Download PAP Geometry Summer Assignment 2016

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! 