Introduction to Geometry
Given any two points A and B, there is exactly one of these passing through them
What is a LINE
The distance from the center of the circle to the edge is called this
What is the radius
To dilate means this
To make smaller or larger
When this type of polygon rotates about its center, the number of times it maps back onto itself in one complete rotation is equal to the number of sides n of the polygon
What is REGULAR (Pentagon, Octagon, Etc.)
In a reflection, any point in the preimage and the corresponding point in the image are at equal this from the line of reflection.
What is distances
Consider the terms pyramid, line, square, and triangle. Which one is not a term in Euclidean Geometry?
What is a LINE
Whenever two lines intersect at an angle measuring 90 degrees the two are said to be this
What is Perpendicular
When a polygon is FLIPPED across a line, it is called this
What is a reflection
This formula can be used to find how many degrees it takes to map one vertex exactly onto the next vertex in the preimage
What is 360 degrees divided by n (# of sides in the polygon)
In a translation, all points are moved the same this from the preimage to the image
What is distance
What is construction...architecht, sculptor, designer, etc.
When two lines are parallel, the perpendicular distance between the two lines is this
What is the SAME
The original figure in any transformation
What is a Preimage
A regular polygon with n sides has this many lines of reflection
What is n (number of sides)
If the preimage ABCDE becomes MNOPQ, which vertices match up with each other?
What is A and M, B and N, C and O, D and P, and E and Q
Which Greek mathematician wrote the most definitive text on geometry (The Elements), one that is still referred to today?
Who is Euclid
An angle is formally defined as two rays that extend from a common point called this
What is a VERTEX
In contrast to dilation, this type of stretch changes the coordinate along ONE axis while keeping the coordinate along the other axis unchanged
What is Horizontal or Vertical
Through which angle of rotation does the image of a regular pentagon coincide with its preimage?
What is 72 degrees
A combination of translations, rotations, or reflections is called this
What is a sequence of transformations
Name the 4 structures of the axiomatic system.
What is undefined terms, axioms, definitions, and theorems
The relationship between a radius of a circle and a diameter is this
What is the radius is half a diameter
Polygon ABCD is defined by points A(-3, 2), B(-6, 2), C(-3, -5), and D(-6, -5). If the polygon is rotated 90 degrees clockwise (or 270 degrees counterclockwise) what is the coordinate of D'
What is (-5, 6)
If n is even, half of the lines are these type of bisectors joining the midpoints of the opposite sides and half of the lines are these type of bisectors joining the opposite vertices.
What is perpendicular and angle bisectors
Go to the board and draw the following sequences:
Start with the point (-3, 2)
Reflect over the y axis
Reflect across the line y = -x
See Mrs. Williams