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NORTH THURSTON PUBLIC SCHOOLS
END OF COURSE
GEOMETRY
PRACTICE TEST
** Video Tutorial Edition**
Most questions below are linked to a video tutorial on the internet. To access a video, hold the
control button while clicking on the link of the video you wish to watch.
Name: _________________________________________________
Date: __________________________________________________
Day 1
1. Determine the value of x if ΔABC is equilateral.
Write your answer on the line.
(Related Tutorial Video: Video 1)
2. Write the converse of the conditional statement. Determine if the converse is true or false. If it is false,
find a counterexample.
If you have a dog, then you are a pet owner.
0 A. If you are a pet owner, then you have a dog. True
0 B. A dog owner owns a pet. True
0 C. If you are a pet owner, then you have a dog. False, you could have a hamster.
0 D. If you have a dog, then you are a pet owner. False, you could have a hamster.
(Related Tutorial Video: Video 1)
3. Given a║b, determine which equation must be true.
0 A. m 1 + m 5 = 180---No,
0 B. m 3 + m 6 = 180---No
0 C. m 2 + m 7 = 180---No
0 D. m 4 + m 6 = 180---Yes, same side interior angles are supplementary!
(Related Tutorial Videos: Video 1, Video 2, Video 3)
Day 2
4. Determine measure of angle 2.
Write your answer on the line.
(Related Tutorial Videos: Video 1, Video 2)
B
6x + 3 7.5x
10x – 5 A C
What is the value of x? ______2_________
1 2 3 4
5 6
7 8
a
b
70°
1 2 60°
40°
3 4
What is the measure of angle 2? ______50°_________degrees
Equilateral means all three sides are congruent, so
one possible equation might be:
Original Statement: If P, then Q
Converse Statement: If Q, then P
5. ΔDEF has vertices D(4, 1), E(2, –1), and F(–2, –1). Classify ΔDEF based on its sides.
0 A. equilateral
0 B. isosceles
0 C. scalene
0 D. right
(Related Tutorial Videos: Video 1, Video 2)
6. Determine the equation of a line through the point (3, –4) that is perpendicular to the line y = 3x + 7.
0 A. y = 3x – 13
0 B. y = –3x + 5
0 C. y = 3
1 x – 3
0 D. y = 3
1 x – 5
(Related Tutorial Videos: Video 1, Video 2)
Day 3
7. Joe and Sara were standing on a pier sailing a toy sail boat. The boat was 6 feet from the base of the pier
and the pier was 4 feet above the water.
Determine the angle of depression from the pier to the toy sail boat.
Show your work using words, numbers and/or diagrams.
(Related Tutorial Video: Video 1, Video 2, Video 3)
O A
B T
4 ft
6 ft
What is the angle of depression from the pier to the sail boat?______33.7°________degrees
Work---see addendum
at end of answer key!
Perpendicular to y=3x + 7 means the slope of my line will be
the opposite reciprocal of 3, which is
So….the equation is:
Ɵ
4ft
8. Joanna’s teacher said “The diagonals of a square bisect each other.”
Joanna drew this figure and said “The diagonals of this figure bisect each other, so it must be a square.”
Joanna made an error in her mathematical argument. What is the error?
0 A. There is no error. The figure Joanna drew is a square.
0 B. In the figure Joanna drew, the diagonals do not bisect each other.
0 C. Joanna used the converse of the teacher’s statement and the converse is false.
0 D. Joanna’s teachers statement is false. The diagonals of a square do not bisect each other.
(Related Tutorial Video: Video 1)
9. Determine the midpoint of JK , where J(–1, 2) and K(6, 8).
0 A. (2
13 , 5)
0 B. (2
12 , 5)
0 C. (2
13 , 3)
0 D. (2
12 , 3)
(Related Tutorial Videos: Video 1, Video 2)
The vertical diagonal is not bisected. Bisecting a
line segment means the segment is separated into
two congruent pieces.
Midpoint Formula:
Midpoint:
Midpoint:
Midpoint:
Day 4
10. Look at the diagram.
What theorem or postulate can you use to prove ?
0 A. Corresponding Parts of Congruent Triangles are Congruent
0 B. Side-Angle-Side Congruence
0 C. Angle-Side-Angle Congruence
0 D. Side-Side-Side Congruence
(Related Tutorial Video: Video 1, Video 2, Video 3)
11. Three vertices of a square have coordinates (3, 1), (4, -4) and (-1, -5). The diagonals of the square intersect
at point Q.
Determine the coordinates of point Q.
You may use the blank grid to help determine the solution.
Write your answer on the line.
What are the coordinates of point Q? ( __1___ , __-2___ )
(Related Tutorial Videos: Video 1, Video 2
L
J
K M
N
L
(Vertical angles are congruent)
Since the diagonals of a square bisect
each other, point Q will be the midpoint
of either of the diagonals. Find the
midpoint of the line segment joining
points
12. 3, 5, 7, and 11 are prime numbers. 4, 6, 8, 9, and 10 are composite numbers. Tiana makes the conjecture
that prime numbers must be odd.
Which statement is true?
0 A. This is an example of inductive reasoning and the conjecture is valid.
0 B. This is an example of inductive reasoning and the conjecture is not valid.
0 C. This is an example of deductive reasoning and the conjecture is valid.
0 D. This is an example of deductive reasoning and the conjecture is not valid.
(Related Tutorial Videos: Video 1, Video 2, Video 3)
Day 5
13. One leg of a triangle is 8 cm long.
Determine the length of the hypotenuse.
0 A.
0 B.
0 C.
0 D.
(Related Tutorial Videos: Video 1, Video 2)
14. Look at the conditional statement.
“If an angle measures 30 , then it is acute”
Which statement is the converse?
0 A. If an angle does not measure 30 , then it is not acute.
0 B. If an angle is not acute, then it does not measure 30 .
0 C. If an angle is acute, then it measures 30 .
0 D. If an angle measures 30 , then it is not acute.
(Related Tutorial Video: See question 2)
15. Which equation represents the line through the points (-1, -2) and (2, 7)?
0 A. y = 3x + 1
0 B. y – 2 = 3(x – 1)
0 C. y – 7 = -3(x – 2)
0 D. x – 3y = 5
(Related Tutorial Videos: Video 1, Video 2, Video 3)
2 is a prime number which
is even
So…
Original Statement: If P, then Q
Converse Statement: If Q, then P
Slope:
Day 6
16. Which statement is true about all parallelograms?
0 A. The diagonals bisect pairs of opposite angles.
0 B. The diagonals are congruent.
0 C. The diagonals bisect each other.
0 D. The diagonals are perpendicular
(Related Tutorial Video: Video 1)
17. Quadrilateral ABCD is a rhombus and m∠BCE = 50 .
Determine the m∠EBC.
Write your answer on the line.
What is the m∠EBC? ____40_____
(Related Tutorial Videos: Video 1, Video 2 )
18. Look at the conditional statement.
“If a figure is a pentagon, then it has five sides”
Which statement is the inverse?
0 A. If a figure has five sides, then it is a pentagon.
0 B. If a figure is a pentagon, then it does not have five sides.
0 C. If a figure does not have five sides, then it is not a pentagon.
0 D. If a figure is not a pentagon, then it does not have five sides.
(Related Tutorial Videos: Video 1, Video 2)
A
D
B
C
E
The diagonals of a rhombus are perpendicular
bisectors of each other, so
Original Statement: If P, then Q
Inverse Statement: If NOT P, then
NOT Q
Day 7
19. Triangle JKE is an obtuse isosceles triangle with m∠E = 10 and .
What is the m∠J ?
0 A. 170
0 B. 160
0 C. 85
0 D. 10
(Related Tutorial Videos: Video 1, Video 2)
20. A proof is shown.
Fill in the blanks for steps 5 and 6 to complete the proof.
Given: B is the midpoint of .
B is the midpoint of .
Prove: .
Statements Reasons
1. B is the midpoint of . 1. Given
2. 2. Definition of midpoint
3. B is the midpoint of . 3. Given
4. 4. Definition of midpoint
5. m<ABD m<CBE 5. Vertical Angles Theorem
6. 6. Side-Angle-Side Congruency
21. Which ordered pair is the midpoint of the line segment with endpoints (2,-5) and (-6, 4)?
0 A. (-4, -1)
0 B.
0 C.
0 D. (-2, -1)
(Related Tutorial Video: See question 9)
A
D
C
B
E
∆JKE is isosceles, which means two of the angles
are congruent. The fact that means
that the angle opposite is larger than the angle
opposite (or angle J is larger than angle E).
Since angle J is bigger than E and the triangle is
isosceles, then angle K must measure 10° (a
triangle can’t have two obtuse angles) giving us
the equation:
10°
K
J E
Midpoint Formula:
Midpoint:
Midpoint:
Day 8
22. The diagonal of a square is 7 cm.
Determine the length of one side of the square.
0 A.
0 B.
0 C.
0 D.
(Related Tutorial Videos: Video 1, Video 2, Video 3)
23. Which statement is true?
0 A. A postulate is accepted as true without proof.
0 B. A theorem is accepted as true without proof.
0 C. Definitions can never be used as reasons in a proof.
0 D. Theorems can never be used as reasons in a proof.
(Related Tutorial Video: Video 1)
24. Two unique planes intersect. Which geometric term describes the intersection?
0 A. line
0 B. plane
0 C. point
0 D. segment
(Related Tutorial Video: Video 1
7 cm
The diagonal of a square creates an isosceles triangle (or a
45°-45°-90° triangle) with the following side ratios:
Since the hypotenuse of the triangle (or the diagonal of the
square) is 7, we can write the following equation:
If we divide each side of the equation by , we get:
Mathematical conventions do not allow us to have a radical
(square root sign) in the denominator of a fraction. We
rationalize the fraction by multiplying by
, which looks
like:
X
X
A plane is like a never-ending sheet of paper. To visualize two planes
intersecting, hold the edges of two sheets of paper together. They
intersect in an infinite arrangement of points in a straight line
Day 9
25. Look at the diagram.
Determine the values for a and b that would make the quadrilateral a parallelogram.
0 A. a = 13.5, b = 166.5
0 B. a = 16.7, b = 93.2
0 C. a = 13.5, b = 106
0 D. a = 16.7, b = 86.8
(Related Tutorial Video: See question 16)
26. Look at the triangle.
Determine the length of y. Express your answer in simplified radical form.
Write your answer on the line.
What is the length of y?
(Related Tutorial Video: Video 1)
27. Lines l, m, and n lie in the same plane. Line m is perpendicular to line l. Line n is perpendicular to line l.
Which statement is true?
0 A. Line m and line n are perpendicular.
0 B. Line m and line n are parallel.
0 C. Line m and line n will intersect.
0 D. Line m and line n are skew
5 y
18
13
Opposite angles in a parallelogram are
congruent. Therefore,
Consecutive angles in a parallelogram are
supplementary (add up to 180°). Therefore,
Work---see addendum at
end of answer key!
Line l
Line m
Line n
Day 10
28. While walking around Seattle, Mary climbed several steep streets. One of the steepest
streets, Roy Street has a slope angle of 11.9° according to the tour guide. After walking
100 feet up the hill, she wanted to determine how high she had climbed.
Use a trigonometric ratio (sine, cosine, tangent) to determine how high Mary climbed.
Be sure to write the equation and show the steps you used to solve the equation. Round your answer to the
nearest foot.
(Related Tutorial Videos: See question 7, Video 1)
29. Determine how many miles a person will run during a 5-kilometer race. Write your answer on the line.
1 km ≈ 0.62 mi
(Related Tutorial Videos: Video 1, Video 2)
30. Which statement is an example of inductive reasoning?
0 A. M is a midpoint of AB. Therefore AM = MB.
0 B. Squares have equal sides. This figure has equal sides, therefore this figure is a square.
0 C. The base angles of an isosceles triangle are equal. The base angles of this triangle are equal.
Therefore, this triangle is isosceles.
0 D. Triangular numbers have a pattern. 1, 3, 6, 10, and 15 are triangular numbers. Therefore, the next
triangular number is 21.
(Related Tutorial Videos: See question 12)
100 feet 11.9° Height climbed
Horizontal distance
How high did Mary climb?
How many miles will a person run during a 5-kilometer race?
Inductive Reasoning: Based on observation and
predictions.
Day 11
31. The rhombus QRST is made of two congruent triangles. Given mQRS = 34° determine the measure of
S.
What is the measure of S?
0 A. 56°
0 B. 73°
0 C. 112°
0 D. 146°
(Related Tutorial Videos: Video 1)
32. Determine whether the conjecture is true or false. Give a counterexample for a false conjecture.
Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar
(Related Tutorial Video: Video 1)
33. Identify the congruent triangles in the diagram and write a congruence statement.
0 A. Δ LSM Δ KSN
0 B. Δ LSK Δ MSN
0 C. Δ LKS Δ MSN
0 D. Δ LSK Δ NSM
(Related Tutorial Video: Video 1)
T
Q R
S
True or false? False
L M
N K
S
Rhombus means 4 equal sides, so triangle TSR
mush be isosceles. Diagonal TR bisects angle QRS,
so angle TRS measures 17°.
Since , (both angles are
17°)
Coplanar means all fitting on the same plane (imagine an endless sheet of paper). Any 4 points do not
necessarily have to be in the same plane. Consider the 4 points that make up the vertices of a cube----these 4
points do not all lie in the same plane.
Although Choices B, C, and D all name the same two triangles, the
order in choices C and D are wrong. Corresponding sides must match
up in naming congruent triangles ( so the LS in naming
∆LSK must be in the same position as the MS in naming ∆MSN)
Day 12
34. Determine cos I in ΔGHI.
0 A. 72
21
0 B. 75
21
0 C. 72
75
0 D. 75
72
(Related Tutorial Video: Video 1)
35. Write the contrapositive of the conditional statement. Determine if the contrapositive is true or false. If it
is false, find a counterexample.
“Two angles measuring 180 degrees are supplementary”
0 A. Two angles not measuring 180 degrees are supplementary. True
0 B. More than two angles measuring 180 degrees are non-supplementary. True
0 C. Non-supplementary angles are not two angles measuring 180 degrees. True
0 D. Non-supplementary angles are two angles measuring 180 degrees. False; supplementary angles
must measure 180 degree.
(Related Tutorial Videos: See question 18)
36. Complete this chart.
Figure # of edges
e
# of faces
f
# of vertices
v
f + v
Triangular Pyramid 6 4 4 8
Triangular Prism 9 5 6 9
Square Pyramid 8 5 5 10
Cube 12 6 8 14
Hexagonal Pyramid 12 7 7 14
Hexagonal Prism 18 8 12 20
(Related Tutorial Videos: Video 1, Pyramid Definition, Prism Definition)
H
G
21
72 I
75
Original Statement: If P, then Q
Contrapositive: If not Q, then not P
Day 13
37. Determine which statement is a property of all rectangles.
0 A. Four congruent sides.
0 B. Diagonals bisect the angles.
0 C. Diagonals are perpendicular.
0 D. Four right angles.
(Related Tutorial Video: Video 1, Video 2)
38. The figure is a rectangular prism with dimensions 12 inches long, 5 inches wide and 7 inches tall.
Determine the length of BI .
Write your answer on the line.
(Related Tutorial Video: Video 1)
39. Given B(–4, –6), determine which reflection would result in B’(6, 4).
0 A. Reflected over the x-axis.
0 B. Reflected over the y-axis.
0 C. Reflected over the line y = –x.
0 D. Reflected over the line y = x.
(Related Tutorial Video: Video 1)
Day 14
40. Determine the exact length of x in ΔHJK.
0 A. 25
0 B. 35
0 C. 10
0 D. 15
(Related Tutorial Videos: Video 1, Video 2)
A
B C
D
F
G H
I 5
12
7
What is the length of BI ?__________________
60°
30°
H J
K
5 x
Work---see addendum at end
of answer key!
The ratio for a 30°-60°-90° triangle are:
30°
60°
41. If you are going 50 miles per hour, determine how many feet per second you are traveling.
Write your answer on the line.
(Related Tutorial Videos: See question 29)
42. The ratio of a pair of corresponding sides in two similar triangles is 5:3. The area of the smaller triangle is
108 in2. What is the area of the larger triangle?
0 A. 300 in2
0 B. 180 in2
0 C. 64.8 in2
0 D. 38.9 in2
(Related Tutorial Videos: Video 1
Day 15
43. Jessie is working on the roof of her house. She has measured the angle of the roof and the length of the
roof. Determine the width of the house, w.
0 A. 18.31 ft.
0 B. 24.57 ft.
0 C. 12.29 ft.
0 D. 26.15 ft.
(Related Tutorial Video: See question 28, Video 1, Video 2)
How many feet per second are you traveling?
15 ft.
w
15 ft.
If the Ratio of Similarity is a:b, then the Ratio of Area is
The Ratio of Area for the two triangles is: OR 25:9
Write a proportion to solve:
Cross-products gives us the equation:
Begin by dropping an altitude from the peak of the roof to form two congruent right triangles (the base will be half the length of
). Since the triangle is a right triangle, we can use trigonometry to solve.
15 ft
35°
44. The segment bisector is the midpoint.
(Related Tutorial Video: See question 18)
45. ΔRST has vertices R(3, 3), S(6, –2), and T(0, –2). Classify ΔRST based on its sides.
0 A. isosceles
0 B. scalene
0 C. equilateral
0 D. right
(Related Tutorial Videos: See question 5)
Write the inverse.
The point that does not bisect a segment is not the midpoint
Determine if the statement is true or false. ____________TRUE_________________________
If it is false, write a counterexample.
R
S T
(by counting)
∆RTS is Isosceles
Day 16
46. Look at the given information for quadrilateral ABCD.
is not parallel to
Draw and label a shape that satisfies all of the given information.
Determine the most specific name for the shape.
What is the most specific name for quadrilateral ABCD? Isosceles Trapezoid
(Related Tutorial Video: Video 1)
47. Martina has a calculator box that has a volume of 29 cubic inches.
1 inch = 2.54 centimeters
Determine the volume of the calculator box to the nearest cubic centimeter.
Write your answer on the line.
What is the volume of the calculator box
to the nearest cubic centimeter?
(Related Tutorial Video: Video 1)
48. Determine the image of Y(–4, 7) under the translation of (x, y) (x + 3, y – 5).
0 A. Y’(–1, 2)
0 B. Y’(–1, 12)
0 C. Y’(–7, 2)
0 D. Y’(–7, 12)
(Related Tutorial Video: Video 1)
A B
C D
>
>
literally means The conversion looks like:
(x, y) (x + 3, y – 5)
Day 17
49. Look at the figure.
What additional information do you need to show the triangles below are similar using the Side-Angle-Side
Similarity Theorem?
0 A. FH = 12
0 B. ∠E H
0 C. GH = 15
0 D. ∠D ∠G
(Related Tutorial Videos: Video 1, Video 2
50. Find sin C as a decimal rounded to the nearest hundredth.
0 A. 0.49
0 B. 60.44
0 C. 0.87
0 D. 0.87
(Related Tutorial Video: Video 1)
51. Two similar figures have a ratio of volumes of 64:27. What is the ratio of similarity?
Write your answer on the line.
What is the ratio of similarity?
(Related Tutorial Video: Video 1)
E
F
D
G
H 12
18
10
8
C
A B
16.9 8.3
14.7
Since we have an angle already (the vertical angle) and we want Side-Angle-
Side congruency, choice B and C will be eliminated as possibilities as they
give us additional angles. Choice C gives us a side with the correct ratio
, however will not result in Side-Angle-Side similarity. Choice A
will give us the correct ration still
Note: Taking the cube root of
the Ratio of Volume will give
you the Ratio of Similarity.
Day 18
52. Michael is 5
feet tall. Michael measures his shadow as 8 feet long. A tree in his backyard has a shadow
that is 25 yards long. How tall is the tree?
0 A. 51.56 yards
0 B. 17.19 feet
0 C. 51.56 feet
0 D. 36.36 yards
(Related Tutorial Video: Video 1)
53. Look at the pair of triangles.
Which statement is true?
0 A. The triangles are congruent.
0 B. The triangles are similar but not congruent.
0 C. The triangles are not similar or congruent.
0 D. There is not enough information to determine similarity or congruence.
(Related tutorial Videos: See question 10)
54. Steven built a box for his vegetable garden in the shape of a rectangular prism. The volume of the
vegetable garden was 24 cubic feet. He built another garden box that was two times longer and two times
higher. He thinks the volume will be twice as much.
Explain why Steven is not correct.
54 continued on next page
5 ½ ft
8 ft
25 yd
A B
C D
Set up a proportion:
Using cross products we find the tree’s height . Since 17.1875 yards isn’t a choice, we
have to convert the yards to feet by multiplying by the
conversion factor of
, which gives us
x y
z
Volume =
2x
y
2z
Volume= By doubling 2
dimensions, Steve has
actually increased the
Volume by a factor of 4
54 cont.
If Steven wants his second garden box to have twice the volume, what should he do instead?
(Related Tutorial Video: See question 51)
Day 19
55. To the nearest degree, what is m∠G?
0 A. 2
0 B. 57
0 C. 50
0 D. 33
(Related Tutorial Video: Video 1, See question 7)
56. JKLM is an isosceles trapezoid with J(0, –1), K(–2, 3) and M(6, –1). Determine the coordinates of L.
0 A. L (6, 1)
0 B. L (9, 4)
0 C. L (2, 3)
0 D. L (8, -3)
(Related Tutorial Video: Video 1)
57. Given a║b, determine which relationship must be true.
0 A. 1 and 3 are congruent.
0 B. 2 and 8 are supplementary.
0 C. 4 and 5 are similar.
0 D. 3 and 7 are complementary.
(Related Tutorial Video: See question 3)
G
E
F 7.8
12.1
1 2 3 4
5 6
7 8
a
b
If Steve wants to double the volume he should consider only doubling one dimension…so
Make the box twice as long
OR
Make the box twice as high
OR
Make the box twice as wide
OR
Increase all three dimensions by a factor of
Work---see addendum at end
of answer key!
Day 20
58. Determine which triangle is similar to ΔDEF.
0 A.
0 B.
0 C.
0 D.
(Related Tutorial Videos: Video 1, Video 2)
59. Name all segments skew to BC .
0 A. DIFAADFI ,,,
0 B. FIHIGHFG ,,,
0 C. CHBGABCD ,,,
0 D. AFDIHIGF ,,,
(Related Tutorial Video: Video 1)
D
5
12 E F
13
3
5
12
10
18
17
36
15 39
3
4
5
A
B C
D
F
G H
I
The triangle from C has the same side length ratios as the
triangle above:
60. Determine which theorem or postulate can be used to prove that these two triangles are similar.
0 A. AA
0 B. SAS
0 C. SSA
0 D. SSS
(Related Tutorial Videos: See question 58)
Day 21
61. Cody is standing 14 feet from the base of the tree. The top of the tree makes a 60 angle with the ground at
the point where he is standing.
Determine the height of the tree. Round your answer to two decimal places.
Write your answer on the line.
What is the height of the tree? feet
(Related Tutorial Videos: See question 28, Video 1)
62. Given a║b and m 3 = 5x + 10 and m 5 = 3x + 10, determine the value of x.
0 A. 110
0 B. 70
0 C. 20
0 D. 2.5
(Related Tutorial Videos: See question 3)
8
6
27°
4
63°
14 ft
60
1 2 3 4
5 6
7 8
a
b
Since both triangles have two angles which are given, we can use the
triangle sum theorem (which says the sum of the angles in any
triangle must add up to 180°) to find the missing angles of both
triangles. By doing this we find that both triangles have angle
measures of
Tree
14 ft
60°
Angle 1 and Angle 5 are co-interior (or same side interior) angles on
parallel lines and are therefore supplementary. We can write the equation:
63. In circle C, = 72 and is a diameter. Determine m BCD.
Write your answer on the line.
(Related Tutorial Videos: Video 1)
Day 22
64. Determine which set of measures could represent the sides of a right triangle.
0 A. 2, 3, 4
0 B. 7, 11, 14
0 C. 8, 10, 12
0 D. 9, 12, 15
(Related Tutorial Video: Video 1)
65. Determine the exact value of x in ΔLMN.
0 A. 25
0 B. 225
0 C. 325
0 D. 100
(Related Tutorial Video: See question 40)
66. ΔRST has vertices R(-2 5), S(1, 1), and T(-6, 2). Classify ΔRST based on its sides.
0 A. isosceles
0 B. scalene
0 C. right isosceles
0 D. right
(Related Tutorial Video: See question 5)
D
A
B
C
What is the m BCD? 108° degrees
60° L M
N
50 x
Since , then the measure of
angle ACB is 72°. Since is a diameter
and measures 180°, <BCD = 180-72 =
108°
The only triple that satisifies the Pythagorean Theorem is the side
lengths of 9, 12, and 15 because
Work---see addendum at end
of answer key!
Day 23
67. In the diagram:
Given: EBAB
CD
Prove: EBCABD
(Related Tutorial Video: See question 10)
68. Determine the value of y.
0 A. 18
0 B. 12
0 C. 6
0 D. 4.5
(Related Tutorial Video: Video 1, Video 2)
69. For rhombus GHJK, determine m 1.
0 A. 45°
0 B. 60°
0 C. 90°
0 D. 120°
(Related Tutorial Video: See question 17)
A
B C
D
E
Proof:
6
3
y
9
G H
J K
1
Statement Justification
1. 1. Given
2. 2. Given
3. 3. Vertical Angles are Congruent
4. 4. AAS Congruency
The product of segments of an intersecting
chords are equal, so we know:
Day 24
70. Given quadrilateral XYWZ, determine whether WX and YZ are parallel, perpendicular or neither.
W(0, –3), X(–1, 5), Y( 2, 5) Z(–1, 2)
Show your work using words, numbers and/or diagrams.
Are WX and YZ parallel, perpendicular or neither? Neither
(Related Tutorial Video: See question 6)
71. Determine the value of x and y so that QRST will be a parallelogram.
0 A. x = 6, y = 42
0 B. x = 6, y = 22
0 C. x = 20, y = 42
0 D. x = 20, y = 22
(Related Tutorial Video: See question 16)
T
Q R
S
32°
4x°
24° (y-10)°
There is neither a perpendicular or parallel relationship
between the sides
If QRST is a parallelogram, then alternate interior angles should be equal. That means:
And
72. Two angles measuring 90° are complementary.
(Related Tutorial Video: See question 18)
Day 25
73. Which statement is an example of deductive reasoning?
0 A. This bird is white. Swans are white. Therefore, this bird is a swan.
0 B. Dogs are mammals. Mammals breathe oxygen. Therefore dogs breathe oxygen.
0 C. This rock is not heavy. Lava rocks are not heavy. Therefore this rock is lava rock.
0 D. When the sidewalks get icy, they get slippery. The sidewalks are slippery. Therefore the
sidewalks are icy.
(Related Tutorial Video: See question 12)
74. If FCABDEAF , and AB ║ FC , determine which theorem or postulate can be used to prove
FCDABE .
0 A. AAS
0 B. ASA
0 C. SAS
0 D. SSS
(Related Tutorial Video: See question 10)
Write the inverse.
Determine if the statement is true or false. ______TRUE_______________________________
If it is false, write a counterexample.
A
B C
D E F
Two angles whose sum is not 90° are not complementary
<BAC <CFE because they are corresponding
angles from parallel lines, so we have a Side-Angle-
Side
75. Identify which of the following is a property of a parallelogram.
0 A. The diagonals are congruent.
0 B. The diagonals bisect the angles.
0 C. The diagonals are perpendicular.
0 D. The diagonals bisect each other.
(Related Tutorial Video: See question 16)
Addendum to Answer Key
5. ΔDEF has vertices D(4, 1), E(2, –1), and F(–2, –1). Classify ΔDEF based on its sides.
***All sides are a different length---this is a Scalene triangle!
26. Look at the triangle.
Determine the length of y. Express your answer in simplified radical form.
Write your answer on the line.
What is the length of y?
D
E F
5 y
18
13 X
Find X first by using the Pythagorean Theorem:
Find Y by using the Pythagorean Theorem a second time:
38. The figure is a rectangular prism with dimensions 12 inches long, 5 inches wide and 7 inches tall.
Determine the length of BI .
Write your answer on the line.
A
B C
D
F
G H
I 5
12
7
What is the length of BI ?
We need to use the Pythagorean Theorem TWICE to solve this problem. To begin, draw line segment to form Right ∆BGI.
Begin by finding the length of , which is the hypotenuse of Right ∆GFI (bottom of the rectangular prism)
So…..
Now use the length of and to find the length of using the Pythagorean Theorem a second time on Right ∆BGI
So….
56. JKLM is an isosceles trapezoid with J(0, –1), K(–2, 3) and M(6, –1). Determine the coordinates of L.
0 E. L (6, 1)
0 F. L (9, 4)
0 G. L (2, 3)
0 H. L (8, -3)
65. Determine the exact value of x in ΔLMN.
0 A. 25
0 B. 225
0 C. 325
0 D. 100
Work---see addendum at end
of answer key!
M J
K
In order for JKLM to be an isosceles trapezoid, the
length of side . To get from point J to
point K, we go down two and over two. In order to
get to point L from point M, we must also travel
down two and over (in order to establish the same
length) The coordinates of point L will be at
60° L M
N
50 x
The ratio for a 30°-60°-90° triangle are:
Since the hypotenuse is 50 and equal to 2X, we can set up an
equation and solve for X:
The long leg is the value of
So the value of the long leg is
30°
60°
2
3
66. ΔRST has vertices R(-2 5), S(1, 1), and T(-6, 2). Classify ΔRST based on its sides.
0 A. isosceles
0 B. scalene
0 C. right isosceles
0 D. right
Length
R
S
T
Since the slopes are opposite reciprocals
the lines are perpendicular making it a
right triangle. Since two sides are the
same length, it is also isosceles.
