from the tiling occurs infinitely many times.It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes and coverings.