What are the essential characteristics that define two shapes as being similar?
Same shape and proportional size (Also accept congruent angles and proportional lengths or equivalent)
100
What are the two fundamental pieces of information needed to define a rotation?
Center of rotation and angle of rotation.
100
Trigonometric ratios are typically applied to what type of triangles?
Right triangles
100
How many total degrees are contained in a complete rotation around a circle?
360 degrees
100
Suppose that a circle is divided into 6 arcs of equal length. How many degrees will be spanned in a single arc?
60 degrees
200
What term is used to define the number that describes the level of magnification (shrinking or enlarging) between two similar figures?
Scale factor
200
List all the angles of rotation, up to 360 degrees, that are angles of rotational symmetry for a square.
90, 180, 270, and 360 degrees.
200
What are the three primary trigonometric ratios?
Sine, Cosine, Tangent
200
An angle that is formed by two radii that meet at the center is known as what?
Central angle
200
A single arc of a circle spans 72 degrees. What fraction of the circle's circumference will be spanned in that arc?
1/5 of the circumference
300
Suppose segments AB and CD are similar such that AB is 4 units long, and CD is 5 units long. What is the scale factor that takes AB to CD?
5/4 (or 1.25)
300
What general formula will allow you to find the base angle of rotational symmetry for a regular polygon with N number of sides?
360/n
300
Refer to the image provided on the board to answer the question:
What is the sine value of Angle A?
sinA = 4/5
300
An angle that is formed by connecting any three points that lie on a circle is known as what?
Inscribed angle
300
Describe the relationship that exists between the length of an arc of a circle compared to the degrees of the circle spanned within that arc.
The ratio of the arc to the circumference of the circle is the same as the ratio of the degrees spanned out of 360.
400
Describe as best you can in words the process of finding the center of dilation between a pre-image and image figure.
Draw lines connecting each pre-image point to its image point; the point where each of those lines coincides defines the center of dilation.
400
Given a Triangle ABC and its rotated image, Triangle A'B'C', describe in general the process for finding the center of rotation that maps Triangle ABC to Triangle A'B'C'.
Connect each pre-image point to its image point with a line segment. Find the perpendicular bisectors of each line segment. The point where those bisectors coincide is your center of rotation.
400
Refer to the image on the board to answer this question: What is the length of Segment BC?
5 units
400
State the primary theorems that show the relationships between central or inscribed angles and their intercepted arcs.
Central: measure of central angle = measure of inscribed arc
Inscribed: measure of inscribed angle = half of measure of inscribed arc
400
A circle with circumference of 60 units is divided into equal arcs such that the central angle of any given arc is 30 degrees. Find the entire perimeter of a single arc sector in this case.
43 units
500
Given Triangle ABC with A(4,0); B(8,2); and C(6, 6); find the coordinates of Triangle A'B'C' if Triangle ABC is dilated by a scale factor of 1/2 centered at the origin.
A(2,0); B(4,1); C(3,3)
500
Given Point A(2,4) and A'(10,8), find at least three possible centers of rotation that could map Point A to Point A'.
Any points that fall on the line y=-2x+18 will work
500
Refer to the picture on the board to answer the question:
Find all missing sides and angles of the figure.
AB = 6 units, Angle A = 53 degrees, Angle C = 37 degrees
500
Refer to the diagram on the board to answer the question:
Find the measures of all central/inscribed angles and related intercepted arcs.
Measure of Angle BCD = 120 degrees
Measure of Angle BAD = 60 degrees
Measure of Arc AD = 120 degrees
Measure of Arc AB = 120 degrees
500
A circle with a radius of 5 units is partitioned into equal segments, each of which spans 36 degrees. Find the area of a single arc sector of the circle.