Download Geometry Semester 1 Instructional Materials

Geometry Semester 1 Instructional Materials
2013-2014
2013-2014
Geometry Semester 1
Instructional Materials for the WCSD Math Common Finals
The Instructional Materials are for student and teacher use and are aligned
to the Math Common Final blueprint for this course. When used as test
practice, success on the Instructional Materials does not guarantee success
on the district math common final.
Students can use these Instructional Materials to become familiar with the
format and language used on the district common finals. Familiarity with
standards vocabulary and interaction with the types of problems included
in the Instructional Materials can result in less anxiety on the part of the
students.
Teachers can use the Instructional Materials in conjunction with the course
guides to ensure that instruction and content is aligned with what will be
assessed. The Instructional Materials are not representative of the depth
or full range of learning that should occur in the classroom
Sent on 9/27/13
Geometry Semester 1 Instructional Materials
2013-2014
Multiple Choice: Identify the choice that best completes the statement or answers the
question. Figures are not necessarily drawn to scale.
1. Excluding straight angles, how many angles are shown in the figure?
A. 7
B. 18
C. 19
D. 21
(
2. In the figure
A.
and
B.
and
C.
and
D.
and
) and
(
) . Find
and
3. What are coordinates for the image of quadrilateral ABCD after the translation of
(
) (
)?
A.
(
)
B.
(
)
(
)
(
C.
(
)
(
)
(
D.
(
)
(
(
)
)
(
(
)
(
)
(
)
)
)
)
(
(
)
)
B
C
A
D
Sent on 9/27/13
.
Geometry Semester 1 Instructional Materials
4. What are the coordinates for the image of
) (
origin and a translation of (
A.
(
)
(
)
B.
(
)
(
C.
(
)
(
)
(
D.
(
)
(
)
(
)
(
(
2013-2014
after a rotation
)?
clockwise about the
)
)
)
)
K
G
H
is (
5. Point Y of
translation (
A.
(
B.
(
)?
). What is the image of Y after
)
)
C.
(
D.
(
6. Find the coordinates of the image of the point (
.
is transformed using the
)
)
) when it is reflected across the line
A. (
)
C.
(
)
B. (
)
D.
(
)
) is rotated
7. The point (
counterclockwise about the origin, and then the image is
reflected across the line
. What are the coordinates of the final image ?
A. (
B. (
)
)
8. Reflect point H across the line ⃡
A. ̅̅̅̅ ̅̅̅̅
B. ̅̅̅̅
̅̅̅̅̅
C. ̅̅̅̅
̅̅̅̅̅
D. ̅̅̅̅
̅̅̅̅̅
Sent on 9/27/13
C.
(
)
D.
(
)
to form point H’, which of the following is true?
H
G
F
Geometry Semester 1 Instructional Materials
9.
is the angle bisector of
2013-2014
. What is the value of x?
A.
B.
C.
D.
10. In the figure, which pair of angles is supplementary?
A.
B.
1
4
C.
D.
11. In the figure,
the
in terms of x.
. Find
E
A
A.
B.
C.
D.
Sent on 9/27/13
B
C
6
5
2
3
8
7
Geometry Semester 1 Instructional Materials
2013-2014
For #12-13 use the following:
Given:
bisects
Prove:
J
K
3
1
2
M
L
Statements
bisects
Reasons
Given
12.
13.
Substitution Property of Equality
12. 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.
13. Choose one of the following to complete the proof.
A. Definition of complementary angles- If the angle measures add up to
are supplementary
, then angles
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 angle’s
measures add to
.
D. Vertical Angle Theorem- If two angles are vertical angles, then they have equal angle
measures.
Sent on 9/27/13
Geometry Semester 1 Instructional Materials
2013-2014
For #14 use the following:
Given:
and
are supplementary, and
Prove:
Statements
and
are supplementary
Reasons
Given
Given
[1]
[2]
Substitution Property of Equality
[3]
14.
Fill in the blanks to complete the two column proof:
A. [1]
[2] Definition of Supplementary Angles
[3] Subtraction Property of Equality
B. [1]
[2] Definition of Supplementary Angles
[3] Substitution Property
C. [1]
[2] Definition of Supplementary Angles
[3] Subtraction Property of Equality
D. [1]
[2] Definition of Complementary Angles
[3] Subtraction Property of Equality
15. Point A is reflected over the line ⃡ .
Which of the following is NOT true of line ⃡ ?
A. line ⃡
B. line ⃡
is perpendicular to line ⃡
C. line ⃡
bisects line segment ̅̅̅̅
D. line ⃡
bisects line segment ̅̅̅̅̅
Sent on 9/27/13
is perpendicular to line ⃡
65
60
110
120
Geometry Semester 1 Instructional Materials
2013-2014
16. Which statement is true based on the figure?
b
A.
a
c
B.
C.
65
110
d
60
D.
120
17. Draw two lines and a transversal such that
are corresponding angles, and
and
angle pair is
and ?
A.
e
and
are alternate interior angles,
and
are alternate exterior angles. What type of
C.
and
are supplementary angles
B.
and
are corresponding angles
and
are alternate exterior angles
D.
and
Sent on 9/27/13
are vertical angles
Geometry Semester 1 Instructional Materials
2013-2014
For #18-19 use the following:
Given:
Prove:
t
1
4
8
Statements
2
3
p
5 6
7
q
Reasons
Given
Alternate Interior Angles Theorem
18.
19.
Substitution Property of Equality
18. Choose one of the following to complete the proof.
A.
B.
C.
D.
19. Choose one of the following to complete the proof.
A. Vertical Angle Theorem- If two angles are vertical angles, then they have equal angle
measures
B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then
they are congruent
C. Linear Pair Theorem- If two angles form a linear pair, then the angles are
supplementary and their angle measures add to
D. Definition of complementary angles- If two angles are a linear pair, then the angles are
complementary and their angle measures add to
20. What are the coordinates of the point P that lies along the directed segment from
(
) to ( ) and partitions the segment in the ratio of 2 to 1?
A. (
)
C.
(
)
B. (
)
D. (
)
Sent on 9/27/13
Geometry Semester 1 Instructional Materials
2013-2014
21. An 80 mile trip is represented on a gridded map by a directed line segment from point
( ) to point (
). What point represents 60 miles into the trip?
A. (
B. (
)
)
C.
(
)
D.
(
)
22. Which equation of the line passes through (
) with a slope of
A.
C.
B.
D.
23. Which equation of the line passes through (
?
?
) and is parallel to the graph of the line
A.
C.
B.
D.
24. Which equation of the line passes through ( ) and is perpendicular to the graph of the
)?
line that passes through the points ( ) and (
A.
C.
B.
D.
25. Line k is represented by the equation,
. Which equation would you use to
determine the distance between the line k and point ( )?
A.
C.
B.
D.
Sent on 9/27/13
Geometry Semester 1 Instructional Materials
2013-2014
26. In a coordinate proof, which of the following would be most useful to prove that triangles
are congruent by the Side-Side-Side Triangle Congruence Theorem?
A. Distance formula
B. Midpoint formula
C. Corresponding parts of congruent triangles are congruent (CPCTC)
D. Slope formula
27.
( ) is the midpoint of ̅̅̅̅. The coordinates of S are (
of R?
A. (
)
B. (
)
C. (
)
D. (
), what are the coordinates
)
28. Use slope or the distance formula to determine the most precise name for the figure:
(
) (
) ( ) (
).
A. Kite
B. Rhombus
C. Trapezoid
D. Square
29. Which conclusion can be drawn from the given facts in the diagram?
A. ̅̅̅̅ bisects
B.
C. ̅̅̅̅
D.
Sent on 9/27/13
̅̅̅̅
Geometry Semester 1 Instructional Materials
2013-2014
30. Which of the following 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 angles.
31. If
, which of the following is true?
A.
B.
C.
D.
and ̅̅̅̅
32. In the figure
̅̅̅̅. What information is needed to prove that
by SAS?
A. ̅̅̅̅
̅̅̅̅
B. ̅̅̅̅
̅̅̅̅
G
L
C.
D.
A
D
E
O
33. In the figure
congruence is true?
and
A.
by ASA
B.
by SSS
C.
by SAS
D.
by SAS
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. Which of the following statements is about
Geometry Semester 1 Instructional Materials
2013-2014
34. Refer To the figure to complete the congruence statement,
.
A.
B.
C.
D.
35. Which theorem can be used to conclude that
?
A. SAA
E
B
B. SAS
C
C. SSS
D
D. AAA
A
36. In the figure, identify which congruence statement is true. Then find
A.
by HL
B.
by HL
C.
by HL
D.
by HL
.
37. Determine which postulate or theorem can be used to prove the pair of triangles congruent.
A. AAS
B. SAS
C. ASA
D. SSS
Sent on 9/27/13
Geometry Semester 1 Instructional Materials
For #38-39 use the following:
Given: is the midpoint of ̅̅̅̅̅ ;
Prove:
2013-2014
Q
M
N
P
Statements
is the midpoint of ̅̅̅̅̅ ;
Reasons
Given
Definition of Midpoint
38.
Given
̅̅̅̅
̅̅̅̅
Reflexive property of congruence
39.
38. Choose one of the following to complete the proof.
A. ̅̅̅̅̅
̅̅̅̅
B. ̅̅̅̅̅
̅̅̅̅
C. ̅̅̅̅̅
̅̅̅̅
D. ̅̅̅̅
̅̅̅̅
39. Choose one of the following to complete the proof.
A. Reflexive property of equality
B. SSA Congruence
C. SAS Congruence
D. AAS Congruence
40. Given
her proof?
, Anna is proving
. Which statement should be part of
A.
N
B.
2
C.
D.
1
M
Sent on 9/27/13
3
4
P
Geometry Semester 1 Instructional Materials
41. In the figure,
. What is the value of y?
A.
B.
C.
D.
42. Reflecting over which line will map the rhombus onto itself?
A.
B.
C.
D.
43. What is the measure of
in Parallelogram
(
A.
B.
C.
D.
Sent on 9/27/13
)
, given the following:
2013-2014
Geometry Semester 1 Instructional Materials
2013-2014
44. What is the value of x in the rectangle?
A.
B.
C.
D.
45. Which of the following is NOT always true of Parallelogram
A. ̅̅̅̅
̅̅̅̅ ̅̅̅̅
̅̅̅̅
B. ̅̅̅̅
̅̅̅̅ ̅̅̅̅
̅̅̅̅
?
C.
D.
) ( ) and (
46. Given points (
point A in order for the quadrilateral
A.
(
)
B.
(
)
C.
(
)
D.
(
)
47.
is a rhombus. If
A.
B.
C.
D.
Sent on 9/27/13
). Which of the following points must be
to be a parallelogram?
, what is the value of
?
Geometry Semester 1 Instructional Materials
2013-2014
48. Based on the figure below, which statements are true?
I.
The figure is a rectangle
II.
The figure is a parallelogram
III.
IV.
V.
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
49. 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. ̅̅̅̅ ̅̅̅̅ and ̅̅̅̅ ̅̅̅̅, even when the angles
change. Why is the frame always a parallelogram?
A. The angles always stay the same, so
B. All sides are congruent, so
is a parallelogram.
is a parallelogram.
C. One pair of opposite sides is congruent and parallel, so
D. One pair of opposite sides is congruent, so
50. Which statement is true?
A. All quadrilaterals are rectangles.
B. All rectangles are parallelograms.
C. All parallelograms are rectangles.
D. All quadrilaterals are squares.
Sent on 9/27/13
is a parallelogram.
is a parallelogram.
Geometry Semester 1 Instructional Materials
2013-2014
1.
B
11.
B
21.
D
31. A
41.
B
2.
D
12.
A
22.
B
32. B
42.
A
3.
D
13.
D
23.
A
33. A
43.
B
4.
B
14.
C
24.
B
34. B
44.
B
5.
C
15.
C
25.
D
35. B
45.
A
6.
B
16.
D
26.
A
36. D
46.
C
7.
A
17.
C
27.
D
37. A
47.
A
8.
D
18.
D
28.
B
38. B
48.
C
9.
A
19.
C
29.
C
39. C
49.
C
10. B
20.
B
30.
C
40. D
50.
B
Sent on 9/27/13