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Basic Calculations
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Multistep Problems
100
Line segment RT was rotated 90 degrees CC, translated 7 units to the left, then reflected over the y-axis to produce R'T'. Are these two lines congruent? Explain how you know.
Yes RT and R'T' are congruent because rotations, translations, and reflections are all rigid motions, which preserve congruency.
100
Point A’(-4, 10) is the image of A(10, 4) under a rotation. What is the image of B(2, -9) under that same rotation?
B' (9, 2)
*Bonus 100 points: What is the name of this rotation?
100
If the sum of the interior angles of a regular polygon is 2,520°, how many sides does the polygon have?
16
BONUS 100 POINTS: What is a 6-sided figure called?
100
If the radius of the circle is 7.2 cm, what is the area of the shaded region in terms of pi?
S = 7.22 * (220/360)
S = 31.68 pi cm^2
100
Write the mapping rule for the following sequence:
rx=0 o D2 o R90
(x,y)
(-y, x)
(-2y, 2x)
(2y, 2x)
*BONUS 100 points: Name 2 transformations that would get you from the preimage to the image.
200
What are the shapes of the perpendicular cross sections of a square pyramid? (+100 each)
Triangle and Trapezoid
*BONUS 100 points: If the cross section was parallel to the base, what shape would it be?
200
Line segment BD is an angle bisector to angle ABC. If angle ABD is 36, what is the measure of angle ABC?
72
200
What is the measure of angle 4?
angle 4 = 145
200
State the equation of a circle with a center of (-2, 4) and a radius of 8 in simplest form.
(x+2)^2+(y-4)^2=64
200
Rectangle ABCD has diagonals AC and BD that interest at point E. Given the measures in the figure, what is the length of BD?
BD = 34
300
Name an pair of angles and their relationship that would prove m is parallel to n.
1 and 5, 2 and 6, 3 and 7, 4 and 8, 9 and 13, 10 and 14, 11 and 15, 12 and 16 = corresponding
1 and 7, 2 and 8, 9 and 15, 10 and 16 = alternate exterior angles
3 and 5, 4 and 6, 11 and 13, 12 and 14 = alternate interior angles
1 and 8, 2 and 7, 9 and 16, 10 and 15 = same-side exterior angles
4 and 5, 3 and 6, 11 and 14, 12 and 13 = same-side interior angles
*BONUS 100 points: If you were trying to prove a || b by corresponding angles, what is one angle pair that would satisfy this?
300
What is the equivalent value to cos(59)?
A. Sin(59)
B. Cos(31)
C. Sin(31)
D. Tan(59)
E. Tan(31)
C
300
What is the length of BC?
BC = 14
*BONUS 100 points: Is B the midpoint of the segment? Why or why not?
300
Calculate the value of x. Round to the nearest tenths place if needed.
x = 27.5
300
What shape is created by the points A (0, 4), B (4, 0), C (0, -3), and D (-4, 0)?
State the figure's name and at least two properties of the figure.
Kite
1. 2 sets of congruent sides
2. 1 set of congruent angles
400
State the triangle congruent postulate for each of the sets below. (+100 each)
a - ASA
b - SSS
c - none
d - HL
400
Triangle ABC has coordinates A(-2, -4), B(-8, -6) and C(-5, 3). What are the coordinates of C’’ when (x, y) --> (-y, x), then applying (x, y) --> (y, x)?
C" (-5, -3)
400
What is the value of the x, the altitude, in simplest radical form?
x =
9sqrt3
400
What is the length of AD?
AD = 104
400
What is the value of x?
x = 14.3
*Bonus 100 points: What kind of triangles are these?
500
Which angles are congruent to angle 7?
Angle 5, angle 3, and angle 1
*BONUS 100 points: Which angles are supplementary to angle 7?
500
A can of chicken has a volume of 100 cm3. If you triple the dimensions of the cylinder, what is the new volume?
2,700 cm3
500
Rhombus ABCD has diagonals AC and BD that intersect at E. If AC = 18, and BD = 24, what is the perimeter of the rhombus?
60
500
Given the regular pentagon, what is the value of x?
x = 11
500
What is the volume of the composite figure? Use 3.14 for pi and round to the hundredths place if needed.
V = 334.93 cm3