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Geometry Reference Sheet
Note: You may use these formulas throughout this entire test.
Linear Quadratic
Slope π =π¦2 β π¦1
π₯2 β π₯1
Vertex-Form π¦ = π(π₯ β h)2 + π
Midpoint π = (π₯1 + π₯2
2,π¦1 + π¦2
2) Standard Form π¦ = ππ₯2 + ππ₯ + π
Distance π = β(π₯2 β π₯1)2 + (π¦2 β π¦1)2 Intercept Form π¦ = π(π₯ β π)(π₯ β π)
Slope-Intercept Form π¦ = ππ₯ + π
Exponential Probability
(h, k) Form π¦ = πππ₯βh + π π(π΄ πππ π΅) = π(π΄) β π(π΅)
π(π΄ πππ π΅) = π(π΄) β π(π΅|π΄)
π(π΄ ππ π΅) = π(π΄) + π(π΅) β π(π΄ πππ π΅)
Volume and Surface Area
π = ππ2β
ππ΄ = 2(ππ2) + β(2ππ)
π =4
3ππ3
ππ΄ = 4ππ2
π =1
3ππ2β
ππ΄ = ππ2 +1
2(2ππ β π)
π =1
3π΅β
ππ΄ = π΅ +1
2(ππ)
Where π΅ =base area
and π =base perimeter
Student Work Area
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale.
1. Which quadrilateral would be carried on to itself after a reflection over the diagonal π΄πΆΜ Μ Μ Μ ?
A.
C.
B.
D.
2. Reflecting over which line will map the rhombus onto itself?
A. π¦ = β2π₯
B. π¦ = 0
C. π¦ =1
4π₯
D. π¦ = π₯
3. Find the coordinates of the image of the point (β5, 7) when it is reflected across the
line π¦ = 11.
A. (β5, 18) C. (β5, β4)
B. (β5, 15) D. (β5, β7)
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
4. Draw line πΉπΊ β‘ and point π» not on the line. Reflect point H across the line πΉπΊ β‘ to form
point π»β². Based on your diagram, which of the following is true?
A. π»πΉΜ Μ Μ Μ β πΉπΊΜ Μ Μ Μ
B. π»πΉΜ Μ Μ Μ β π»β²πΊΜ Μ Μ Μ Μ
C. πΉπΊΜ Μ Μ Μ β π»β²πΊΜ Μ Μ Μ Μ
D. π»πΊΜ Μ Μ Μ β π»β²πΊΜ Μ Μ Μ Μ
5. What are coordinates for the image of quadrilateral ABCD after the translation of
(π₯, π¦) β (π₯ + 7, π¦ β 2) ?
A. π΄β²(8, β5), π΅β²(2, β1), πΆβ²(12, β4), π·β²(10, β7)
B. π΄β²(β6, β1), π΅β²(β5, 1), πΆβ²(β2, 0), π·β²(β4, β3)
C. π΄β²(β6, β5), π΅β²(2, β1), πΆβ²(12, β4), π·β²(10, β7)
D. π΄β²(8, β5), π΅β²(9, β3), πΆβ²(12, β4), π·β²(10, β7)
6. Figure ABC is rotated 90Β° clockwise about the point (2, 0). What are the coordinates of
π΄β² after the rotation?
A. π΄β²(β1, 4)
B. π΄β²(3, β6)
C. π΄β²(5, β4)
D. π΄β²(6, β3)
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
7. Describe the transformation π: (β2, 5) β (2, β5).
A. A reflection across the y-axis
B. A reflection across the x-axis
C. A rotation 180Β° with center of rotation (0, 0)
D. A rotation 90Β° clockwise with center of rotation (0, 0)
8. What are the coordinates for the image of βπΊπ»πΎ after a rotation 90Β° counterclockwise
about the origin and a translation of (π₯, π¦) β (π₯ + 3, π¦ + 2) ?
A. πΎβ²β²(β2, 0), π»β²β²(2, β1), πΊβ²β²(0, β4)
B. πΎβ²β²(2, 0), π»β²β²(β2, 1), πΊβ²β²(0, 4)
C. πΎβ²β²(β4, β4), π»β²β²(β8, β3), πΊβ²β²(β6, 0)
D. πΎβ²β²(4, 4), π»β²β²(8, 3), πΊβ²β²(6, 0)
9. The point π(β2, β5) is rotated 90Β° counterclockwise about the origin, and then the
image is reflected across the line π₯ = 3. What are the coordinates of the final image πβ²β²?
A. (1, β2) C. (β2, 1)
B. (11, β2) D. (2, 11)
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
10. Which composition of transformations maps βπ·πΈπΉ into the first quadrant?
A. Reflection across the line π¦ = π₯ and then a
translation of (π₯ β 1, π¦ + 6).
B. Translation of (π₯ β 1, π¦ β 6) and then a
reflection in the line π¦ = π₯.
C. Clockwise rotation about the origin by 180Β° and then reflection across the y-axis.
D. Counterclockwise rotation about the origin by
90Β° and then a translation of (π₯ β 1, π¦ + 6).
11. Which of the following transformations map βπΊπ»πΌ onto βπΊβ²π»β²πΌβ²?
A. The triangle is first rotated clockwise 180Β° about the origin and then reflected
across π¦ = 3.
B. The triangle is rotated 90Β° clockwise about point πΉ and then translated up 3 units
and right 1 unit.
C. The triangle is reflected across the x-axis and then reflected across the y-axis.
D. The triangle is first translated up 5 units and then reflected across the y-axis.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
12. In the diagram below, ππ = 30, ππ = 5, ππ = ππ, and ππ = ππ.
Which of the following statements is not true?
A. ππ = ππ + ππ C. ππ = 3 β ππ
B. ππ = ππ D. ππ = ππ
13. Point A is reflected over the line π΅πΆ β‘ .
Which of the following is not true of line π΅πΆ β‘ ?
A. line π΅πΆ β‘ is perpendicular to line π΄π΄β² β‘
B. line π΅πΆ β‘ is perpendicular to line π΄β²π΅ β‘
C. line π΅πΆ β‘ bisects line segment π΄π΅Μ Μ Μ Μ
D. line π΅πΆ β‘ bisects line segment π΄π΄β²Μ Μ Μ Μ Μ
14. Find πΆπΈ given the following information:
π΄πΆΜ Μ Μ Μ is the perpendicular bisector of π·π΅Μ Μ Μ Μ
πΈπ΄ = 16
π·πΆ = 13
π΄π΅ = 20
A. πΆπΈ = 15.9
B. πΆπΈ = 5
C. πΆπΈ = 17.7
D. πΆπΈ = 16
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
15. πΈπ΅ is the angle bisector of β π΄πΈπΆ. What is the value of x?
A. π₯ = 35
B. π₯ = 51.5
C. π₯ = 70.5
D. π₯ = 142
For #16-17 use the following:
Given: πΎπ bisects β π½πΎπΏ
Prove: πβ 2 = πβ 3
Statements Reasons
πΎπ bisects β π½πΎπΏ Given
β 1 β β 2 18.
πβ 1 = πβ 2 Definition of Congruence
β 1 β β 3 19.
πβ 1 = πβ 3 Definition of Congruence
πβ 2 = πβ 3 Substitution Property of Equality
16. Choose one of the following to complete the proof.
A. Definition of angle bisector- If a ray is an angle bisector, then it divides an angle into
two congruent angles.
B. Definition of opposite rays- If a point on the line determines two rays are collinear,
then the rays are opposite rays.
C. Definition of ray- If a line begins at an endpoint and extends infinitely, then it is ray.
D. Definition of segment bisector- If any segment, line, or plane intersects a segment at
its midpoint then it is the segment bisector.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
17. Choose one of the following to complete the proof.
A. Definition of complementary angles- If the angle measures add up to 90Β°, then
angles are supplementary
B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then
the two angles are congruent
C. Definition of supplementary angles- If the angles are supplementary, then the
angleβs measures add to 180Β°.
D. Vertical Angle Theorem- If two angles are vertical angles, then they have congruent
angle measures.
18. In the figure πβ πΉπΊπΌ = (2π₯ + 9)Β° and πβ π»πΊπΌ = (4π₯ β 15)Β°. Find πβ πΉπΊπΌ and
πβ π»πΊπΌ.
A. πβ πΉπΊπΌ = 71Β° and πβ π»πΊπΌ = 109Β°
B. πβ πΉπΊπΌ = 45Β° and πβ π»πΊπΌ = 45Β°
C. πβ πΉπΊπΌ = 33Β° and πβ π»πΊπΌ = 33Β°
D. πβ πΉπΊπΌ = 41Β° and πβ π»πΊπΌ = 49Β°
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
19. Which of the following options correctly explains how to find the value of π₯ in the figure
below?
A. Since πΈπ΄ and πΈπ· are opposite rays, and πΈπ΅ and πΈπΆ are opposite rays, β π΄πΈπ΅ and
β π·πΈπ΅ are vertical angles. Vertical angles are congruent and have the same
measure, so πβ π΄πΈπ΅ = πβ π·πΈπΆ. Using substitution gives the equation, 2π₯ = 30.
Dividing by 2 on both sides gives π₯ = 15.
B. Since πΈπ΄ and πΈπ· are opposite rays, and πΈπ΅ and πΈπΆ are opposite rays, β π΄πΈπ΅ and
β π·πΈπ΅ are vertical angles. Vertical angles are complimentary meaning their
measures add up to 90Β°, so πβ π΄πΈπ΅ + πβ π·πΈπΆ = 90Β°. Using substitution gives the
equation, 2π₯ + 30 = 90. Subtracting both sides by 30, and then dividing both sides
by 2 gives π₯ = 30.
C. Since β π΄πΈπ· is a straight angle, its measure is 180Β°. By the Angle Addition
Postulate, πβ π΄πΈπ΅ + πβ π΅πΈπΆ + πβ πΆπΈπ· = πβ π΄πΈπ·. Using substitution gives the
equation, 2π₯ + 4π₯ + 30 = 180. After combining like terms the equation becomes
6π₯ + 30 = 180. Subtracting both sides by 30, and then dividing both sides by 6
gives π₯ = 25.
D. Since β π΄πΈπ· is a straight angle, its measure is 90Β°. By the Angle Addition
Postulate, πβ π΄πΈπ΅ + πβ π΅πΈπΆ + πβ πΆπΈπ· = πβ π΄πΈπ·. Using substitution gives the
equation, 2π₯ + 4π₯ + 30 = 90. After combining like terms the equation becomes
6π₯ + 30 = 90. Subtracting both sides by 30, and then dividing both sides by 6
gives π₯ = 10.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
For #20 use the following:
Given: β 1 and β 2 are supplementary, and πβ 1 = 135Β° Prove: πβ 2 = 45Β°
Statements Reasons
β 1 and β 2 are supplementary Given
[1] Given
πβ 1 + πβ 2 = 180Β° [2]
135Β° + πβ 2 = 180Β° Substitution Property of Equality
πβ 2 = 45Β° [3]
20. Fill in the blanks to complete the two column proof:
A. [1] πβ 2 = 135Β°
[2] Definition of Supplementary Angles
[3] Subtraction Property of Equality
B. [1] πβ 1 = 135Β°
[2] Definition of Supplementary Angles
[3] Substitution Property of Equality
C. [1] πβ 1 = 135Β°
[2] Definition of Supplementary Angles
[3] Subtraction Property of Equality
D. [1] πβ 1 = 135Β°
[2] Definition of Complementary Angles
[3] Subtraction Property of Equality
21. Draw two lines and a transversal such that β 1 and β 2 are alternate interior angles, β 2
and β 3 are corresponding angles, and β 3 and β 4 are alternate exterior angles. What type
of angle pair is β 1 and β 4?
A. β 1 and β 4 are corresponding angles C. β 1 and β 4 are supplementary angles
B. β 1 and β 4 are vertical angles D. β 1 and β 4 are alternate exterior angles
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
22. Solve for x and y so that π β₯ π β₯ π.
A. π₯ = 9, π¦ = 10.1 C. π₯ = 29, π¦ = 3.2
B. π₯ = 9, π¦ = 9.9 D. π₯ = 29, π¦ = 11.0
23. In the diagram below, line π is parallel to line π and line π‘ is perpendicular to π΄π΅ . What
is the measure of β π΅π΄πΆ?
A. πβ π΅π΄πΆ = 37Β° C. πβ π΅π΄πΆ = 45Β°
B. πβ π΅π΄πΆ = 53Β° D. πβ π΅π΄πΆ = 127Β°
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
24. Based on the figure below, which statements are true if π β₯ π and π β₯ π ?
I. πβ 1 = πβ 5
II. πβ 2 + πβ 3 = 180Β°
III. πβ 4 = πβ 8
IV. πβ 6 + πβ 9 = 180Β°
V. πβ 1 + πβ 9 = 180Β°
A. All of the above C. II, III, and IV
B. I, III, and IV D. III, IV, and V
25. Which statement is true based on the figure?
A. π β₯ π
B. π β₯ π
C. π β₯ π
D. π β₯ π
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
For #26-27 use the following:
Given: π β₯ π
Prove: πβ 3 + πβ 6 = 180
Statements Reasons
π β₯ π Given
28. If two parallel lines are cut by a transversal, then
each pair of alternate interior angles is congruent.
πβ 3 = πβ 5 Definition of Congruence
β 5 and β 6 are supplementary If two angles form a linear pair, then they are
supplementary.
πβ 5 + πβ 6 = 180 29.
πβ 3 + πβ 6 = 180 Substitution Property of Equality
26. Choose one of the following to complete the proof.
A. β 4 β β 5
B. β 2 β β 8
C. β 3 β β 6
D. β 3 β β 5
27. Choose one of the following to complete the proof.
A. Vertical Angle Theorem- If two angles are vertical angles, then they have congruent
angle measures
B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then
they are congruent
C. Definition of supplementary angles- If two angles are supplementary, then their
angle measures add to 180Β°.
D. Definition of complementary angles- If two angles are a complementary, then their
angle measures add to 90Β°
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
28. Which equation of the line passes through (5, β8) and is parallel to the graph of the line
π¦ =2
3π₯ β 4?
A. π¦ =
2
3π₯ β
34
3 C. π¦ =
2
3π₯ β 8
B. π¦ = β3
2π₯ β
1
2 D. π¦ = β
3
2π₯ β 8
29. Which equation of the line passes through (4, 7) and is perpendicular to the graph of the
line that passes through the points (1, 3) and (β2, 9) ?
A. π¦ = 2π₯ β 1 C. π¦ =
1
2π₯ β 5
B. π¦ =1
2π₯ + 5 D. π¦ = β2π₯ + 15
30. Given the two lines below, which statement is true?
πΏπππ 1: π₯ β 3π¦ = β15 and πΏπππ 2: π¦ = 3(π₯ + 2) β 1
A. The lines are parallel.
B. They are the same line.
C. The lines are perpendicular.
D. The lines intersect but are not perpendicular.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
31. Given the lines π¦ = β1
3π₯ + 2 and π¦ = π₯ β 4, find the equation for a third line that
would complete a right triangle in the coordinate plane.
A. π¦ = π₯ + 4
B. π¦ = βπ₯ β 5
C. π₯ = β3
D. π¦ = β3π₯ + 5
32. Rectangle π»πΌπ½πΎ has coordinates π»(1, β1), πΌ(6, 4), π½(8, 2) and πΎ(3, β3). Which of the
following statements is true?
A. The length of π»πΎΜ Μ Μ Μ is 4 units.
B. The perimeter of the rectangle is 14 units.
C. The perimeter of the rectangle is 14β2 units.
D. The area of the rectangle is 100 square units.
33. Archeologists use coordinate grids on their dig sites to help document where objects are
found. While excavating the site of a large ancient building, archeologists find what they
believe to be a wooden support beam that extended across the entire building. One end
of the beam was located at the coordinate (β13, 12) and markings on the beam indicate
that the midpoint of the beam was located at (2, 4). Assuming the beam is still intact,
where should the archeologists begin digging to find the other end of the beam?
A. (β17, 4)
B. (β7.5, 4)
C. (β5.5, 8)
D. (17, β4)
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
34. What are the coordinates of the point P that lies along the directed segment from
πΆ(β3, β2) to π·(6, 1) and partitions the segment in the ratio of 2 to 1?
A. (0, 3) C. (1.5, 0.5)
B. (3, 0) D. (4.5, 1.5)
35. An 80 mile trip is represented on a gridded map by a directed line segment from point
π(3, 2) to point π(9, 13). What point represents 60 miles into the trip?
A. (8, 14.6) C. (9, 11.25)
B. (3.75, 9.75) D. (7.5, 10.25)
36. In the diagram below, reflect βπ΄π΅πΆ over π΄π΅Μ Μ Μ Μ .
Which of the following statements is true after the reflection?
A. ABΜ Μ Μ Μ β ACβ²Μ Μ Μ Μ Μ
B. β ACB β β CACβ²
C. β C β β Cβ²
D. βπ΄π΅πΆβ² is equilateral.
37.
If a triangle has two sides with lengths of 8 ππ and 14 ππ. Which length below could
not represent the length of the third side?
A. 7 ππ C. 15 ππ
B. 13 ππ D. 22 ππ
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
38. Find the range of values containing x.
A. 2 < π₯ < 5
B. π₯ < 5
C. 0 < π₯ < 9
D. π₯ > 0
39. Given βπππ, Anna is proving πβ 1 + πβ 2 = πβ 4. Which statement should be part of
her proof?
A. πβ 1 = πβ 2
B. πβ 1 = πβ 3
C. πβ 1 + πβ 3 = 180Β°
D. πβ 3 + πβ 4 = 180Β°
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
40. Which conclusion can be drawn from the given facts in the diagram?
A. ππΜ Μ Μ Μ bisects β πππ
B. β πππ β β π ππ
C. ππΜ Μ Μ Μ β π πΜ Μ Μ Μ
D. ππ = ππ
41. Which of the following statements is true?
A. All triangles are congruent.
B. All congruent figures have three sides.
C. If two figures are congruent, there must be some sequence of rigid motions that
maps one to the other.
D. If two triangles are congruent, then they must be right triangles.
42. If βπΆπΈπ· β βππ π, which of the following is true?
A. β πΆ β β π, β πΈ β β π , β π· β β π
B. β πΆ β β π, β πΈ β β π, β π· β β π
C. β πΆ β β π, β πΈ β β π , β π· β β π
D. β πΆ β β π , β πΈ β β π, β π· β β π
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
43. Refer To the figure to complete the congruence statement, βπ΄π΅πΆ β _________.
A. βπ΄πΆπΈ
B. βπΈπ·πΆ
C. βπΈπ΄π·
D. βπΈπ·π΄
44. In the figure β π» β β πΏ and π»π½ = π½πΏ. Which of the following statements is about
congruence is true?
A. βπ»πΌπ½ β βπΏπΎπ½ by ASA
B. βπ»πΌπ½ β βπΎπΏπ½ by SSS
C. βπ»πΌπ½ β βπΎπΏπ½ by SAS
D. βπ»πΌπ½ β βπΏπΎπ½ by SAS
45. Determine which postulate or theorem can be used to prove the pair of triangles
congruent.
A. AAS
B. SAS
C. ASA
D. SSS
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
46. Which theorem can be used to conclude that βπΆπ΄π΅ β βπΆπΈπ·?
A. SAA
B. SAS
C. SSS
D. AAA
47. In the figure β πΊπ΄πΈ β β πΏππ· and π΄πΈΜ Μ Μ Μ β π·πΜ Μ Μ Μ . What information is needed to prove that
βπ΄πΊπΈ β βππΏπ· by SAS?
A. πΊπΈΜ Μ Μ Μ β πΏπ·Μ Μ Μ Μ
B. π΄πΊΜ Μ Μ Μ β ππΏΜ Μ Μ Μ
C. β π΄πΊπΈ β β ππΏπ·
D. β π΄πΈπΊ β β ππ·πΏ
48. Which of the following sets of triangles can be proved congruent using the AAS
Theorem?
A.
C.
B.
D.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
For #49-50 use the following:
Given: π is the midpoint of ππΜ Μ Μ Μ Μ ; β πππ β β πππ
Prove: βπππ β βπππ
Statements Reasons
π is the midpoint of ππΜ Μ Μ Μ Μ Given
55. Definition of Midpoint
β πππ β β πππ Given
ππΜ Μ Μ Μ β ππΜ Μ Μ Μ Reflexive property of congruence
βπππ β βπππ 56.
49. Choose one of the following to complete the proof.
A. ππΜ Μ Μ Μ Μ β ππΜ Μ Μ Μ
B. ππΜ Μ Μ Μ Μ β ππΜ Μ Μ Μ
C. ππΜ Μ Μ Μ Μ β ππΜ Μ Μ Μ
D. ππΜ Μ Μ Μ β ππΜ Μ Μ Μ
50. Choose one of the following to complete the proof.
A. Reflexive property of equality
B. SSA Congruence
C. SAS Congruence
D. AAS Congruence
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
51. In the figure, identify which congruence statement is true. Then find πβ πππ.
A. βπππ β βπππ by HL
πβ πππ = 22Β°
B. βπππ β βπππ by HL
πβ πππ = 78Β°
C. βπππ β βπππ by HL
πβ πππ = 22Β°
D. βπππ β βπππ by HL
πβ πππ = 68Β°
52. In the figure, βπππ β βπππ. What is the value of y?
A. π¦ = 8
B. π¦ = 10
C. π¦ = 42
D. π¦ = 52
53. Which of the following is not always true of Parallelogram π΄π΅πΆπ·?
A. π΄π΅Μ Μ Μ Μ β π΅πΆΜ Μ Μ Μ , π·πΆΜ Μ Μ Μ β π΅πΆΜ Μ Μ Μ
B. π΄π΅Μ Μ Μ Μ β π·πΆΜ Μ Μ Μ , π΅πΆΜ Μ Μ Μ β π΄π·Μ Μ Μ Μ
C. πβ π΄ + πβ π΅ = 180Β°
D. π΄π΅ + π΅πΆ = π΄π· + π·πΆ
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
54. A student is given the following information and then asked to write a paragraph proof.
Determine which statement would correctly complete the studentβs proof.
Given: Parallelogram ππ ππ and Parallelogram ππππ
Prove: β π β β π
Proof:
We are given Parallelogram ππ ππ and Parallelogram ππππ. Since opposite angles of a
parallelogram are congruent, β π β β π and β π β β π. __________________.
A. Therefore, β π β β π by the Transitive Property of Congruence.
B. Therefore, β π β β π by the Transformative Property of Congruence.
C. Therefore, β π β β π by the Reflective Property of Congruence.
D. Therefore, β π β β π by the Reflexive Property of Congruence.
55. A wooden frame has screws at A, B, C, and D so that the sides of it can be pressed to
change the angles occurring at each vertex. π΄π΅Μ Μ Μ Μ β πΆπ·Μ Μ Μ Μ and π΄π΅Μ Μ Μ Μ β₯ πΆπ·Μ Μ Μ Μ , even when the
angles change. Why is the frame always a parallelogram?
A. The angles always stay the same, so π΄π΅πΆπ· is a parallelogram.
B. All sides are congruent, so π΄π΅πΆπ· is a parallelogram.
C. One pair of opposite sides is congruent and parallel, so π΄π΅πΆπ· is a parallelogram.
D. One pair of opposite sides is congruent, so π΄π΅πΆπ· is a parallelogram.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
56. Which statement is true?
A. All quadrilaterals are rectangles.
B. All rectangles are parallelograms.
C. All parallelograms are rectangles.
D. All quadrilaterals are squares.
57. What is the measure of π»π½ in Parallelogram πΉπΊπ»π½, given the following:
πΉπΊ = π₯ + 7
πΊπ» = 5π₯ + 3
πβ πΉ = 46Β° πβ π» = (3π₯ + 10)Β°
A. π»π½ = 63
B. π»π½ = 19
C. π»π½ = 12
D. π»π½ = 8
58. π½πΎπΏπ is a rhombus. If πβ π½ππΏ = 70 and πβ π½πΎπ = (5π₯ + 16)Β°, find the value of π₯.
A. π₯ = 18.8
B. π₯ = 10.8
C. π₯ = 7.8
D. π₯ = 3.8
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
59. What is the value of x in the rectangle?
A. π₯ = 42
B. π₯ = 24
C. π₯ = 8
D. π₯ = 4
60. Based on the figure below, which statements are true?
I. The figure is a rectangle
II. The figure is a parallelogram
III. 6π₯ β 4 = 9π₯ + 3
IV. 9π₯ + 3 = 10π₯ β 2
V. π₯ = 8
VI. The longest side has a length of 60.
A. I, III, and V C. II, IV, and VI
B. I, IV, and VI D. II, III, and V
61. Given points π΅ (β3,3), πΆ(3, 4), and π·(4, β2). Which of the following points must be
point A in order for the quadrilateral π΄π΅πΆπ· to be a parallelogram?
A. π΄(β2, β1)
B. π΄(β3, β2)
C. π΄(β2, β3)
D. π΄(β1, β2)
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
Geometry Semester 1 Instructional Materials 2017-18 Answers
1. C 13. C 25. D 37. D 49. B
2. A 14. B 26. D 38. A 50. C
3. B 15. A 27. C 39. D 51. D
4. D 16. A 28. A 40. C 52. B
5. D 17. D 29. B 41. C 53. A
6. C 18. D 30. D 42. A 54. A
7. C 19. C 31. B 43. B 55. C
8. D 20. C 32. C 44. A 56. B
9. A 21. A 33. D 45. A 57. B
10. A 22. D 34. B 46. B 58. D
11. B 23. A 35. D 47. B 59. B
12. D 24. B 36. C 48. B 60. C
61. C
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
Alternative Item Formats: As part of the evolution of District Common Math Finals, multiple select and gridded response
item types may be piloted on the Fall 2017 exam. The following are examples of items that have
been revised from a multiple choice format to a multiple select or gridded response format.
These examples are not necessarily reflective of which actual test items will appear in a multiple
select or gridded response format.
Possible Item Types: Multiple Choice
o 4 possible answer choices, listed as A, B, C, D options
o exactly 1 correct answer
Multiple Select or Multiple Response
o 5 or more possible answer choices, listed as F, G, H, I, J, etc. options
o At least 2 or more correct answers
Gridded Response
o Free-response item, requiring students to bubble in the digits of their numeric
answer for machine scoring
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
1.
alt
Which quadrilateral would be carried on to itself after a reflection over the diagonal π΄πΆΜ Μ Μ Μ ?
Select all that apply.
F.
G.
H.
I.
J.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
11.
alt
Which of the following transformations map βπΊπ»πΌ onto βπΊβ²π»β²πΌβ²? Select all that apply.
F. The triangle is rotated 90Β° clockwise about point πΉ and then translated up 3 units
and right 1 unit.
G. The triangle is first rotated clockwise 180Β° about the origin and then reflected
across π¦ = 3.
H. The triangle is first rotated 270Β° counterclockwise about the origin and then
translated up 1 unit and right 3 units.
I. The triangle is reflected across the x-axis and then reflected across the y-axis..
J. The triangle is first translated up 5 units and then reflected across the y-axis.
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
14.
alt
Find πΆπΈ given the following information:
π΄πΆΜ Μ Μ Μ is the perpendicular bisector of π·π΅Μ Μ Μ Μ
πΈπ΄ = 16
π·πΆ = 13
π΄π΅ = 20
24.
alt
Based on the figure below, which statements are true if π β₯ π and π β₯ π ?
Select all that apply.
F. πβ 1 = πβ 5
G. πβ 2 + πβ 3 = 180Β°
H. πβ 4 = πβ 8
I. πβ 6 + πβ 9 = 180Β°
J. πβ 1 + πβ 9 = 180Β°
K. πβ 5 + πβ 7 = 90Β°
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
32.
alt
Rectangle π»πΌπ½πΎ has coordinates π»(1, β1), πΌ(6, 4), π½(8, 2) and πΎ(3, β3). Which of the
following statements are true? Select all that apply.
F. The length of π»πΎΜ Μ Μ Μ is 4 units.
G. The length of π»πΎΜ Μ Μ Μ is 2β2 units.
H. The perimeter of the rectangle is 14 units.
I. The perimeter of the rectangle is 14β2 units.
J. The area of the rectangle is 20 square units.
K. The area of the rectangle is 100 square units.
52.
alt
In the figure, βπππ β βπππ. What is the value of y?
GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: #2211 Geometry S1 and #7771 Foundations in Geometry S1 2017-2018
60.
alt
Based on the figure below, which statements are true? Select all that apply.
F. The figure is a rectangle
G. The figure is a parallelogram
H. 6π₯ β 4 = 9π₯ + 3
I. 9π₯ + 3 = 10π₯ β 2
J. π₯ = 8
K. The longest side has a length of 60.
Alternative Item Answers
# IM Ans
1.
alt H, I
11.
Alt F, H
14.
Alt +5.00
24.
Alt F, H, I
32.
Alt G, I, J
52.
Alt +10.0
60.
Alt G, I, K