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Spring Final Exam Review
Name___________________________________________
6. State whether the transformation appears to be an isometry. Explain.
1. What type of quadrilateral has exactly one pair of parallel sides?
2. Isosceles trapezoid ABCD has legs AB and CD,and base BC. If
AB =4y–3, BC=3y–4, and CD=5y– 10, find the value of y.
3. One side of a kite is 6 cm less than 4 times the length of another. The
perimeter of the kite is 68 cm. Find the length of each side of the kite.
7. In the diagram, the dashed figure is the image of the solid figure.
4. For parallelogram PQRS, find the values of x and y. Then find PT, TR,
ST, and TQ. The diagram is not to scale.
a. List all pairs of corresponding sides.
b. Name the image of point D.
8. Draw the image of ABC reflected in the x-axis.
5. Give the name that best describes the parallelogram and find the
measures of the numbered angles. The diagram is not to scale.
9. Make a tessellation with the figure.
10. Use scalar multiplication to find the image vertices for a dilation
with center (0, 0) and the given scale factor. Scale Factor: 4
14. In circle O, PA and PB are tangents. (The figure is not drawn to
scale.)
a.
b.
Prove that APO BPO.
Find mBOD for mAOP = 64. Explain your reasoning.
15. In NML, NL = NM, and the perimeter is 46 cm. A, B, and C are
points of tangency to the circle. MC = 4 cm. Find NL. Explain your
reasoning. (The figure is not drawn to scale.)
11. The endpoints of AB are A(9, 4) and B(5, –4). The endpoints of its
image after a dilation are A(6, 3) and B(3, 3).
a. Explain how to find the scale factor.
b. Locate the center of dilation. Show your work.
12. The regular polygon has radius 9 m. Find each angle measure to the
nearest tenth of a degree, each linear measure to the nearest tenth of a
meter, and the square measure to the nearest square meter.
a. mAOX
b. mAOB
c. OX
d. AB
e. the perimeter
f. the area
13. Determine whether a tangent line is shown in the diagram, for AB = 7,
OB = 3.75, and AO = 8. Explain your reasoning. (The figure is not drawn
to scale.)
16. CD=42, OM=17, ON=16, CDOM, EFON (The figure is not drawn
to scale.)
a. Find the radius. If your answer is not an integer, express it in radical
form.
b. Find FN. If your answer is not an integer, express it in radical form.
c. Find EF. Express it as a decimal rounded to the nearest tenth.
17. a. Find x. (The figure is not drawn to scale.)
b. Is the triangle equilateral, isosceles, or scalene? Explain.
20. The diameter of a circle has endpoints P(–10, –8) and Q(4, 4).
a. Find the center of the circle.
b. Find the radius. If your answer is not an integer, express it in radical
form.
c. Write an equation for the circle.
21. Graph the circle with equation x  1  y  3  9 .
2
  y  3  169 models the position and
22. The equation x  5
range of the source of a radio signal.
Describe the position of the source and the range of the signals.
2
18. Given: m X = 1 5 0, WZ YZ, m Y = 9 2. Find each
measurement. (The figure is not drawn to scale.)
2
2

23. Explain how you can determine, without measuring any angles,
whether a quadrilateral is a rectangle.
a. mZ
b. m(arc WZ)
c. mW
d. m(arc WX)
19. mA = 20 and m(arc BC) = 88 (The figure is not drawn to scale.)
a.
b.
Find x.
Find y.
24. The endpoints of AB are A(0, 0) and B(6, 8).
a. Describe a transformation of AB that results in the image whose
endpoints are A’(8, 4) and B’(-2, 4).
Graph the preimage and image. Label all elements of the transformation
on your graph.
b. What are the endpoints of the image of ABafter a dilation whose
scale factor is 4/5 and whose center is A?
25. a. Find the area of a regular hexagon with sides 2 cm long. Leave
your answer in simplest radical form.
b. Use your answer from part (a) to find the area of a regular hexagon of
side length 8.
26. Use this triangle.
30. A design on the surface of a balloon is 5 cm wide when the balloon
holds 71 cm2 of air. How much air does the balloon hold when the design
is 10 cm wide? Explain the method you use to find the amount of air.
31. These two noncongruent circles intersect in exactly one point. Their
common tangent is 24 cm, and the distance between their centers is 25
cm.
a. Find the length of the hypotenuse using the special relationships for a
45- 45- 90triangle. Explain the relationships.
b. Write the exact value for sin 45as a fraction in simplest form.
c. Use the formula for the area of a triangle given SAS to find the area of
the triangle. Explain your steps.
d. Use a different method to find the area of the triangle. Explain your
steps.
27. The diameter of a basketball rim is 18 inches. A standard basketball
has a circumference of 30 inches. About how much room is there between
the ball and the rim in a shot in which the ball goes in exactly in the
center of the rim? Show your work.
a. What is the sum of the two radii?
b. Express the radius of circle B in terms of r, the radius of circle A.
c. Find the radius of circle B. Show your work.
32. Given: The circles share the same center, O, mMON = 120, and m(arc
AX) = m(arc BY) = 106.
28. Jason designed an arch made of wrought iron for the top of a mall
entrance. The 11 segments between the two concentric circles are each
1.25 m long. Find the total length of wrought iron used to make the
structure. Round the answer to the nearest meter.
a. Find mP. Show your work.
b. Find a and b. Explain your reasoning.
29. An hourglass, composed of two identical cones, is 12 cm tall. The
radius of each cone is 3 cm. If you want to fill the bottom half of the
hourglass 2/3 full of salt, how much salt will you need? Explain the
method you use to find the amount of salt.
33. For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at each
vertex?
d. What is the measure of each exterior angle.
e . Find the sum of your answers to parts b and d. Explain why this sum
makes sense.
34. Is the quadrilateral a parallelogram? Explain. The diagram is not to
scale.
35. Give a convincing argument that quadrilateral ABCD with A(–3, –4),
B(0, –2), C(6, –2), and D(3, –4) is a parallelogram.
36. Two consecutive angles of a quadrilateral are right angles, but the
quadrilateral is not a rectangle. Can the quadrilateral be a parallelogram?
Explain.
37. Can this quadrilateral be a parallelogram? Explain.
38. Can this quadrilateral be a parallelogram? Explain.
39. Do all hexagons tessellate? Explain.
40. Explain why the radius of a regular polygon is greater than the
apothem.
41. A parent group wants to double the area of a playground. The
proposed diagram shows both the width and the length of the existing
playground doubled. They ask you to comment on their proposal. What
would you say?
42. The Parent’s Club is planning to build a sandbox for the school
playground. In order to be unique, they plan to make a regular hexagon
with radius of 6 meters for the sandbox.
a. Find the area of the top of the sandbox. Draw a diagram and explain
your method for finding the area.
b. Several members of the club feel that the area of the top of the
sandbox should be about 500 square meters. What should be the radius of
the hexagon in order for the area to be 500 square meters? Explain how
you find the radius.
43. Tyler built a dollhouse for his sister as shown in the diagram below.
Find the volume of the dollhouse. Explain your method for finding the
volume.
44. Three balls are packaged in a cylindrical container as shown below.
The balls just touch the top, bottom, and sides of the cylinder. The
diameter of each ball is 13 cm.
a. What is the volume of the cylinder? Explain your method for finding
the volume.
b. What is the total volume of the three balls? Explain your method for
finding the total volume.
c. What percent of the volume of the container is occupied by the three
balls? Explain how you find the percent.
45. Katie approximated the volume and the surface area for a ball she was
using for some exercises by assuming the ball is a sphere. She was
surprised when the numerical value of the volume in cubic inches was the
same as the numerical value of the surface area in square inches. What is
the radius of the ball? Explain your method for finding the radius.
49. If ABCD is a rectangle inscribed in circle O, do both diagonals contain
the center of the circle? Explain.
Consider the pattern below. Is the pattern a net for a cube? If so,
name the letters that will appear on opposite faces.
46.
47.
48. Show that it is not possible for the lengths of the segments of two
intersecting chords to be four consecutive integers.
50. Which statement is false? Explain.
A. An equiangular polygon has all angles congruent.
B. A regular polygon is both equilateral and equiangular.
C. An equilateral polygon has all sides congruent.
D. A polygon is concave if no diagonal contains points outside the
polygon.