Download Hon Geometry Midterm Review

Name________________________________________________Period_____Date__________________ Hon Geometry Midterm Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. One way to show that two triangles are similar is to show that ______.
a. two angles of one are congruent to two angles of the other
b. two sides of one are proportional to two sides of the other
c. a side of one is congruent to a side of the other
d. an angle of one is congruent to an angle of the other
____
2. For the figure shown, which statement is not true?
a.
b.
c.
d.
____
3. Choose the statement that is NOT ALWAYS true. For a rhombus ________.
a. each diagonal bisects a pair of opposite angles
b. all four sides are congruent
c. the diagonals are congruent
d. the diagonals are perpendicular
____
4. Which statement is false?
a. If a quadrilateral is a square, then it is not a kite.
b. Some parallelograms are rhombuses.
c. All parallelograms are quadrilaterals.
d. If a quadrilateral is a rectangle, then it is a kite.
Numeric Response
1. Armando lives on one end of a street with a newsstand on the other. Armando picks up newspapers at the
newsstand and then delivers them to 14 equally-spaced houses on his way back. He travels from the
newsstand to the first house, then delivers a newspaper to each house. At the end of his route, he continues
GRZQWKHVWUHHWDQGJRHVKRPH)LQGWKHGLVWDQFHIURPWKHODVWKRXVHWR$UPDQGR¶VKRPH
Event
$UPDQGR¶V
newspaper
delivery route
Distance from
Newsstand to
$UPDQGR¶V
Home
Distance from
Newsstand to
First House
Distance
Between
Houses
Distance from
Last House to
$UPDQGR¶V
Home
340 m
30 m
20 m
?
Name________________________________________________Period_____Date__________________ 2. The supplement of an angle is 26 more than five times its complement. Find the measure of the angle.
3. Find the value of x so that
.
m
(6x + 5)º
(5x - 12)º
n
4. Find the value of x.
(2.5x + 6)o
Short Answer
1. Name a plane that contains
.
R
W
C
A
T
2. D is between C and E.
C
=
D
4x + 8
6x
,
=
27
, and DE = 27. Find CE.
E
Name________________________________________________Period_____Date__________________ 3. Find the measure of
. Then, classify the angle as acute, right, or obtuse.
C
D
B
O
4. m
and m
A
. Find m
.
I
L
K
J
5.
bisects
,m
6. Tell whether
, and m
and
. Find m
.
are only adjacent, adjacent and form a linear pair, or not adjacent.
F
B
1
A
2
3
4
C
G
7. Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4, ±
2) to U(±2, 3).
Name________________________________________________Period_____Date__________________ 8. Name all pairs of vertical angles.
J
M
L
K
N
9. Find the coordinates of the midpoint of
with endpoints C(1, ±6) and M(7, 5).
y
8
6
M
4
2
±
±
±
±
2
4
6
8
x
±
±
±
C
±
10. Name three collinear points.
P
G
N
R
11. Identify the property that justifies the statement.
and
. So
.
12. Write a justification for each step, given that
E
F
G
.
H
Given information
[1]
Segment Addition Postulate
[2]
Subtraction Property of Equality
Name________________________________________________Period_____Date__________________ 13. Write a two-column proof of the statement
.
Given: AB = CD; BF = FC
Prove:
A
B
F
C
D
Two-column proof:
Statements
1.
;
2. [1]
3. [2]
4.
5.
14. Write a two-column proof.
Given: m + m = 90 , m
Reasons
1. Given
2. Addition Property of Equality
3. Segment Addition Postulate
4. Substitution
5. Definition of congruent segments
+m
= 90 , m
=m
4
3
2
1
Prove: m
=m
Complete the proof.
Proof:
1. m
2. [1]
3. m
4. m
5. m
6. m
+m
+m
=m
+m
=m
Statements
= 90
=m
+m
=m
+m
Reasons
1. Given
2. Given
3. Substitution Property
4. Given
5. [2]
6. [3]
Name________________________________________________Period_____Date__________________ 15. Write a flowchart proof.
Given:
Prove:
1
2
3 4
Complete the proof.
Flowchart proof:
Given
[1]
Definition of linear pair
[2]
Definition of
congruent segments
16. Write a two-column proof.
B
1
3
2
A
Given:
Prove:
C
is a right angle.
are complementary.
Complete the proof.
Two-column proof:
Statements
1.
is a right angle.
2. m
3.
4.
5.
6.
7.
are complementary.
Reasons
1. Given
2. Definition of a right angle
3. [1]
4. Substitution
5. [2]
6. Substitution
7. Definition of complementary angles
Name________________________________________________Period_____Date__________________ 17. Identify the transversal and classify the angle pair
n
m
1
2
3
4
9 10
5 6
l
8
18. Find m
12 11
7
.
>>
A
xº
C
(3x - 70)º
>>
B
19. Find m
.
R
>>
U
[±ž
T
S (3x)º
>>
V
and
.
Name________________________________________________Period_____Date__________________ 20. Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two transversals
to the violin strings. Find x and y in the diagram.
100º
(4x + y)º
(8x + y)º
60º
21. Use slopes to determine whether the lines are parallel, perpendicular, or neither.
22. Use the information
show that
.
, and the theorems you have learned to
l
1
2
23. Find
m
in the diagram. (Hint: Draw a line parallel to the given parallel lines.)
>>
)
)
1
>>
Name________________________________________________Period_____Date__________________ 24. Write a two-column proof.
Given:
Prove:
t
1 2
m
l
Complete the proof.
Proof:
Statements
Reasons
1. [1]
2.
3.
1. Given
2. [2]
3. [3]
25. Write the equation of the line with slope 2 through the point (4, 7) in point-slope form.
26. Determine whether the lines
and
are parallel, intersect, or coincide.
27. Use the slope formula to determine the slope of the line.
y
8
6
4
2
±
±
±
±
±
2
4
6
x
8
±
A
±
B
±
28. Graph the line
29. Classify
.
by its angle measures, given m
D
25º
60º
A
75º
B
C
,m
, and m
.
Name________________________________________________Period_____Date__________________ 30. Classify
by its side lengths.
A
8
B
C
8
31.
is an isosceles triangle.
is the longest side with length
.
=
and
=
. Find
.
8 x+ 5
A
B
3 x +9
4x+ 4
C
32. Daphne folded a triangular sheet of paper into the shape shown. Find
, and m
.
E
D
C
A
61º
42º
22º
B
, given
,
Name________________________________________________Period_____Date__________________ 33. Given:
Identify all pairs of congruent corresponding parts.
A
M
B
C
34. Given:
O
N
,
,
. T is the midpoint of
.
R
S
T
U
Prove:
Complete the proof.
Proof:
Statements
Reasons
1.
2.
and
are right angles.
3.
4.
5.
6.
7. T is the midpoint of
.
8.
9.
10.
35.
.
B to C to D to E.
and
B
are equilateral.
D
C
A
G
F
1. Given
2. [1]
3. Right Angle Congruence Theorem
4. Given
5. [2]
6. Given
7. Given
8. Definition of midpoint
9. [3]
10. Definition of congruent triangles
E
and
. Find the total distance from A to
Name________________________________________________Period_____Date__________________ 36. Given the lengths marked on the figure and that
bisects
, use SSS to explain why
.
4 cm
E
A
3 cm
3 cm
D
4 cm
C
B
37. The figure shows part of the roof structure of a house. Use SAS to explain why
.
R
||
S
||
T
U
Complete the explanation.
It is given that [1]. Since
and
are right angles, [2] by the Right Angle Congruence Theorem. By
the Reflexive Property of Congruence, [3]. Therefore,
by SAS.
38. Use AAS to prove the triangles congruent.
Given:
,
Prove: 'ABC 'HGF
,
G
>
>>
A
>
F
C
|
|
H
>>
B
Proof:
Given
1.
'ABC 'HGF
Given
2.
AAS
Name________________________________________________Period_____Date__________________ 39. Determine if you can use the HL Congruence Theorem to prove 'ACD 'DBA. If not, tell what else you
need to know.
P
A
B
|
^
^
|
C
D
Q
40. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
L
J
K
B
A
C
Name________________________________________________Period_____Date__________________ 41. Given:
Prove:
,
bisects
F
B
)
C
)
A
D
G
Complete the flowchart proof.
Proof:
Given
bisects
Given.
1.
2.
'ACB 'ACD
Definition of
angle bisector.
4.
5.
3.
42. Given: A(3, ±1), B(5, 2), C(±2, 0), P(±3, 4), Q(±5, ±3), R(±6, 2)
Prove:
Complete the paragraph proof.
,
'ABC >@ by [4], and
, and
. So
by [5].
,
, and
. Therefore
Name________________________________________________Period_____Date__________________ 43. Write an equation for the line parallel to the line shown that passes through the point (±2, 3).
y
5
4
3
2
1
±
±
±
±
±
±
1
2
3
4
x
5
±
±
±
±
44. Find CA.
A
)
s+ 2
)
)
C
2 s 10
B
45. Find the measure of each numbered angle.
>
|
|
3 1
R
117
2
>
46. Given that
bisects
Y
X
Z
W
and
, find
.
Name________________________________________________Period_____Date__________________ 47. Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as
shown in the diagram. What is the width of the reservoir (BC across the base)?
120 m
B
X
120 m
A
150 m
100 m
Y
100 m
C
48. If two polygons are SIMILAR, then the corresponding sides must be _____.
49. The perimeter of 'PQR is 80, PQ = 30, 'PQR a'STU, and ST = 18. What is the perimeter of 'STU?
50. Two ladders are leaning against a wall at the same angle as shown.
How far up the wall does the shorter ladder reach?
51.
Triangles LMN and NWR are right triangles. What is the length of
Name________________________________________________Period_____Date__________________ 52. The postulate or theorem that can be used to prove that the two triangles are similar is _____.
53. Consecutive angles in a parallelogram are always ________.
54. Find the value of the variables in the parallelogram.
55. (2, 3) and (3, 1) are opposite vertices in a parallelogram. If (0, 0) is the third vertex, then the fourth vertex is
_____.
56. Isosceles trapezoid JKLM has legs
find the value of x.
and
, and base
If
and
57. For the trapezoid shown below, the measure of the midsegment is _______.
58. Use slope or the Distance Formula to determine the most precise name for the figure: A(±1, ±4), B(1, ±1), C(4,
1), D(2, ±2).
Name________________________________________________Period_____Date__________________ 59. In the diagram,
is similar to
. Write the statement of proportionality.
60. In
and
In
triangles are similar, and if so, write a similarity statement.
61. Given:
. Find the length of
.
62. Find the value of x to one decimal place.
The polygons in each pair are similar. Find the value of each variable.
63.
and
State whether the
Name________________________________________________Period_____Date__________________ 64.
Find the sum of the measures of the interior angles in the figure.
65. Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 2880°.
66. Find AM in the parallelogram if
and
67. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure?
68. In what type of trapezoid are the base angles congruent?
Performance Task:
69. Draw a Venn diagram showing the relationships among the various types of quadrilaterals.
Name________________________________________________Period_____Date__________________ Other
1. Complete the steps of this proof.
Given: parallelogram WXYZ
Prove:
2. Given:
#
and
Prove: VX = XT
V
U
X
S
T
Name________________________________________________Period_____Date__________________ 3. Use the distance formula to determine whether ABCD below is a parallelogram.
Name________________________________________________Period_____Date__________________ Hon Geometry Midterm Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
A
B
C
D
NUMERIC RESPONSE
1.
2.
3.
4.
50
74
17
21.6
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
plane WRT
CE = 105
m
; right
m
m
= 20°
only adjacent
7.8 units
;
1
9. (4, 2 )
10. R, G, and N
11. Transitive Property of Congruence
12. [1] Segment Addition Postulate
[2] Substitution Property of Equality
13. [1]
[2]
14. [1] m + m = 90
[2] Substitution Property
[3] Subtraction Property of Equality
15. [1]
and
are supplementary;
and
are supplementary
[2] Congruent Supplements Theorem
16. [1] Angle Addition Postulate
[2] Definition of congruent angles
17. The transversal is line l. The angles are corresponding angles.
18. m
= 35°
19. m
=
20.
Name________________________________________________Period_____Date__________________ 21. neither
22. By substitution,
and
By the Substitution Property of Equality,
.
By the Converse of the Alternate Interior Angles Theorem,
23.
= 135°
24. [1]
[2] 2 intersecting lines form linear pair of
s
lines .
[3] 2 lines to the same line
lines .
25.
26. intersect
2
27. 3
28.
y
12
10
8
6
4
2
±
±
±
±
±
2
4
6
8
10
12
x
±
±
±
29. obtuse triangle
30. equilateral triangle
31.
= 45
32.
=
33.
,
,
,
34. [1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Reflexive Property of Congruence
35. 98
36.
37. [1]
[2]
[3]
38. 1. Alternate Interior Angles Theorem
2. Alternate Exterior Angles Theorem
39. Yes.
40.
, HL
41. 1. Congruent Supplements Theorem
2.
3. Reflexive Property of Congruence
,
,
.
.
Name________________________________________________Period_____Date__________________ 42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
4. AAS
5. CPCTC
[1] PQ
[2]
[3] 'RPQ
[4] SSS
[5] CPCTC
y = 3x ± 3
CA = 14
m =
,m
=
300 m
proportional
48
18 ft
15.6 cm
AA Similarity Postulate
supplementary angles
x = 21°, y = 55°, z = 104°
11
2
57. 29
58. rhombus
56. 59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
,m
not similar
40
4.7
x = 12, y = 6
540°
18
9.5
A rhombus
an isosceles trapezoid
=
Name________________________________________________Period_____Date__________________ OTHER
1.
2.
3. Since AB = CD =
and BC = AD = 8, ABCD is a parallelogram.