Trig/Math Anal - cloudfront.net
... Name_________________________ No._____ 90. In the figure below, AB is tangent to circle O at point A, secant BD intersects circle O at points C and D, mAC 70 and mCD 110 . What is mABC ? ...
... Name_________________________ No._____ 90. In the figure below, AB is tangent to circle O at point A, secant BD intersects circle O at points C and D, mAC 70 and mCD 110 . What is mABC ? ...
Definition: A triangle is the union of three segments (called its sides
... segments (called its sides), whose endpoints (called its vertices) are taken, in pairs, from a set of three noncollinear points. Thus, if the vertices of a triangle are A, B and C, then its sides are ...
... segments (called its sides), whose endpoints (called its vertices) are taken, in pairs, from a set of three noncollinear points. Thus, if the vertices of a triangle are A, B and C, then its sides are ...
What is a Triangle?
... Let ABC be a triangle. We can find the 3 angle bisectors of the triangle. By the Concurrence Theorem, the angle bisectors intersect at the incenter, labeled I, of the triangle where the distances from the sides of the triangle (called points X, Y, and Z) to the incenter are equal. Hence, the line se ...
... Let ABC be a triangle. We can find the 3 angle bisectors of the triangle. By the Concurrence Theorem, the angle bisectors intersect at the incenter, labeled I, of the triangle where the distances from the sides of the triangle (called points X, Y, and Z) to the incenter are equal. Hence, the line se ...
Algebra/Geometry Institute Summer 2006
... triangle on the second sheet. Trace the triangle so that the two copies of the triangle are now on one of the patty papers. Step 3 Continue tracing the triangles in this manner filing the paper with tessellations of equilateral triangles. What is the measure of each angle of an equilateral triangle? ...
... triangle on the second sheet. Trace the triangle so that the two copies of the triangle are now on one of the patty papers. Step 3 Continue tracing the triangles in this manner filing the paper with tessellations of equilateral triangles. What is the measure of each angle of an equilateral triangle? ...
Penrose tiling
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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.