04spfinv2 - Math131 FINAL Name A 1 A rotation has been...

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Unformatted text preview: Math131 FINAL Name A 1. A rotation has been performed that sends triangle A to triangle B. Find the center of the rotation (any method). Wm 2. State the Pythagorean theorem. 3. Give a proof of the Pythagorean theorem. You may use any proof you Wish. You may want to base your proof on the figure below. [0 4a. What rigid motion sends A into B? Circle the correct one. Translation Rotation Reflection Slide-flip. A 4b.What rigid motion sends A into B? Circle the correct one. Translation Rotation Reflection Slide—flip. A 5. Refer to the picture below. If we refle net effect is a rotation. ct about L1, and reflect the result about L2, the Locate the center of this rotation If we View the rotation as clockw ise, then the angle of rotation is If we View the rotation as counterclockwise, then the angle of rotation is L2 145 6. If a convex polyhedr on has 21 edges and 10 faces then how many ve 35 L1 rtices does it have? Answer: . triangle B. Label all lines. , . . ., such that the reflection ' iangle A to lden rectangle using straight—edge and compass only. IWhere does the 8. Construct a go rightmost edge go? 9. Suppose a given regular polygon has a vertex angle with ~measure 174 degrees. (a) How many vertices does this polygon have? (b) What is its central angle? 10. Suppose n m 11 12 13 14 15 16 17 18 19 2O 21 22 23 24 25 26 11. How many distinct star polygons are there which have 22 vertices? CLTLS : 12. Circle the numbers below that are Fermat primes. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 13. Can a regular 340— your answer. — 22. Circle the integers d below for which the star polygon { gon be constructed with compass and straightedge onl y? Explain 14. With straight~edge and compass alone, construct a regular S—gon. Show your work. 3 correspond to a semi—regular tesselation? For perfectly around a vertex, mine if the configuration 15. Which of the following vertex sequence each of the five cases below, determine if the required polygons fit with no overlapping or missing space. If this can be done deter can be extended to a semi-regular tesselation. Vertex sequence Perfect fit around a vertex? Extendable? (if applicable) (3,3,6,6) Y N Y N (4,12,12) Y N Y N (4,6,12) Y N Y N (3,6,3,6) Y N Y N (3,4,3,3,4) Y N Y N 16. For the polygon below, find the sum of the vertex angles. Sum is f 17. Sketch the Schlegel diagram for the icosahedron. 10 umber of axes of rotational symmetry of order 3 is equal to 18a. For the tetrahedron, the n ______’______‘———————- and the number of planes of reflectional symmetry is equal to . 18b. For the octahedron, the number of axes of rotational symmetry of order 3 is equal to and the number of planes of refiectional symmetry is equal to . 18c. For the icosahedron, the number of axes of rotational symmetry of order 2 is equal to f and the number of planes of reflectional symmetry is equal to . 19. Consider the dodecahedron. The number of faces is The number of edges is The number of vertices is What does Eulers formula say about these three quantities? 11 ge and compass alone find the circumcenter, the centroid, the or— 20. Using a straight-ed thocenter and the Euler line. Label your results. 12 21. Apply a 90 degree clockwise rotation about the centerpoint a: to the triangle A below, to get a triangle A’. Apply a 90 degree clockwise rotation about the centerpoint y to A’, to get a triangle A”. 'What single rigid motion sends A to‘A”? Describe this rigid motion completely. Ans __________________...————————-—— . a 6 0 o ' 0 n s O o u 0 ‘ 0 0 O I e I o ' 0 o o o a a o O I a v n n O I ' i‘ O 9 a Q 0 o . u u o a a e o c U o o o o u D D o o o n o . O o X Y i o 0 O a 5 o c o t o 0 O O o o . I ‘ U c I v d o . g a a b o c o o o a a 9 o . o O D I v a o ...
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04spfinv2 - Math131 FINAL Name A 1 A rotation has been...

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