Download Day 1: Show all work. 1. Write a counterexample for the following

Review for Geometry Benchmark #1
Day 1: Show all work.
1. Write a counterexample for the following conditional?
If you live in Peoria, then you live in Illinois.
2. Which conditional does not have the same
truth value as its converse?
a.
b.
c.
d.
If x – 11 = 4, then x = 15.
If a figure is a quadrilateral, then it has
four sides.
If x = 14, then
.
If an angle has a measure of 90, then it is
right angle.
3. Which two lines are parallel?
I.
II.
III.
4. In the figure shown,
the following statements is false?
a.
b.
c.
Name ___________________Period ____
8. Write a recursive formula for the sequence
7, 13, 19, 25, 31, ... Then find the next term.
9. Write a recursive formula for the sequence
15, 26, 48, 92, 180, ... Then find the next term.
a.
b.
c.
d.
where
= 15; 356
where
= 15; 356
where
= 15; 356
, where
= 15; 356
10. Generate the first five terms in the sequence
Using the explicit formula.
. Which of
11. What is the name of the ray that is opposite
D
DEC and DEA are
vertical angles.
C
DEA and AEB are
adjacent angles.
B
A
d.
5. Draw a three-dimensional figure for this net?
?
12. What is the intersection of plane WXYZ
and plane VUYZ?
13.
6. What is the equation for the line, in point-slope form,
that passes through points (8, –8) and (9, 3)?
7. Are the lines y = –x – 4 and 4x + 4y = 12
perpendicular? Explain.
and
are complementary angles.
m
=
, and m
=
.
Find the measure of each angle.
14.
and
are a linear pair.
, and
. Find the measure of each angle.
19. Complete the two-column proof.
15. Draw a Venn diagram to illustrate this conditional:
Two points are always collinear.
Given:
Prove:
16. Find the perimeter of parallelogram ABCD with vertices
A(–2, 6), B(1, 2), C(–2, –2), and D(1, –6).
y
10
A
5
20. Find the value of x given f //g.
The diagram is not to scale.
B
f
2x
–10
–5
5
10 x
4 x + 18
C
–5
D
g
21. Find the value of x for which l is parallel to m. The
diagram is not to scale.
92°
–10
( 2 x - 20 )º
22. What is an equation in point-slope form for the
AC = BD =
line perpendicular to y = 5x – 4 that contains (7, –6)?
AB = CD =
Perimeter =
17. Use the Law of Detachment and the Law of Syllogism to
draw a conclusion from the three given statements.
If a person lives in Los Angeles, then they live in California.
If a person lives in California, then they live in North
America.
Bonnie lives in Los Angeles.
18. Find the values of x and y.
23. Generate the first five terms in the sequence
using the explicit formula.
24. Write a recursive formula for the sequence
8, 4, 0, –4, –8, .... Then find the next term.
5y°
130°
2x + 8°
25. Write an explicit formula for the sequence
6, 5, 4, 3, 2, ... Then find
.
Drawing not to scale
l
m
Review for Geometry Benchmark #1
Review for Geometry Benchmark #1
Name ___________________Per-Seat # ____
Name ___________________Per-Seat # ____
Day 2: Show all work on this paper.
34. Find the value of x. The diagram is not to scale.
26. Name the intersection of plane RNP and plane MNP.
119°
27. If
find the
values of x, EF, and FG. The drawing is not to scale.
E
F
G
45°
x°
35. Write the conditional statement that the
Venn diagram illustrates.
Quadrilaterals
28. If T is the midpoint of
Squares
what are ST, TU, and SU?
S
T
8x
U
36. Is the following conditional true or false? If it is true,
4 x + 24
explain why. If it is false, give a counterexample.
If an animal is a chicken, then it lays eggs.
29. Supplementary angles are two angles whose measures
have a sum of _______.
Complementary angles are two angles whose measures
have a sum of _______.
30.
bisects
37. Write the converse of the statement. If the converse
is true, write true; if not true, provide a
counterexample.
and
Solve for x and find
The diagram is not to scale.
If x = 11, then x2 = 121.
38. What is the value of x given
Identify the missing justifications.
.
(2x)°
31. M is the midpoint of
for the points
C(1, 10) and F(5, 4). Find MF.
4(x – 1)°
Drawing not to scale
32. T(10, 12) is the midpoint of
The coordinates of D
are (10, 16). What are the coordinates of C?
33. Find the values of x and y.
The diagram is not to scale.
(x – 5)°
59°
(y + 10)°
72°
?
39. What is the value of x? Justify each step.
41. Fill in the missing reasons in this proof?
n
4x
p
d
2x + 1
l
b
c
Drawing not to scale
h
j
Given:
Prove:
and
are supplementary.
m
k
40. State the missing reasons in this proof.
42. Which diagram suggests a correct construction of a
line parallel to given line w and passing through
given point K?
Given:
Prove:
q
1 2
3 4
5 6
7 8
c.
a.
p
r
K
K
w
w
d.
b.
K
K
w
w
43. Construct the line that is perpendicular to the
given line through the given point.
46. Find the values of x, y, and z.
The diagram is not to scale.
42°
13°
C
55°
A
x°
z°
y°
B
47. What is the equation in point-slope form for the
line parallel to y = 2x + 12 that contains P(–1, –7)?
44. What are the names of four coplanar points?
WRITE YES OR NO FOR EACH CHOICE.
A
D
48. Two points are ____ collinear.
L
J
K
a. Always
b. Sometimes
c. Never
B
____ a.
____b.
____c.
____d.
____e.
____f.
Points A, D, J, and K are coplanar.
Points B, J, K, and L are coplanar.
Points A, L, J, and K are coplanar.
Points A, B, D and J are coplanar.
Points A, D, L, and J are coplanar.
Points A, B, J and L are coplanar.
49. Which conditional has the same truth value as its
converse?
a.
b.
c.
d.
If an angle has a measure of 75, then it is acute.
If Bob lives in Cottonwood, then he lives in AZ.
If a figure is a triangle, then it has three sides.
If x = 9, then x  9 .
45. Find the area of the circle in terms of .
50. Use the Law of Detachment and the
Law of Syllogism to draw a conclusion from
the three given statements.
42 in.
If you do a lot of reading, then you will improve your
vocabulary.
If you improve your vocabulary, then you will do well on
your SAT’s.
Brandon does a lot of reading.
CONCLUSION: ________________________________
________________________________
________________________________
________________________________.
Review Geometry Benchmark #1 ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Justin lives in Peoria, AZ.
C
II & III
A
cube 
(y + 8) = 11(x – 8)
Yes; their slopes have product –1.
; 37
A
–7, –18, –29, –40, –51
36.
False; Sample: Roosters
(male chickens that do not lay eggs)
37.
If x2 = 121, then x = 11.
False; if x2 = 121, then x can be equal to –11.
38.
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
39.
a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
40.
a. Vertical angles.
b. Transitive Property.
c. Alternate Interior Angles Converse.
11.
12.
13.
14.
15.
= 50,
= 40
Collinear
2 points
16. 26 units
17. Bonnie lives in North America.
18. x = 61, y = 10
19.
a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
20. 27
21. 56
1
22. y + 6 =  (x – 7)
5
23. 6, 9, 12, 15, 18
24.
41.
.
42.
A
C
; –12
25.
; –7
26.
27.
28.
29.
30.
x = 8, EF = 6, FG = 12
ST = 48, TU = 48, and SU = 96
180; 90
x = 11,
31.
32.
33.
34.
35.
13
(10, 8)
x = 77, y = 39
16
If a figure is a square, then it is a quadrilateral.
43.
A
44.
45.
46.
47.
48.
49.
50.
B
N,Y,Y,N,Y,N
441 in.2
x = 83, y = 70, z = 97
y + 7 = 2(x + 1)
A
C
Brandon will do well on his SAT’s.