A. Proof:
Suppose you have a triangle with three angles: <A, <B, and <C.
Consider line AC.
If you extend this line, you create an exterior angle for a <A.
Lets call this angle <D.
Since this angle creates a straight line with <A, <D and <A are supplementa
Kelsey Baker
A. Undefined Terms
Elements: Point, Line
Relations: On
1. Proof: According to axiom 3, there exists at least 3 points, point A, B, and C. Axiom 1 states that
for any two points, there exists a line. By axiom 2, there exist at least two point
Kelsey Baker
All of the following problems are solved using the figure given in Task 3.
A. Point B is stated to be the midpoint between point A and point C, or line AC.
Point A is at (1,1). Point C is at (2,1)
Using the midpoint theorem, we can solve for
Crystal Stidman (revision 12/22/2015)
EXP Task 1 (0514)
Requirements:
(A1) Create 2 additional axioms
Axiom 1: Each game is played by two distinct teams
Axiom 2: There are at least four teams.
Axiom 3: Each team has at least three distinct players.
Axiom
Charles Aaron Anderson
Cand221
College Geometry
Task 4
A)
This transformation is a translation: (x,y)(x+2,y-4)
A(4,4) (x,y)(x+2,y-4)A(6,0)
B(3,6) (x,y)(x+2,y-4)B(5,2)
C(-2,2) (x,y)(x+2,y-4)C(0,-2)
As y=-2x-3, the reflection across y=-2x-3, we get:
A(6,0)
College Geometry (UG, C281, XGT1-0516)
Aaron Anderson
Task 3
CAND221
May 31, 2017
A) By way of Analytic Methods, we will compute the coordinates for the mid-point,
point B.
B is the mid point of the line segment joining the points A(1,1) and C(2,1).
We kn
Let ABC be a triangle as shown below. Angles a, b and c are interior with measure
greater than zero so that it is a valid Euclidean triangle. We want to prove the exterior angle
of b, d, has to be larger in value than a or c.
Here, line AB is a straight
College Geometry (UG, C281, XGT1-0516)
Aaron Anderson
Task 5
CAND221
November 21, 2016
Consider the two isometries 90 degree counterclockwise rotation, and reflection over x-axis:
The first isometry:
Given that 90 degree counterclockwise rotation is shown
College Geometry (UG, C281, XGTl-0516) Task 1
Aaron Anderson CAN D221
May 19, 2017
Consider the axiomatic system and theorem below:
Axiom 1: For any two points, there exists a line so that each of the two points is on the line.
Axiom 2: There exist at lea
In order to provide a proper counterexample we must first state the which two translations will be
performed to our isometries, in which will be defined as P and Q, below P and Q are defined and then
the translations are preformed to a single point (x,y),
Dylan Mullins
March 22, 2017
Linear Algebra Task 2
1. To prove R2 is a vector space, we must start from property 3. Therefore:
(3) Let vectors x=(a,b)
R
2
and y=(c,d)
R
2
, then:
x+ y=( a , b ) + ( c , d ) substituting the coordinate form of the vectors
A. From the given drawing, we know that point B is the midpoint of A and C. Therefore, we can
calculate the value of this point using the midpoint theorem as depicted below:
a=( 1,1 )c=(2,1)
( x b , y b ) =(
x a + x b y a+ y b
,
)
2
2
1+2 1+ 1
( x b , y b
Alyx Millward
Axiom systems
Task 1
Theorem 1- Each point is on at least 2 distinct lines.
A. The undefined terms are point and lines (elements) and on (relation).
1. Axiom 3 states the exists at least 3 distinct points, lets say X, Y and Z. Axiom 1 adds,
Alyx Millward
Axiom systems
Task 1
Theorem 1- Each point is on at least 2 distinct lines.
A. The undefined terms are point and lines (elements) and on (relation).
1. Axiom 3 states the exists at least 3 distinct points, lets say X, Y and Z. Then axiom 2 t
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supplementary information in this document was created by a newer version of
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A. Use analytic methods to compute the coordinates for point B, showing all work.
( 1+22 , 1+12 )
B=
B=( 1.5,1)
B. Use analytic methods to demonstrate that one of the following triangles is an isosceles
right triangle, showing all work:
AFG
AG =( 11 ) +
The following is a theorem of Euclidean geometry:
Euclidean angle sum theorem: The sum of the measures of the angles of a triangle is 180.
Theorem 1: An exterior angle of a triangle is greater than either of the nonadjacent interior angles of the
triangle
Axiom
Axiom
Axiom
Axiom
1:
2:
3:
4:
For any two points, there exists a line so that each of the two points is on the line.
There exist at least two points on any line.
There exist at least three distinct points.
Not all points are on the same line.
Theore
A. Use Geometers Sketchpad to graph a triangle and two transformations as described
below. You should submit a single image showing the original triangle specified in part A1
and the two transformations specified in parts A2 and A3 with all points labeled
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supplementary information in this document was created by a newer version of
Sketchpad and cann
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supplementary information in this document was created by a newer version of
Sketchpad and cannot be read. The document will open as a copy.#Some
supplementary information in this document was created by a newer version of
Sketchpad and cann
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supplementary information in this document was created by a newer version of
Sketchpad and cannot be read. The document will open as a copy.#Some
supplementary information in this document was created by a newer version of
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Alyxandra Millward
Task 2
C281
ProofWe are given the Euclidean theorem, the sum of the measures of the angles of a triangle is 180.
Let's make the 3 interior angles A, B and C. A+B+C=180.
For every interior angle there is only there is only one exterior a
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supplementary information in this document was created by a newer version of
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supplementary information in this document was created by a newer version of
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1. Proof:
2. Given: ABC
adjacent: Two angles are adjacent if they share a common vertex and common side,
and they do not overlap. Otherwise, the two angles are nonadjacent.
supplementary: Two angles are supplementary if their measures sum to 180.
exterior
Axiom 1: For any two points, there exists a line so that each of the two points is on the line.
Axiom 2: There exist at least two points on any line.
Axiom 3: There exist at least three distinct points.
Axiom 4: Not all points are on the same line.
Undefi
Stephanie Guynn
College Geometry C281
Task 1
Given Axiomatic System:
Consider the following axiomatic system below to complete the requirements for this task.
Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
A. B