Download cp geom midterm reviewANSW

Manchester High School
Geometry Midterm
REVIEW
E
1. Find the area of the rectangle EFGH.
Use Pythagorean theorem
20 in
F
25in
H
G
Answer: 300 sq. in.
m•
2. Which is a group of coplanar points?
a) W,X,Y,Z
b) A,W,Y,Z
c) B,W,X,Y
d) A,B,Y,Z
A
•W
X
• Y
l
•Z
•
B
3. Points S,T, and W are collinear, with W between S and T. Find SW if ST = 52 and WT = 27.
Answer: 25
•
R
S
4. WR and WT are opposite rays, as are WS and WV.
Which angle forms a linear pair with ∠TWU?
Answer:
V
Angle RWU
W
•
•
•T
•
U
Questions
Question9 4& 10
5. Which point is in the exterior of ∠AXB?
•F
•E
Answer: Point E, C or D
B
•
C
•
•
•C
•
X
D
Questions
12
&
13
Question 5
A
6. If the m ∠DAE = 65 and m∠DAF = 132, find m∠EAF.
Answer: 67
B
•A
•F
•
D•
E
7. Find m∠2 given that m∠1 = 33, m∠3 = 19, and m∠RTV = 105.
Answer: 53
U
S •
•
•
2
•R
1
3
T
V
Question 7
Manchester High School
Geometry Midterm
REVIEW
In the figure l ∣∣ m, and n and p are transversals.
m
l
10
8. Which type of angles are ∠8 and ∠10?
9
2

1
8 7
5 6
3
4

Answer: Corresponding
9. If m∠7 = 9x +5 and m∠9 = x +37, find the value of x.
p
Question 54 - 56
Questions 8-9
Questions 46 - 48
9x + 5 = x + 37
8x = 32
x=4
10. What is the m∠7? 113
Given: m∠ 6 = 67 and l ∣∣ m
t
1 8
2 7
3 6
4 5
11. Find m∠4.
Answer: 67
m
l
Questions 10-11
12. Find the slope of the line passing through points at (0,5) and (-1,2)
-3/-1 = 3 Slope = 3
13. Which selection is correct for the network?
a) m1 = 50, m2 = 130, m3 = 50
b) m1 = 50, m2 = 130, m3 = 130
c) m1 = 130, m2 = 50, m3 = 50
d) m1 = 130, m2 = 50, m3 = 130
6
1
130
5
3
75
2
4
16. What is the measure of ABC?
Answer: 79
C
A
◀
E
◀
D
B
F
101
H
G
n
Manchester High School
Geometry Midterm
REVIEW
17. The circumference of a circle is 84 cm. Find the diameter and the radius.
84∏ = 2∏r
C = 2∏r
42 = radius. 84 = diameter
18. ∠ABC is an obtuse angle. Sketch ∠ABC and give a possible m∠ABC.
Answers will vary
19. Find the area, perimeter, circumference, or missing dimension for the figures below.
A =452.16 sq.cm
C = 75.36 cm
a.
24 cm.
b.
15 in.
12 in.
P = 36 in A = 54 sq. in
10 ft.
c. All angles are right angles in the figure at the right
2 ft.
CHECK
7 ft.
A = 109 sq. ft P = 56 feet
9 ft.
16 ft.
20. What is WX?
a.W
X
Y
Z
Y is mid point of WZ
X is mid point of WY
YZ = 10.5 cm.
WX = 5.25 cm.
90
Given : m ∥ n
21.
n
(2x + 10)
What is x? x = 40
m
4 ft.
Manchester High School
Geometry Midterm
REVIEW
Write an equation of a line that is parallel to y =
30 = ¾ (16) + b
30 = 12 + b
18 = b
New equation
y = ¾ x + 18
3
x + 9 and goes through the point (16, 30).
4
1
3
22. Write an equation of a line that is perpendicular to y = x - 10 and goes through point (-4, -9).\
-9 = -3(-4) + b
-9 = 12 + b
-21 = b
New equation:
y = -3x - 21
23. Find the cost of carpeting the 1st floor lobby of a museum. There are twelve rooms. Each room
is 10 feet high and 15 feet long by 12 feet wide. Carpet is $22.50 a square yard, padding is
$2.25 a square yard, and installation is $.75 a square foot.
Carpet is based on floor area: 15 X 12 = 180 sq. ft X 12 rooms = 2160 sq. feet
Divide 2160 by 9 to get square yards: = 240 square yards.
240 sq. yards @ $24.75/sq. yd (carpet plus padding) = $5940
Installation is $.75/sq. ft for 2160 sq. ft = $1620
Total cost = 5940 + 1620= $7560.00
24. Find the area of the figure below. Note: The figure is a rectangle and a semi circle.
Answer:
The rectangle area is 18.75 sq. cm
The semicircle is:
2.5 cm
7.5 cm.
½(3.14)(3.752) =22.1 sq. cm
Total area = 40.85 sq. cm
Manchester High School
Geometry Midterm
REVIEW
A pendulum on a clock can only swing so to each side, as marked in the picture below. Find the
area available to the clock pendulum.
Length of pendulum hanging below = 6 inches.
The tip of the pendulum sweeps the path shown, making a
semicircle.
Bottom of clock
Answer:
The radius of the sweep is 6 inches, so the area
of the semicircle is:
½ (3.14) 62 =
56.52 sq. inches
27. Find the value of x and z.
The linear pairs add to 180
(8z + 12) + (4z + 12) = 180
12z + 24 = 180
z = 13
x = 10
28. XY is the angle bisector of UXB .
Find m UXY .
4r + 1 = 3r + 7
r = 6 so angle UXY = 3(6) + 7 =
(5x + 14) + (10x + 16) = 180
15x + 30 = 180
25
Manchester High School
Geometry Midterm
REVIEW
29. Find the value of x.
These are Alternate Interior angles and are congruent, so
5x - 10 = 2x + 50
3x = 60
\
x = 20
30. Write the slope of the line containing the points (3, -4) and (-2, 5).
9/-5
31. The endpoints of a segment have the coordinates (-2, 5) and (4, -6). Write the coordinates of the
midpoint of the segment.
32. The measure of angle 1 is 65 because it was given.
The m 2 is
The m 3 is
The m 4 is
The m 5 is
5
65 because: Incoming/Outgoing
65 because: Alternate Interior
65 because : Incoming/Outgoing
25because it completes a triangle
4
3
2
1
Manchester High School
Geometry Midterm
REVIEW
33. Find the area of a rectangle with length of 5.4 in and width of 3.7 in.
Area = 5.4 X 3.7 = 19.98 sq. in.
34. Draw 4 collinear points A, B, C, and D.
35. Two distinct planes intersect. Describe their intersection. Draw a sketch to support your answer.
36. Lines m and k are parallel. The slope of line m is -⅔. What is the slope of line k?
The slope of line k is also -⅔.
37. Line c and d are perpendicular. The slope of line d is ⅝. What is the slope of line c?
The slope of line c is -8/5
38. NASA Dryden is 117 degrees longitude and 34 degrees latitude. NASA Ames is 122 degrees
longitude and 37 degrees latitude. You can consider the longitude and latitude as a coordinate
pair (latitude, longitude). What is the distance between these two locations?
Use the distance formula
39. Explain the Exterior Angle Theorem.
The measure of an exterior angle of a triangle is equal to the sum of the measures of
the two nonadjacent interior angles. (page 197 of your text)
Manchester High School
Geometry Midterm
REVIEW