131-unknown-06fafin

131-unknown-06fafin - Math131 FINAL (MWF 12:05PM Section)...

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math131 FINAL (MWF 12:05PM Section) Fall 2006 Name 1. (Straightedge and compass construction) Find the reflection of triangle A about the given line. RN 2. By folding this page, find at most 3 lines of reflection L1, L2, . . . such that the reflection V about L1, followed by the reflection about L2, etc. has the net effect of sending triangle A to triangle B. Label all lines. 3. Apply a 90 degree counterclockwise rotation about the centerpoint z to the triangle A below, to get a triangle A’. Apply a. 90 degree counterclockwise 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 0 o O O o 0 Q o 6 0 o g 0 g g g o o o o o g o . O O O a O o o o t c. . . O U C o O . . . 5 ' . . ° 0 o ' O a 3 0 O 4 o L o o I o c , . ' l o a . ' a o a I o .0 c a o o a a q I a o v 9 .X o 0 0 o O O I O p g g , . . ' . a a y C o o o q a Y O . a g . . ' . . ‘ 6 o 0 g g . ' . C d f O I I o . . . O . 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. Tianslation Rotation Reflection Slide-flip. A 5. Reflect triangle A about-the line L1 to get a triangle A’. Reflect triangle A’ about the line L2 to get a triangle A". What single rigid motion sends A to A”? Describe this rigid motion completely. Ans 6. Consider the translation that sends triangle, A to triangle B. Draw an arrow that represents this translation. Assuming that adjacent grid points below are one centimeter apart, find the distance of this slide. 0 § 0 o o . Q . . O . ' ' I o 9 Q o g o . o o a o p o 0» O o O O t ¢ 0 o O a . g ‘ . 5 ' . 0 Q o v 0 a, 3 0 o a o o d a o c . g ' ‘ o o 0 a o u I 0 0 0 O o a 5 0 v q o u . o . , . o a n 0 a a a . I 0 y i 0 q 0 o l I u q 0 . | a 6 a Q . a . :4 C I g g . ‘ ¢ 0 p a o . Q g , 7. If a convex polyhedron has 22 edges and 10 faces then how many vertices does it have? Answer: 8. In the space below, sketch a 6—gon that is simple but not convex. In this polygon there are six vertex angles. What is the sum of the measures of these six angles? 9. In the space below, sketch a convex 6-gon that has order 3 rotational symmetry ,but no lines of refiectional symmetry. ' 10. In the space below, sketch anexample of a star polygon that has 8 vertices. 11. State the Pythagorean theorem. 12. 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. 13. Construct a golden rectangle using straight-edge and compass only. Where does the rightmost edge go? ' 14. Suppose a given regular polygon has a vertex angle with measure 170 degrees. (a) How many vertices does this polygon have? (b) What is its central angle? 10 15. Suppose n = 24. Circle the integers at below for which the star polygon exists. 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 16. How many distinct star polygons are there which have 24 vertices? ans = 17. Circle the numbers below that are Fermat primes. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 18. Can a regular 680~gon be constructed with compass and straightedge only? Explain your answer. ' 11 19. With straight—edge and compass alone, construct a regular 5-g0n. Show your work. 12 20. Which of the following vertex sequences correspond to a semi—regular tesselation? For each of the five cases below, determine if the required polygons fit perfectly around a vertex, with no overlapping or missing space. If this can be done determine if the configuration can be extended to a semi-regular tesselation. Vertex sequence Perfect fit around a vertex? Extendable? (if applicable) (4, 6, 12) Y N Y N (4, 12, 12) Y N Y N (3, 6, 3, 6) Y N Y N (3, 3, 6, 6) Y N y N (3, 4, 3, 3, 4) Y N Y N 13 21. Sketch the Schlege] diagram for the icosahedron. 14 22a. For the dodecahedron, the number of axes of rotational symmetry of order 2 is equal to and the number of planes of reflectional symmetry is equal to 22b. For the tetrahedron, the number of axes of rotational symmetry of order 3 is equal to and the number of planes of reflectional symmetry is equal to 220. For the octahedron, the number of axes of rotational symmetry of order 4 is equal to and the number of planes of reflectional symmetry is equal to 15 23. For the regular polygon below, find the measures of the given angles. 16 24. Consider an equilateral triangle with side length 4\/§ inches. Find the distance from each vertex to the circumcenter. 17 ...
View Full Document

Page1 / 17

131-unknown-06fafin - Math131 FINAL (MWF 12:05PM Section)...

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online