Download Basic Geometric Measurement and Vocabulary:

Pre-Algebra Semester 2 Review (1)
Name___________________________________
Basic Geometric Measurement and Vocabulary:
1 and 2 are complementary angles. Given the measure of 1, find m2.
1.
m1 = 22
2.
m1 = 89
3 and 4 are supplementary angles. Given the measure of 3, find m4.
3.
m3 = 14
4.
m3 = 100
Use the diagram to tell whether the angles are vertical angles, a linear pair, or neither.
5.
1 and 2
6.
2 and 4
Sketch (provide) a counterexample to disprove the conjecture.
7.
The value of x2 is always greater than the value of x.
8.
Supplementary angles always form a linear pair.
Use the diagram to list all pairs of the defined angles.
9.
Vertical angles
10.
Corresponding angles
11.
Alternate Interior angles
12.
Consecutive Interior angles
13.
Alternate Exterior angles
Find the value of x. (Write an equation and show work in algebraic format!)
14.
15.
Find the value of x. (Write an equation and show work in algebraic format!)
16.
18.
17.
In the diagram, CD  FG .
Find the value of x.
19.
In the diagram, AB  BC .
Find the value of x.
Find the value of x. Then classify the triangle by its sides (scalene, isosceles or equilateral)
20.
EQ: ___________; x = _____; __________ ∆
22.
EQ: ___________; x = _____; __________ ∆
21.
EQ: ___________; x = _____; __________ ∆
23.
EQ: ___________; x = _____; __________ ∆
Formulaic Geometry:
Find the exact distance between the two points, then find the midpoint.
1.
A(2, 3) and B(5, -1)
2.
C(4, -7) and D(-8, -2)
3.
E(-1, 5) and F(3, 10)
4.
G(7, 1) and H(5, 9)
Given an endpoint and the midpoint, find the missing endpoint.
6. Endpoint: (−2, 6) and Midpoint: (11, −5)
5. Endpoint: (5, 7) and Midpoint: (3, 9)
Find the missing lengths. Give the exact value (as a radical) and then an estimate.
7.
exact: _____________ estimate: _____________
8.
exact: _____________ estimate: _____________
9. Find the area of the triangle:
Transformations:
Sketch the image of the figure after the translation.
1.
( x, y)  ( x  5, y  1)
2
( x, y)  ( x  5, y  2)
Describe the transformation, then use coordinate notation to write the rule from the pre-image (solid lines) to the
image (dashed lines).
3.
4.
(x, y )  ( ______, _______)
(x, y )  ( ______, _______)
7. Triangle ABC undergoes a translation, resulting in Triangle A’B’C. The chart below shows the coordinates for the
vertices of each triangle.
Which of the following describes the translation
depicted to the left?
A. 2 units to the right, 3 units down
B. 3 units to the right, 2 units down
C. 2 units to the left, 3 units up
D. 3 units to the left, 2 units down
8. Draw the translation of the quadrilateral MNOP three units to the left and two units up. Label your new figure with
the appropriate vertices.
Which of the following remain the same in the image?




Angle measure
Lengths of sides
Orientation
Location of any points
9. Draw the dilation of triangle JKL with a scale factor of 0.5 and label each vertex.
5. Name the coordinates of each vertex:
J
K
L
J’
K’
L’
10. Draw the dilation of quadrilateral ABCD with a scale factor of 2 and label each vertex.
Refer to the diagram at left. Are quadrilaterals ABCD and A’B’C’D’ similar or
congruent? Explain.
______________________________________________________________
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11. Draw the reflection of quadrilateral ABCD over the x-axis.
̅̅̅̅?
Which side corresponds to 𝑨𝑩
Which angle corresponds to ∠A?
12. Draw the reflection of triangle XYZ over the diagonal line y = x.
Explain how you determined the coordinate point of Y’:
______________________________________________________
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______________________________________________________
______________________________________________________
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13. Rodney reflects triangle XYZ over the y-axis. The coordinate pair for Z is (2, 5). What are the coordinates for Z’?
a. (2, -5)
b. (-2, 5)
c. (2, 5)
d. (-2, -5)
14. Write an algebraic rule for reflecting a figure over the x-axis:
(x, y) 
Draw a dilation of the polygon with the given vertices using the given scale factor k. (Use graph paper!)
15.
A(1, 2), B(3, -2), C(-1, 0)
k=2
16.
A(0, 6), B(8, 2), C(-10, -8)
k = 12
17. Stephanie transformed triangle ABC and her result is A’B’C’. Which best describes her transformation?
a. Rotation 90 degrees clockwise
b. Rotation 90 degrees counterclockwise
c. Rotation 180 degrees clockwise
d. None of the above
18. Which of the following result in congruent figures? (Choose all that apply)
A]
B]
C]
D]
E]
Rotation
Reflection
Translation
Dilation
Stretch
Similar and Congruent Figures:
1. In the diagram, ALX  GIW .
LX  __________
I  __________
A  __________
WG  __________
mA  __________
mW  __________
mI  __________
mL  __________
IW = __________
LAX  __________
In the diagram, WXYZ ~ MNOP.
2.
Find the scale factor of WXYZ to MNOP.
3.
Find the value of x.
4.
Find the value of y.
5.
Find the value of z.
6.
Find the perimeter of WXYZ.
7.
Find the perimeter of MNOP.
In the diagram, BCDE ~ WXYZ.
8.
Find the scale factor of BCDE to WXYZ.
9.
Find XY.
10.
Find YZ.
11.
Find mC.
12.
Find the perimeter of WXYZ.
Determine whether the triangles are similar. If so, write a similarity statement.
13.
14.
∆_________~ ∆__________
15
∆__________~∆__________
16.
∆__________~∆__________
∆__________~∆__________
Find the missing values in the diagram; redraw facing the same direction if needed (with labels!).
17.
18.
19.
20.
Find the missing measurements for the similar figures.
21.
22.
23.
Volume and Surface Area:
1. How do the volumes of the two cylinders compare?
2. How do the surface areas compare?
3. Find the volume of the following:
b.
3.
Find the volume of the following:
c.
4.
Find the volume of the frustrum
cone that has been ‘chopped’ off the top.
d.
5. Find the volume and surface area of the silo.
6. If the steel that forms the outer shell of the silo costs $35 per square meter, how much would it cost for the silo in
problem 5?
7. If the grain farmer decides he needs to build a silo that is twice as big (as measured by each dimension), what is the
volume of the new silo?
8. How many more times costly would it be to purchase the steel for the larger silo?
Data
1. Which measure of central tendency is most appropriate for the following situations?
a.) A storeowner kept a tally of the sizes of suits purchased in her store. Which measure of central tendency should
the storeowner use to describe the average size suit sold?
b.) A tally was made of the number of times each color of crayon was used by a kindergarten class. Which measure of
central tendency should the teacher use to determine which color is the favorite color of her class?
c.) The science test grades are posted. The class did very well. All students taking the test scored over 75.
Unfortunately, 4 students were absent for the test and the computer listed their scores as 0 until the test is taken.
Assuming that no score repeated more times than the 0's, what measure of central tendency would most likely give
the the best representation of this data?
2.
a)
b)
c)
Describe the scatterplots. Be sure to address change, direction, strength, type, and any special features.
3.
Describe the scatterplots. Be sure to address change, direction, strength, type, and any special features.
4.
5.
6. Find the mean, median and mode for the following: 15, 17, 23, 11, 9, 32, 21, 17, 2, 28
7.
Jason and Jill are two students in Mr. White’s math class. On the last five quizzes, Jason scored an 80, 90, 95, 85,
and 70. Jill scored a 70, 75, 90, 100, and 95. Find the mean and mean absolute deviation for each student. (Use
tables!)
Jason’s Mean = _______
Jill’s Mean =
________
Jason’s MAD = _______
Jill’s MAD =
________
Who has a better quiz average?
_______________
Interpret the mean absolute deviation for Jill.
Who is more consistent? How do you know?
8.
a)
b)
c)
d)
What percent of students scored at least 75% on the test?
What is the IQR?
What is the range?
Would you describe this distribution as skewed or fairly symmetric?
9. Create a box and whisker plot for the following. The number of text messages sent in a week: 39, 41, 30, 14, 45, 40,
48, 39, 40, 35
Based upon this box plot, which measure of central tendency would be most representative of the data?
10. The line plot shows the number of restaurants people went to in the past month. Use the information in the line
plot to answer the questions.
a)
b)
c)
d)
Describe the distribution of the data.
Estimate the center using the graph.
Find the mean and median from the values.
Based upon the distribution, which measure of central
tendency would be most appropriate to use with this
distribution?
11. The following dot plot shows the number of apples picked by Ralph and his cousins.
e)
f)
g)
h)
Describe the distribution of the data.
Estimate the center using the graph.
Find the mean and median from the values.
Based upon the distribution, which measure of central tendency
would be most appropriate to use with this distribution?