Geometry Foundations
Angles and Measuring
Pythagorean Theorem
Distance and Midpoint
Constructions
100
What geometric object is represented below?
A ray with endpoints A and B
100
The name for two angles whose sum is 90 degrees
Complimentary
100
The name of the longest side in a right triangle
The Hypotenuse
100
Find the coordinates of the midpoint of these two points.
Midpoint = (-1, 4)
100
What is the definition of a "geometrical construction"
"To draw shapes, lines, or angles accurately"
200
How many points are Coplanar in the image below? Name them
4 (D, G, F, and H)
200
List 4 different ways to name the angle below
angleJKL, angleLKJ, angleK, angle5
200
Why are the numbers 3, 4, and 5 significant/related to the Pythagorean theorem
3, 4, and 5 represent a Pythagorean Triple
Bonus (x2) name 3 more Pythagorean triples (30 seconds)
200
Who Invented the "Generalized Midpoint Formula"
Mr. Williams
Bonus (x2) A Group member recites the formula from memory
200
Names of the three tools allowed in geometrical constructions
Compass, Straight Edge, and a Pencil
300
Name 3 Collinear Points in the figure below
DGF or IGJ
300
12^o
300
The legs of a right triangle are 10ft and 24ft. What is the length of the third side?
26ft
300
AC = 7.7
300
Which of the 6 basic construction techniques involves drawing two circles, and then drawing a line through where they overlap? (2 words)
Perpendicular Bisector
400
What does the intersection between two planes form
A line (not a segment, not a ray)
400
Given the figure below, find the measure of angle y
y = 76^o
400
Find the missing value in the right triangle below
x = 19.42
400
Find the distance between points
A(-1, 3) and B(2, -1)
distance = 5
400
List the construction steps for finding the center of a circle
1. Draw two line segments that cut through the circle
2. Find the perpendicular bisector of each segment
3. Where they cross is the center of the circle
500
Name a 4th Dimensional Object
Tesseract, Hypercube, Hyperplane, Polychoron, etc.
500
Find the value of x in the figure below
x = 45^o
500
Find the value of d in the figure below (hint: you will have to use the Pythagorean Theorem 2x)
d = 19
500
2/3 point = (0, -2)
500
Which ancient Greek mathematician wrote the book titled "Elements" and essentially founded Geometry?
Euclid