Unit 1: Tools of Geometry
Julian goes on a jog. His path can be modeled by the dotted blue line. If Julian stops halfway through his jog, what will be the coordinates of his stopping point? (Slide X for visual)
(4.5, 5)
The triangles in Slide X are similar. Find the value of x.
57 degrees
What is the center and radius of the circle whose equation is represented by (x-8)^2+(y+9)^2 = 36?
Center: (8, -9)
Radius: 6 units
Given a regular pentagon that is rotated about its center, find 3 angles of rotations that will map the figure onto itself.
72 degrees,
144 degrees,
216 degrees,
288 degrees,
360 degrees.
This is a Rotation
About point P (Center)
that goes counterclockwise (Direction)
90 degrees (Angle of Rotation)
Given the P(2, -3) and Q(-5, 4), find the length of PQ rounded to the nearest tenth.
5.1 units
If sin x = 12/13 and cos x = 5/13, then tan x = ?
12/13
Consider the circle on Slide X with center at point O. What is the length of arc AB to the nearest tenth of a unit?
12.6 units
In parallelogram UTAH, Ang(U) = 2x+10 and Ang(H) = ex. Find the measure of Ang(H) in degrees.
100 points to the other team that can convert this angle measurement to the nearest radian.
102 degrees.
Describe the composition of transformations that maps Tri(ABC) onto Tri(A''B''C''). (Slide X)
1) Translate Tri(ABC) 4 units down, 5 units right
2) Reflect Tri(A'B'C') over the x-axis (y=0)
What is the circumference of a circle whose area is 100pi square inches?
20pi inches
In the diagram on Slide X, Tri(ABC) ~ Tri(DEC). If AC = 12, DC = 7, DE = 5, and the perimeter of Tri(ABC) is 30 cm, what is the perimeter of Tri(DEC)?
12.5 cm
What is 135 degrees in radians? (Keep answer in terms of pi)
(3pi)/8 = (3/8)pi = 0.375pi
Given quadrilateral BRUH, what tool could I use to prove that BRUH is a rhombus and why?
150 points to the other team that can figure out the alternative strategy
Use distance formula to prove all sides are congruent
Use slope to prove diagonals are perpendicular
I translate Point A(6, 22) to Point B(2, 18). How can I express this transformation in translation notation?
T-4, 4
In the figure on Slide X, if the measure of angle Z = 2X + 28, what is the measure of angle Z?
92 degrees
Unit 2 DOUBLE POINTS: Fill out this proof (Slide X)
Statement 1: ?
Reason 1:?
Statement 2: ?
Statement 3:?
Reason 3:?
Statement 1: JK = LK; JM = LM
Reason 1: Given
Statement 2: MK = MK
Statement 3: Tri(KJM) = Tri(KLM)
Reason 3: SSS Congruency
Center: (-2, 1)
Radius: 5 units
In parallelogram FORK, Ang(F) = 3x+20 and Ang(K) = 7x. What is the measure of Ang(F)?
200 points to the other team who can convert the answer to radians
68 degrees
Describe the composition of transformations that maps Tri(ABC) onto Tri(A’'B’'C’').
1) Rotate Tri(ABC) about the center counterclockwise by 90 degrees
2) Reflect Tri(A'B'C') over the x-axis (y=0)
Which of the following is a line that is perpendicular to y=2x-7 and passes through (4, 3)?
y = -0.5x + 5
Can we conclude that these triangles are congruent? Why or why not? (Slide X)
Yes, because the vertical angles (Ang(JGH) and Ang(MGK)) are congruent so we have ASA congruence.
In the diagram of circle O on Slide Z, the area of the shaded sector is 12pi squared inches and the length of OA is 6 inches. Determine the measure of angle AOC in degrees.
(250 points if another team can present me this angle measure in radians!)
120 degrees
Consider the geometric figure ABCD on Slide Y. Make me a FULL step-by-step plan of how you would try to prove that ABCD is a parallelogram. Tell me what I need to see in the end to confirm that ABCD is a parallelogram and why.
There are 3 ways to prove this -- 250 points each to the other 2 teams that can find the alternative solutions
Proving opposite sides are parallel:
- Find and compare slopes of AB and CD
- Find and compare the AD and BC
- Both pairs of opposite sides should have the same slope
Proving opposite sides are congruent
- Find and compare the distances of AB and CD
- Find and compare the distances AD and BC
- Both pairs of opposite sides should have the same distance
Proving diagonals bisect each other:
- Find the midpoint of AC
- Find the midpoint of BD
- The midpoint should be the same for both
In your own words, how are the center point and scale factor used to perform a dilation? (Max 3 sentences)
The distance from each point on the preimage to CENTER is multiplied by the SCALE FACTOR. This new distance to the center for the image is plotted along the same line as the line created by the preimage to the center.