Download Formal Geometry Semester 1 Instructional Materials

Formal Geometry Semester 1 Instructional Materials
2013-2014
2013-2014
Formal 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
Formal 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. Using slope and/or distance formulas, identify which of the following is the best name for
) (
) (
).
the figure: (
A. scalene triangle
B. isosceles triangle
C. equilateral triangle
D. obtuse triangle
2.
(
) is the midpoint of ̅̅̅̅. The coordinates of
are (
). What are the coordinates
of R?
A. (
B. (
)
C. (
)
D. (
3.
)
)
In the figure, which pair of angles is supplementary?
A.
B.
C.
D.
1
4
6
5
2
3
8
7
4. Which of the following are logically equivalent?
A. A statement and its converse
B. A statement and its inverse
C. A statement and its contrapositive
D. A statement, its converse, its inverse and its contrapositive
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
5. Two lines that do NOT intersect are always parallel.
Which of the following best describes a counterexample to the assertion above?
A. coplanar lines
B. parallel lines
C. perpendicular lines
D. skew lines
6. Determine which statement follows logically from the given statements.
If I am absent on a test day, I will need to make up the test. Absent students take the test
during their lunch time or after school.
A. If I am absent, it is because I am sick.
B. If I am absent, I will take the test at lunch time or after school.
C. Some absent students take the test at lunch time.
D. If I am not absent, the test will not be taken at lunch time or after school.
7. Determine whether the conjecture is true or false. Give a counterexample for any false
conjecture.
Given: Two angles are supplementary.
Conjecture: They are both acute angles.
A. False; either both are right or they are adjacent.
B. True
C. False; either both are right or one is obtuse.
D. False; they must be vertical angles.
8. Write the statement in if-then form.
A counterexample invalidates a statement.
A. If it invalidates the statement, then there is a counterexample.
B. If there is a counterexample, then it invalidates the statement.
C. If it is true, then there is a counterexample.
D. If there is a counterexample, then it is true.
Sent on 9/27/13
Formal Geometry Semester
65 1 Instructional Materials
60
110
120
2013-2014
9. Which statement is true based on the figure?
A.
b
B.
a
c
C.
D.
65
110
d
60
120
e
10. Point A is reflected over the line ⃡ . Which of the following is NOT true of line ⃡ ?
A. line ⃡
is perpendicular to line ⃡
B. line ⃡
is perpendicular to line ⃡
C. line ⃡
bisects line segment ̅̅̅̅
D. line ⃡
bisects line segment ̅̅̅̅̅
11. Given the following:
is a complement of
is a supplement of
is a supplement of
is a complement of
is a complement of
is a supplement of
Then
A.
C.
B.
D.
Sent on 9/27/13
Formal 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 the 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
measures.
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
For #14-15 use the following:
Given:
Prove:
t
1
4
8
Statements
2
3
5 6
7
p
q
Reasons
Given
14.
Alternate Interior Angles Theorem
15.
Substitution Property of Equality
14. Choose one of the following to complete the proof.
A.
B.
C.
D.
15. 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. Congruent Supplements 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
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
16. Complete the statement:
If two lines are perpendicular, then ___________________________________________.
A. the lines do not intersect
B. the slopes of the two lines are equal
C. the product of the slopes for the two lines is equal to negative one
D. the product of the slopes for the two lines is equal to zero
17. A student proves that every right triangle is isosceles by assigning coordinates as shown
and by using the distance formula to show that
and
. Which of the
following best explains the student’s error?
A. The proof is not correct because the
assigned coordinates do not result in a
general right triangle.
B. The proof is correct because the assigned
coordinates result in a general right
triangle.
C. The proof is not correct because the
assigned coordinates result in a rectangle.
D. The proof is not correct because the
assigned coordinates result in an obtuse
triangle.
18. Which equation of the line passes through (
) with a slope of
A.
C.
B.
D.
?
19. The equations of four lines are given. Identify which lines are parallel.
I.
II.
(
)
III.
IV.
A. I, II, and IV
C. III and IV
B. I and II
D. None of the lines are parallel
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
20. Which equation of the line passes through (
line
?
2013-2014
) and is perpendicular to the graph of the
A.
C.
B.
D.
21. 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.
22. 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.
23. 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 transformations that
maps one to the other.
D. If two triangles are congruent, then they must be right angles.
24. If
, which of the following is true?
B.
̅̅̅̅
̅̅̅̅
̅̅̅̅
̅̅̅̅
C.
̅̅̅̅
̅̅̅̅
D.
̅̅̅̅
̅̅̅̅
A.
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
and ̅̅̅̅
25. In the figure
2013-2014
̅̅̅̅. What information is needed to prove that
by SAS?
A. ̅̅̅̅
̅̅̅̅
B. ̅̅̅̅
̅̅̅̅
G
L
C.
D.
D
A
E
O
26. In the figure
congruence is true?
and
A.
by ASA
B.
by SSS
C.
by SAS
D.
by SAS
. Which of the following statements is about
27. Refer To the figure to complete the congruence statement,
.
A.
B.
C.
D.
28. Which theorem can be used to conclude that
?
A. SAA
B. SAS
C. SSS
E
B
C
D
D. AAA
A
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
and ̅̅̅̅
29. In The figure
2013-2014
̅̅̅̅ . Which theorem can be used to conclude that
?
A. SSA
B. AAA
C. SAS
D. HL
30. Determine which postulate or theorem can be used to prove the pair of triangles congruent.
A. AAS
B. SAS
C. ASA
D. SSS
31. Given
her proof?
, Anna is proving
. Which statement should be part of
A.
N
B.
2
C.
D.
1
M
32. In the figure,
A.
B.
C.
D.
Sent on 9/27/13
. What is the
?
3
4
P
Formal Geometry Semester 1 Instructional Materials
2013-2014
For #33 use the following:
Given: is the midpoint of ̅̅̅̅̅ ;
Prove:
Statements
is the midpoint of ̅̅̅̅̅ ;
Reasons
Given
Definition of Midpoint
[1]
Given
̅̅̅̅
̅̅̅̅
Reflexive property of congruence
[2]
33. Choose one of the following to complete the proof.
A. [1] ̅̅̅̅̅ ̅̅̅̅
[2] SAS Congruence
B. [1] ̅̅̅̅̅ ̅̅̅̅
[2] SAS Congruence
C. [1] ̅̅̅̅̅ ̅̅̅̅
[2] Linear Pair Theorem
D. [1] ̅̅̅̅̅ ̅̅̅̅
[2] AAS Congruence
34. In the figure,
A.
B.
C.
D.
Sent on 9/27/13
. What is the value of y?
Formal Geometry Semester 1 Instructional Materials
2013-2014
35. In a coordinate proof, which of the following would be most useful to prove that triangles
are congruent by the SSS Triangle Congruence Theorem?
A. Distance formula
B. Midpoint formula
C. Corresponding parts of congruent triangles are congruent (CPCTC)
D. Slope formula
36. For a coordinate proof concerning an isosceles triangle, which coordinates might be easiest
to use?
A. (
)(
)(
B. (
)(
C. (
)(
)(
D. (
)(
)(
)
)(
)
)
)
37. In the figure,
the
in terms of x.
. Find
E
A
A.
B.
C.
B
D.
C
38. Suppose you wish to prove the following using indirect proof.
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Which of the following would you try to contradict in an indirect proof.
A. Two parallel lines are cut by a transversal.
B. Alternate interior angles are congruent.
C. Alternate interior angles are not congruent.
D. Two parallel lines are not cut by a transversal.
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
For #39 use the following:
Given: ̅̅̅̅ ̅̅̅̅ and
⃡
Prove: ⃡
Statements
̅̅̅̅ ̅̅̅̅
Reasons
Given
39.
Given
Transitive property of congruence
⃡
⃡
Corresponding Angles Theorem
39. Choose one of the following to complete the proof.
A. Isosceles Triangle Symmetry Theorem- If the line contains the bisector of the vertex
angle of an isosceles triangle, then it is a symmetry line for the triangle.
B. Isosceles Triangle Coincidence Theorem- If the bisector of the vertex angle of an
isosceles triangle is also the perpendicular bisector of the base, then the median to the
base is the same line
C. Isosceles Triangle Base Angle Converse Theorem- If two angles of a triangle are
congruent, the sides opposite those angles are congruent
D. Isosceles Triangle Base Angle Theorem- If two sides of a triangle are congruent, then
the angles opposite those sides are congruent
40. Which of the following best describes the shortest distance from a vertex of a triangle to the
opposite side?
A. altitude
B. diameter
C. median
D. segment
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
For #41-42 use the following:
Given: ̅̅̅̅ is a median of isosceles
Prove:
Statements
̅̅̅̅ is a median
Reasons
̅̅̅
41.
42.
̅̅̅̅
̅̅̅
Given
Definition of isosceles triangle
̅̅̅̅
Reflexive property of congruence
SSS Congruence
41. Choose one of the following to complete the proof.
A. Definition of angle bisector- If a ray divides an angle into two congruent angles, then it
is an angle bisector.
B. Definition of segment bisector- If any segment, line, or plane intersects a segment at its
midpoint, then it is a segment bisector.
C. Definition of isosceles triangle- If a triangle has at least two congruent sides, then it is
an isosceles triangle.
D. Definition of median- If a segment is a median, then it has endpoints at the vertex of a
triangle and the midpoint of the opposite side.
42. Choose one of the following to complete the proof.
A. ̅̅̅
̅̅̅̅
B. ̅̅̅
̅̅̅
C. ̅̅̅̅
̅̅̅̅
D. ̅̅̅
̅̅̅̅
43.
is the angle bisector of
A.
B.
C.
D.
Sent on 9/27/13
. What is the value of x?
Formal Geometry Semester 1 Instructional Materials
2013-2014
44. Which of the following terms best describe the transformation below?
A. dilation
B. reflection
C. rotation
D. translation
45. What are the coordinates for the image of
) (
origin and a translation of (
A.
(
)
(
)
B.
(
)
(
C.
(
)
(
)
(
D.
(
)
(
)
(
)
(
(
after a rotation
)?
clockwise about the
)
)
)
)
K
G
H
is (
46. Point Y of
translation (
A.
(
B.
(
)
)
)?
). What is the image of Y after
C.
(
D.
(
is transformed using the
)
)
) is rotated
47. 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. (
Sent on 9/27/13
)
)
C.
(
)
D.
(
)
Formal Geometry Semester 1 Instructional Materials
48. Reflect point H across the line ⃡
A. ̅̅̅̅ ̅̅̅̅
B. ̅̅̅̅
̅̅̅̅̅
C. ̅̅̅̅
̅̅̅̅̅
D. ̅̅̅̅
̅̅̅̅̅
2013-2014
to form point H’, which of the following is true?
49. What is the scale factor for the dilation of
H
G
F
to image
?
A.
B.
C.
D.
) (
) to the triangle given below. Which of the
50. Apply the dilation (
following is the perimeter of the image?
A.
B.
C.
D.
Sent on 9/27/13
Formal Geometry Semester 1 Instructional Materials
2013-2014
1.
B
11.
B
21.
B
31. D
41.
D
2.
D
12.
A
22.
D
32. C
42.
B
3.
B
13.
D
23.
C
33. B
43.
A
4.
C
14.
D
24.
A
34. B
44.
C
5.
D
15.
C
25.
B
35. A
45.
B
6.
B
16.
C
26.
A
36. B
46.
C
7.
C
17.
A
27.
B
37. B
47.
A
8.
B
18.
B
28.
B
38. C
48.
D
9.
D
19.
A
29.
D
39. D
49.
D
10. C
20.
C
30.
A
40. A
50.
A
Sent on 9/27/13