Geometry Summer Packet Level 3 Geometry Teachers OVERVIEW This packet is a representation of the type of work and thinking that will be used by High School Geometry students at Columbia High School. The conclusions and answers that students come up with are going to be used to complete chapter 1 of the Geometry course. Students will be expected to take and pass a test on the conclusions and the answers to the questions asked in this packet. If there are problems in completing the packet, the math department is going to have teachers available to answer questions. Materials needed to do this summer packet: Students will need access to a protractor, a compass, a straightedge, tracing paper, and a calculator. Directions: Answer the questions on a separate piece of paper. You will submit your answers during the first week of school. It can be beneficial to compare answers with your classmates and engage in discussion, if you know anyone taking the course, please consult them. When you are asked to do any of the investigations on patty paper, please use tracing paper.
Symbols for marking diagrams: : Congruent: same size. : Perpendicular: intersect to form right angles [use the same number of slashes] : Parallel [use the same number of arrows] [use a box to indicate a right ( ) angle] 1) Define each term and create a diagram to accompany the definition. point line plane collinear coplanar line segment endpoint congruent segments midpoint When reading a diagram there are certain things that can and cannot be assumed: Things you may assume: 1. You may assume that lines are straight, and if two lines intersect, they intersect at one point. 2. You may assume that points on a line are collinear and that all points shown in a diagram are coplanar unless planes are drawn to show that they are noncoplanar. Things you may not assume: 1.You may not assume that just because two lines or segments look parallel that they are parallel they must be marked parallel! 2. You may not assume that two lines are perpendicular just because they look perpendicular they must be marked perpendicular! 3. Pairs of angles, segments, or polygons are not necessarily congruent unless they are marked with information that tells you they must be congruent!
An angle is formed by two rays that share an endpoint. The angle is named by using a point on one ray, the shared endpoint, and a point on the other ray. 2. Diagram 3. Answer each question below.
4. Write a definition for each bold faced word. Be sure to look at differences between what are and what are not.
5. Write a definition for each bold faced word. Be sure to look at differences between what are and what are not. Right Triangle
Polygons Not Polygons 6. A polygon, like a square or a triangle, has a specific definition in Geometry. Write a precise definition for the term polygon. Polygons are named according to the number of sides or angles that they possess. Number of Sides/Angles Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon or Septagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon or Hendecagon 12 Dodecagon 13 Tridecagon or Triskaidecagon N N-gon
7. Write a definition for the special polygons. Be sure to look at differences between what are and what are not.
8. Write a definition for the special quadrilaterals. Be sure to look at differences between what are and what are not. a zoid
9. The circle is another geometric figure with a very specific definition. Write a definition for.
10. Write a definition for the bold faced words, which are parts of circles. Be sure to look at differences between what are and what are not. 10. Can a chord also be a diameter? Explain. 11. Can a chord also be a tangent? Explain. 12. Can 2 circles be tangent to the same line at the same point? Draw a diagram to illustrate.
Nets - a 2 dimensional pattern that you can cut and fold to make a geometric figure. 13. 14. Solids
15. Draw a diagram to determine if each statement below is true or false. a. For any 2 points there is exactly one line that can be drawn through them. b. If 2 lines are perpendicular to the same line in the same plane then the 2 lines are parallel. c. If 2 lines in the same plane do not intersect, then they are parallel. 16. In addition to reading a problem carefully, it is often beneficial to use diagrams to solve a problem. For each of the problems, make an appropriate diagram, chart, or table in order to help you arrive at the correct answer. 17. In the city of Rectangulus, all the streets running east-west are numbered and those streets running northsouth are lettered. The even-numbered streets are one-way east and the odd-numbered streets are one-way west. All the vowel-lettered avenues are one-way north and the rest are two-way. Can a car traveling south on S street make a legal left turn onto 14 th Street?
18. Midway through a 200-meter race, a photo is taken of five runners. It shows Meg 20 meters behind Edith. Edith is 50 meters ahead of Wanda, who is 20 meters behind Olivia. Olivia is 40 meters behind Nadine. Who is ahead? 19. Mary Ann is building a fence around the outer edge of a rectangular garden plot that measures 25 feet by 45 feet. She will set posts 5 feet apart. How many posts will she need? 20. Freddie the Frog is at the bottom of a 30-foot well. Each day he jumps up 3 feet, but then, during the night, he slides back down 2 feet. How many days will it take Freddie to get to the top and out? 21. A 30-foot cable is suspended between the tops of two 20-foor poles on level ground. The lowest point of the cable is 5 feet above the ground. What is the distance between the two poles? 22. Volumes 1 and 2 of a two-volume set of math books sit next to each other on a shelf. They sit in their proper order: Volume 1 on the left and Volume 2 on the right. Each front and back cover is 0.125 inches thick and the pages portion of each book is 1 inch thick. If a bookworm starts at page one of Volume 1 and burrows all the way through to the last page of Volume 2, how far will it travel?