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Transcript
PAP Geometry Summer Assignment 2016 Part 1: Geometry In Your World The world around us is Geometry; shapes and figures that are tangible objects and representations that work together as our surroundings. Most of the math that students have used thus far is number related, however Geometry is a different state of mind. It takes learning vocabulary and learning to logically reason through situations and properties to prove and apply the correct path to a conclusion. For this summer assignment, you will need to find representations of the Unit 1 vocabulary listed below for FIVE of the following categories: A) A building or structure B) An organic object (s) found in nature C) Food or meal D) Art E) Electronics F) Furniture G) Animals H) Used in an occupation I) Transportation J) other For each of the categories chosen, the assignment is to first collect a picture of the object or objects together. It may be taken as a photo, cut from a magazine, printed from the internet, etc, and then put together as a full project (may include but not limited to a visual collage, book, Power Point, Prezi).. Then, write a 4-5 sentence paragraph describing your example and how it relates to the Unit 1 vocabulary. Each description must use at least 5 vocabulary words from the vocabulary list. Each submission will be graded on its depth, originality, and accuracy. The vocabulary words may be repeated, however, please note that depth of the overall subject is graded. Unit 1 Vocabulary Point Line Plane Ray Line Segment Collinear Coplanar Angle Vertex Obtuse angle Right angle Straight angle Midpoint Distance Bisect Supplementary Adjacent angles Vertical angles Linear pair Perpendicular lines Acute angle Parallel lines Congruent Skew lines Complimentary Horizontal line Vertical lines Part 2: Creating an Isosceles Right Triangle During our school year, we will be reasoning through Geometric proofs. This summer, I would like for you to create an isosceles right triangle and prove the triangle is right and isosceles mathematically. To complete this summer assignment, the following must be done: I. Research: To complete this project, you will need to research the listed topics. a. Lines i. Writing equations of lines iv. Standard form ii. Slope-intercept v. Parallel lines iii. Point-slope vi. Perpendicular lines b. Triangle Properties i. Definition of a vertex iv. Distance formula v. Pythagorean Theorem vi. Triangle Sum Theorem ii. Definition of a right triangle iii. Definition of an Isosceles triangle II. Create A Triangle: Use the Cartesian coordinate grid below to lightly sketch a draft of an isosceles right triangle. This will be a draft of your final triangle. This triangle must: 1. Have an area greater than 32 units. 2. NOT include horizontal or vertical lines. 3. NOT be measured but must be calculated (ie. Distance formula or Pythagorean Theorem). y x 4. Write the Equations: Now that you have drawn your isosceles right triangle, write the equations of the lines which make up the sides. Each equation must be written in all three forms: slopeintercept, point-slope and standard form. Use the space provided to show your work/calculations for each equation. You should have a total of nine equations and the domain and range for each equation must be stated. If you need more space to show your work, please attach an additional sheet of paper. Leg #1 Leg #2 Hypotenuse Slope-Intercept Form Slope-Intercept Form Slope-Intercept Form m = _______ m = _______ m = _______ Point-Slope Form Point-Slope Form Point-Slope Form m = _______ m = _______ m = _______ Standard Form Standard Form Standard Form m = _______ m = _______ m = _______ Leg Length Leg Length Leg Length 5. Graph and Label Your Triangle: Make a final graph of your right isosceles triangle on the Cartesian grid below. Be sure to label the vertices on the graph to form ΔHIP and complete the table below using your information from Part III. y x Triangle Legs Leg #1 Equation Leg #2 Equation Hypotenuse Equation Leg Length SlopeIntercept Form Point-Slope Form Standard Form Domain Range 6. Mathematical Proof Your Way (): Now do the math to prove your isosceles triangle is truly an isosceles right triangle by proving your triangle has the following characteristics: A Triangle (Triangle Sum Theorem) An isosceles triangle A right triangle 7. Perimeter and Area: Calculate the perimeter and area of your triangle. Perimeter Area 8. Why can’t this triangle be equilateral? Congratulations…. You are done!