Download 1 - Rancho High School

Geometry Semester 1 Study Guide
4. In the diagram below, mABC  42 .
1. Use the figure below.
A
2
1
3
4
5
D
 7 x  2 
 3x  
B
Which best describes the pair of angles:
4 and 5 ?
C
What is the value of x?
A. vertical
B. adjacent
C. linear pair
D. complementary
5. In the figure below, Y is between X and Z
and XZ  40 cm.
2. In the diagram below, DBF , EBC ,
and EBA are right angles.
a
3a + 8
E
X
F
Y
Z
What is the value of a?
D
3
2
1
A
4
B
C
Which best describes the pair of angles:
1 and 4 ?
6. What are the coordinates of the midpoint
of the segment joining the points
A  3, 4  and B  4, 2  ?
A. vertical
B. adjacent
C. supplementary
D. complementary
7. In the scientific method, after one makes
a conjecture, one tests the conjecture.
What type of reasoning is used?
A. conclusive
3. What is the distance between points
A  2, 6 and B  2, 3 ?
B. deductive
C. inductive
D. scientific
2015–2016
1
Geometry Semester 1 Study Guide
8. Write the inverse statement of:
If x = 5, then x > 3?
11. In the figure below, n m and l is a
transversal.
m
x°
n
117°
9. In the figure below, line m is a
transversal.
l
1
What is the value of x?
2
m
12. In the figure below, mFGH  65 .
What best describes the pair of angles:
1 and  2 ?
 2 x  17  
l
F
G
m
10. In the figure below, n m and l is a
transversal.
65°
H
What value of x would make line l
parallel to line m?
64°
n
 4 x  16 
13. Which is a valid classification for a
triangle?
m
l
A. Acute right
What is the value of x?
B. Isosceles scalene
C. Isosceles right
D. Obtuse equiangular
2015–2016
2
Geometry Semester 1 Study Guide
14. In the figure below, lines l and m are
parallel.
17. In the figures below,
ABCDEF  RSTUVW .
B
5
1
6
2
A
l
3
4
7
C
8
F
m
D
Which statement is true?
E
A. 1 and 3 are congruent.
W
B. 1 and 8 are supplementary.
R
C. 2 and 4 are supplementary.
D. 6 and 7 are congruent.
V
S
15. Use the triangle below.
U
x°
T
 3 x  3 
Which side of RSTUVW corresponds
to DE ?
45°
What is the value of x?
16. Given that PQR  JKL , PQ  4 x  12 ,
JK  7 x  6 , KL  2 x  17 , and
JL  5 x  7 , what is the value of x?
2015–2016
3
Geometry Semester 1 Study Guide
21. The statements for a proof are given
below.
18. Use the triangles below.
Given: Parallelogram ABCD
BX  DY
Prove:
BAX  YCD
X
B
A
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
D
Y
Proof:
19. In the diagram below, AB  DC and
AB DC .
A
C
STATEMENTS
1. Parallelogram ABCD
BX  DY
2. B  D
REASONS
3. AB  DC
4. ABX  CDY
5. 1  2
3.
4.
5.
1. Given
2.
What is the reason that the statement in
Step 4 is true?
C
E
B
22. Given that DEF  LMN ,
mD   2 x  15  , mL   3  x  2    ,
D
Which congruence postulate or theorem
would prove that these two triangles are
congruent?
and DF  4( x  17) , what is LN?
20. Given that RST  XYZ ,
mR   6n  1  , mY  108 , and
23. The RST is constructed with vertices
R  5,2  , S  4,1 , and T  2, 1 . What is
mZ   9n  4  , what is the value of n?
the length of ST ?
2015–2016
4
Geometry Semester 1 Study Guide
24. The statements for a proof are given
below.
Given:
Prove:
26. Three towns form a triangle on the map
below.
Geometria
AB  FD
B  D
A  F
9 miles
BC  DE
E
Euclid
B
Euler
7 miles
Which statement does NOT represent
possible distances between Euclid and
Geometria?
D
A
A. Between 2 and 7 miles apart.
F
C
B. Between 7 and 9 miles apart.
Proof:
C. Between 9 and 16 miles apart.
STATEMENTS
1.
2.
3.
4.
AB  FD
B  D
A  F
ABC  FDE
5. BC  DE
REASONS
1. Given
2. Given
3. Given
4. ______
5. Corresponding Parts
of Congruent Triangles
are Congruent
D. Between 49 and 81 miles apart.
27. In ABC , B is a right angle and
mA  40 . Write the list of sides in
order from longest to shortest?
What is the missing reason that would
complete this proof?
28. A triangle has two sides that have lengths
of 7 cm and 17 cm. Which could
represent the length of the third side of
the triangle?
25. In the isosceles triangle below,
mH  137 .
A. 24 cm
F
B. 18 cm
137°
G
C. 10 cm
D. 7 cm
H
What is the measure of F ?
2015–2016
5
Geometry Semester 1 Study Guide
29. The triangle below contains three
midsegments.
32. The triangle below shows a point of
concurrency. Lines l, m, and n, are
perpendicular bisectors of the triangle’s
sides.
x
m
l
14
11
z
9
n
y
What is the name of the point of
concurrency in the triangle?
What are the values of x, y, and z?
30. In BCD , SR is a midsegment, and
SQ DC .
33. Which figure is a polygon?
B
A.
Q
S
B.
5
D
12
R
C
What is the length of QC ?
C.
31. How many sides does a nonagon have?
2015–2016
D.
6
Geometry Semester 1 Study Guide
38. In the figure below, KLM  ABC .
34. Use the figure below.
A
L
60°
130°
8 cm
x°
40°
47°
K
What is the value of x?
10 cm
M
C
53°
B
Which statement must be true?
A. AC  8cm
B. BC  6cm
35. Parallelogram ABCD is given below.
A
11x + 9
C. mA  53
B
D. mC  80
31
D
6(x + 4)
C
39. Use the rhombus below.
What is the value of x?
B
A
65°
E
36. Which statement is true about a kite?
A. A kite has 4 congruent sides.
C
B. A kite has 2 pairs of parallel sides.
D
What is mCDE ?
C. A kite has perpendicular diagonals.
D. A kite has congruent diagonals.
37. Which statement below is true about an
isosceles trapezoid?
40. Given that FGH is an isosceles right
triangle, what is the measure of an acute
angle of the triangle?
A. Both pairs of opposite sides are parallel.
B. Both pairs of opposite sides are congruent.
C. One pair of opposite sides is congruent and
the other is parallel.
D. One pair of opposite sides is both parallel
and congruent.
2015–2016
7
Geometry Semester 1 Study Guide
For questions 44–46, use the diagram showing
parallelogram ABCD.
41. Use the figure below.
A
E
75°
I
H
41°
D
x°
B
F
G
C
44. A reflection across EG carries
parallelogram ABCD onto itself.
What is the value of x?
A.
True
B.
False
45. A rotation of 90° about I carries
parallelogram ABCD onto itself.
42. Geometric figures are displayed on a
computer screen in the following order:
triangle, concave quadrilateral, convex
pentagon, concave hexagon. Using
inductive reasoning, what prediction can
be made about the next figure?
A.
True
B.
False
46. A rotation of 180° about I carries
parallelogram ABCD onto itself.
A. It will be a concave heptagon.
B. It will be a convex heptagon.
A.
True
C. It will be a convex polygon, but the type
cannot be predicted.
B.
False
47. A transformation T maps all points (x,y)
to (x,-y). What type of transformation is
T?
D. It will be a polygon, but no other details
about it can be predicted.
43. What term describes a transformation
that does not change a figure’s size or
shape?
A.
similarity
B.
isometry
C.
collinearity
D.
symmetry
2015–2016
48. The point A(1, 2) is reflected about the
line x=k, then about the line x=6. The
final image is A’’(7, 2). What is the value
of k?
8
Geometry Semester 1 Study Guide
52. Use the figure.
49. Use the diagram. r s and m n .
s
r
m
3 4
1 2
n
8 7
6 5
List the angles in the diagram that must
be congruent to ?
Which shows the image of figure after a
reflection over the y-axis?
50. Use the diagram.
(A)
(B)
A translation maps GLT to G’L’T’. Write
the vector that describes the translation?
(C)
51. Given point A is located at (1, 3). What is
the final image of A after this series of
transformations?
(1) Reflect A across the y axis.
(2) Translate the image such that
 x, y    x  4, y  2 .
2015–2016
9
Geometry Semester 1 Study Guide
For questions 56–59, use the diagram.
53.
Use the diagram.
E
D
F
C
B
G
A
Which describes a figure formed by two
rays with a common endpoint?
A.
EDF
B.
DF
BG
ABC could map to ABC by a single
translation.
BCD
A.
True
B.
False
56.
C.
D.
In questions 54–55, use the diagram.
57.
B
3.8 cm
5.6 cm
55.
58.
C
A
54.
67°
ABC could map to ABC by a single
rotation.
A.
True
B.
False
ABC could map to ABC by a series
of two reflections.
A triangle DEF is constructed congruent
to triangle ABC.
A.
True
DE = 3.8 cm
B.
False
A.
True
B.
False
59.
AB = DE
A.
True
B.
False
2015–2016
10
ABC could map to ABC by a series
of two translations.
A.
True
B.
False
Geometry Semester 1 Study Guide
63. If you rotate ΔRST 180 about point U,
the most specific name for the resulting
quadrilateral is:
60. Use the diagram.
m

S
k
22°
44°
U
R
A
If a figure is reflected across ¸ then in
reflected across m, what single
transformation results in the same image?
61. Which of the following is not a
characteristic of all parallelograms?
A. Consecutive angles are supplementary
B. Opposite angles are congruent
C. Diagonals bisect each other
D. Diagonals are angle bisectors
62. Rectangle NOPQ. mPNO =25. Find
mPNQ.
O
N
Z
Q
2015–2016
P
11
o
V
x
T
Geometry Semester 1 Study Guide
Free Response
1. Given: 2  x  1  3  17
Prove: x = 8
Supply reasons for each step.
___________________________________________________________________________________
2. Use the figure provided to write a two-column proof.
Given: 2  3
AB  BC
Prove: AD BC
2015–2016
1
GO ON
Geometry Semester 1 Study Guide
Free Response
3. In the figure below, m || n.
(a) Draw rm rn (ABCD)
(b) Is there a single transformation that carries ABCD to its final image? If so, define the
transformation. If not, explain why it cannot exist.
m
C
n
B
D
A
2015–2016
2
GO ON
Geometry Semester 1 Study Guide
Free Response
4.
(a) Construct the perpendicular bisector of segment AB. Label the midpoint M.
A
B
(b) Construct the angle bisector of angle BAC.
B
A
C
2015–2016
3
GO ON
Geometry Semester 1 Study Guide
Free Response
5. Prove that the quadrilateral QUAD, having vertices Q(–1,3), U(4,2), A(1, –1), and D(–4,0), is a
Parallelogram.
6. Use the diagram to find the measure of the following angles, given that m n .
m1=________
m
m2 =________
n
105°
m3 =________
2
m4 =________
40°
m5 =________
2015–2016
1
4
4
3
5