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__SARAI BOBSOTTI____________________________________________ Math 157 Week 5 Checkpoint Assignment -- Due Day 5 (Friday) Instructions:

how do the axes of rotatinal symmetry of an octahedron compare to the axes of rotational symmetry of a cube?
NAME:__SARAI BOBSOTTI____________________________________________  Math 157 Week 5 Checkpoint Assignment -- Due Day 5 (Friday) Instructions: In order to complete your checkpoint in an organized and efficient manner, please use this template to type your work and  answers. Save this template to your computer, complete the problems (showing all work without using a calculator), and post as an  attachment to your <Individual> forum. If you cannot read the problem on this template, refer to your eTextbook.  No work = no credit PROBLEM TYPE YOUR SOLUTIONS HERE Section 11.1 pp. 669-675 #8 In each diagram in Exercises 7–10, identify the motion or combination of motions that would produce the image. Justify your choices. Transformation such as a reflection, rotation, or a translation, there are various  techniques that can be used to find the image of the figure under the specified  transformation. In this figure you use rotation as the figure Plane of rotational  symmetry intersecting an edge and the midpoint of the edge opposite that edge.   Section 11.1 pp. 669-675 #10 In each diagram in Exercises 7–10, identify the motion or combination of motions that would produce the image. Justify your choices. Flipped images in the real world appear when you look in mirrors,  turn transparencies over on the overhead projector, or press an  inked stamp onto a piece of paper. The orientation of the figure  has changed, so it must have been reflected. But the image  doesn’t appear where it would if a mirror had been placed  between the figures. Thus it has been translated and reflected. Section 11.2 pp. 686-690 #4 A plane tessellation is a two-dimensional design or pattern made  up of one or more shapes that completely cover a surface without  any gaps or overlaps. Quadrilaterals are another type of polygon  that can tessellate. Since the sum of the interior angles of a  quadrilateral is 360 degrees and there are four sides, angles and  vertexes to a quadrilateral, each of the four angles equals ¼ of  the 360 degrees.  If you put four of the quadrilaterals together,  with one of each of the four vertexes all touching at one point, the  design will tessellate.  This method only produces a tessellation if  the quadrilateral is “rotated around the midpoint of its sides”-- there are many ways that the four vertexes can be arranged and  the pattern will not tessellate.  If the four shapes are rotated  around in a circle, the pattern will create a tessellation.  Any  quadrilateral can be used to make a tessellation. Section 11.2 pp. 686-690 #10 A tessellation is a special type of pattern that consists of  geometric figures that fit without gaps or overlaps to cover the  plane. Because it has more than six sides and will not tessellate.
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PROBLEM TYPE YOUR SOLUTIONS HERE Section 11.2 pp. 686-690 #14 Equilateral triangles, squares, and regular hexagons are the only  regular polygons that tessellate by themselves. Every triangle  and quadrilateral will tessellate. Several nonregular pentagons  and hexagons will tessellate. No convex polygon with more than  six sides will tessellate, but some nonconvex polygons with more  than six sides will tessellate. Section 11.2 pp. 686-690 #22 Because the ends of the tessellation is not equal and the squares  are not place completely adjacent or congruent. A similar method  uses only tessellating polygons with congruent adjacent sides to  make a basic figure for a curved tessellation.  Section 11.3 pp. 697-700 #4 An isosceles triangle that forms one of the points of the star, such as is called a golden triangle because the ratio of its longer side to its shorter side is the golden ratio. In both a golden triangle and a golden rectangle, the ratio of its longer side to its shorter side is the golden ratio, f = (1 + 15) 2 L 1.618. Section 11.3 pp. 697-700 #12 Star-shaped polygons have n startip points, 2 n congruent sides, n congruent point angles with measure and n congruent dent angles. They differ from star polygons in that they are simple polygons, whereas star polygons are nonsimple. No this in not a star shape polygon if it was 9 and 2 it would be a star polygon. But this has 9 triangle in two polygons that seem to overlap. Section 11.4 pp. 714-718 #8 A prism is a polyhedron with a pair of congruent faces, called  bases, that lie in parallel planes. The vertices of the bases are  joined to form the parallelogram-shaped lateral faces of the  prism. Adjacent lateral faces share a common edge called a  lateral edge. An altitude of a prism is a segment that is  perpendicular to both bases with endpoints in the planes of the  bases. Section 11.4 pp. 714-718 #16 Note: There are two parts to this problem. A. 8 B.16 Section 11.4 pp. 714-718 #40 Note: There are five parts to this problem. A. Octahedron: V=6 F = 8 E = 12 B. Lose, gain, gain C.   D.   E.
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