Name:___________________________________________________
1. Identify all examples
of coplanar lines in
each figure.
Ch 1-10 review worksheet
2. Identify all skew lines in each figure.
3. Use symbols to write the name of each
geometric figure.
5. Determine the midpoint of a line segment with
each set of given endpoints:
(8, 0) and (4, 6)
7.
Period: ____________________
Draw the centroid of the
triangle.
9. Use a protractor to draw an angle that is
supplementary to each given angle. Draw the
angle so it does not share a common side with
the given angle.
11. Solve for x.
13. Complete each statement. The write the
postulate you used.
�� = 𝑚𝑚________
𝑚𝑚______ + 𝑚𝑚𝐺𝐺𝐺𝐺
4. Translate
5
units down and 10
units to the right.
Identify the specific information, the general
information, and the conclusion for each problem
situation.
6. Mario watched 3 parades this summer. Each
parade had a fire truck lead the parade. He
concluded “A fire truck always leads a parade.”
Specific:
General:
Conclusion:
8. Draw the incenter of the
triangle.
10. Use a protractor to draw an angle that is
complementary to each given angle. Draw the
angle so it does not share a common side with
the given angle.
12. Complete each statement. The
write the postulate you used.
𝑚𝑚∠______ + 𝑚𝑚∠______ = 𝑚𝑚∠𝑀𝑀𝑀𝑀𝑀𝑀
14. Identify the property demonstrated in each
example.
15. Identify the property demonstrated in each
example.
16. Write congruence
statements for the pairs of
corresponding angles in
each figure.
17. Draw and label a diagram to illustrate each
theorem.
Alternate Exterior Angle Theorem
18. Draw and label a diagram to illustrate each
theorem.
Exterior Angle Theorem
19. Write the converse of each postulate or
theorem.
Exterior Angle Theorem:
If a transversal intersects two parallel lines, then the
exterior angles on the same side of the transversal
formed are supplementary.
20. Write the inverse of each postulate or theorem.
Exterior Angle Theorem:
If a transversal intersects two parallel lines, then the
exterior angles on the same side of the transversal
formed are supplementary.
Inverse:
Converse:
21. Given:
Prove:
, j is a transversal
Statements
22. Identify the interior angles, the
exterior angle, and the remote
interior angles of each triangle.
Interior:
Exterior:
Remote Interior:
24. Determine whether it is possible to form a
triangle using each set of segments with the
given measurements. Explain your reasoning.
4 meters, 5.1 meters, 12.5 meters
Reasons
23. Without measuring
the angles, list the
angles of each
triangle in order
from least to
greatest measure.
25. Determine the length of the
hypotenuse of each
triangle.
Write your answer as a radical
in simplest form.
26. Determine the area of the triangle.
27. Given the length of the long side of a 30-60-90
triangle, determine the lengths of the short leg
and the hypotenuse. Write your answers as
radicals in simplest form.
28. Determine the area of the triangle. Round your
answer to the nearest tenth, if necessary.
29. Use the Triangle Proportionality Theorem and
the Proportional Segments Theorem to
determine the missing value.
30. Given the image and pre-image, determine the
scale factor.
31. Given the pre-image,
scale factor of 3, and
center of dilation at
the origin, use a
compass and straight
edge to graph the
image.
32.
33.
has vertices G(0, 5), H(4, 2), and I(3,
3). What are the vertices of the image after a
dilation with a scale factor of 9 using the origin
as the center of dilation?
34. Jimmy is hitting a golf ball towards the hole.
The line from Jimmy to the hole bisects the
angle formed by the lines from Jimmy to the
oak tree and from Jimmy to the sand trap. The
oak tree is 200 yards from Jimmy, the sand
trap is 320 yards from Jimmy, and the hole is
250 yards from the sand trap. How far is the
hole from the oak tree?
35. Solve for x.
has vertices G(0, 20), H(16, 24), and
I(12, 12). What are the vertices of the image
after a dilation with a scale factor of 1/2 using
the origin as the center of dilation?
36. Two angles are complementary. One angle is
twice as big as the other angle. What is the
measure of each angle?
37. Minh wanted to measure the height of a statue.
She lined herself up with the statue’s shadow
so that the tip of her shadow met the tip of the
statue’s shadow. She marked the spot where
she was standing. Then, she measured the
distance from where she was standing to the tip
of the shadow, and from the statue to the tip of
the shadow. What is the height of the statue?
38. Reflect
over
the y-axis to form
. Verify
that
39. The vertices of triangle ABC are A (5, 3), B (2,
8), and
. Reflect the triangle over the
x-axis to form triangle
.
40. The vertices of triangle ABC are A (5, 3), B (2,
8), and
. Rotate the triangle about the
origin
counterclockwise to form triangle
.
41. List the corresponding sides and angles, using
congruence symbols, for each pair of triangles
represented by the given congruence statement.
42. Determine the angle measure or side measure
that is needed in order to prove that each set of
triangles are congruent by SAS.
43. Determine the angle measure or side measure
that is needed in order to prove that each set of
triangles are congruent by ASA.
44. Determine the angle measure or side measure
that is needed in order to prove that each set of
triangles are congruent by AAS.
In
, and
. In
, and
.
45. Mark the appropriate sides and angles to make
each congruence statement true by the
Hypotenuse-Angle Congruence Theorem.
46. Given:
bisects
, and
and
are right angles. Which theorem would be used
to show ⊿𝑅𝑅𝑅𝑅𝑅𝑅 ≅ ⊿𝑆𝑆𝑆𝑆𝑆𝑆?
47. Given that LMNO is a kite, what is the
relationship between the triangles formed by
48. The figure shown is an
isosceles trapezoid with
diagonal
?
by SSS.
. Which sides
are congruent?
49. The sum of the measures of the interior angles
of a polygon is 1080°. Determine the number
of sides for each polygon.
50. The measure of each angle of a regular polygon
is
. Calculate the number of sides for
each polygon.
51. Calculate the sum of the measures of the
exterior angles for a pentagon.
52. Identify all of the terms from the following list
that apply to each figure: quadrilateral,
parallelogram,
rectangle, square,
trapezoid, rhombus,
kite.
53. Calculate the tangent of the
indicated angle in each triangle.
Write your answers in simplest
form.
54. Use a calculator to approximate each ratio.
Round your answers to the nearest hundredth.
tan
=
cot
=
55. Solve for x.
56. Solve for x.
57. A surveyor makes the following diagram of a
hill. What is the height of the hill?
58. Calculate the cosecant of the indicated angle in
each triangle. Write your answers in simplest
form.
59. Use a calculator to approximate each ratio.
Round your answers to the nearest hundredth.
60. Solve for x.
sin 90°=
csc 60°=
61. An architect needs to use a diagonal support in
an arch. Her company drew the following
diagram. How long does the diagonal support
have to be?
62. Solve for x.
63. Solve for x.
64. The angle of elevation from a ship to a 135foot-tall lighthouse is 2°. How far is the ship
from the lighthouse?
65. Determine the measure of the
central angle
.
66. Determine the measure of the
inscribed angle
.
67. Determine the measure of
68. The measure of
is
. What is the measure of
?
the intercepted arc
.
69. Write an expression for
the measure of
70. Determine
if
71. If
, how does the
measure of
and
compare?
72. Use each diagram and the
Segment Chord Theorem to
write an equation involving the
segments of the chords.
73. If
74. Use each diagram and
the Secant Segment
Theorem to write an
equation involving the
secant segments.
is a tangent
segment and
is a
radius, what is the
measure of
?
75. In
Determine
.
.
76. Write an expression that you
can use to calculate the
length of
. You do not
need to simplify the
expression.
77. If the length of the radius is
11 centimeters, what is the
arc length of
?
78. Calculate the area of each
sector. Use 3.14 for .
Round to the nearest
hundredth, if necessary.
80. The measure of a central angle is
. The
length of the radius is 40 mm. Determine the arc
length using the formula
79.
_______
.