Download CP Geometry Midterm

2014 CP Geometry
Final Exam Review
1. Find x.
Write answer as simplified radical.
2
2
x
8
2. a. If 1 inch on a map represents 42 miles, how many inches would represent 85
miles? Round to nearest hundredths.
b. If 1 inch on a map represents 10 miles, how many inches would represent 43
miles?
3. The sum of the measures of the interior angles of a dodecagon is:
4. Write a function rule that maps (8, 4) to (−3, 10).
5. A triangle has a hypotenuse of length 32 feet and a leg of length 4 feet. Find the
measure of the other leg. Round to the nearest tenth.
6. If PR = 26 and RS = 25, find PS. Round to nearest tenth.
P
S
R
7. If a rectangle has a length of 11.5 cm and a width of 26 cm, then the perimeter
must equal ______.
8. Find the perimeter of a regular septagon with one side of length 7.5 ft.
9. The perimeter of a square is 116 cm. What is the AREA of the square?
10. Find the area of a right triangle whose sides are 8 in., 15 in., and 17 in.
11. Determine whether the figure has rotational symmetry. If so, describe any
rotations that map the figure onto itself.
1.
2.
12. Find the total area of the figure at the right.
10
4
4
13. Find the altitude of trapezoid ABCD at the right?
D
5
4
C
10
x
A
B
12
14. Find the value of y in the rotation of the triangle about P.
15. Find the value of x. Assume that segments that appear to be tangent are tangent.
C
2x2 +
3x + 8
16. In the figure the missing side, m, would equal _____________.
2
0
1
5
m
P=
92 ft.
2
5
1
6
C
´
2x2 –
7x + 28
17. Find the area of ABC .
B
7
2
6
2
A
C
7
5
18. In
O , DE is called a _______________.
B
DE is called a _______________
D
CB is called a _______________
OA is called a _______________
19. Find the length of AB . Round to the nearest tenth.
20. Find the Circumference. Round to the nearest tenth.
A
●
O
C
E
21. Find the area of a circle with diameter 14 ft. Round to the nearest tenth.
22. Find the area of the sector formed by
ACB . Round to the nearest tenth.
23. If ABC is in Quadrant I and is reflected over the y-axis. In which quadrant
is the image?
24. The sides of a triangle are 4in, 5in and 7in. Is the triangle acute obtuse or right?
25. a) Find the length of MA and MP .
MA = _________
MP = _________
MA = _________
MP = _________
M
3
0
°
A
P
7
a) Find the length of MA and MP .
M
4
5
°
P
A
3
26. DEFG is a Rectangle. Find the value of x.
D
E
EF =
28
3x+
7
F
G
27. Find the area of the triangle below.
6.3
cm
12
cm
5
cm
20
cm
28. Solve for x.
32º
x
45º
53º
18º
29. Solve for x.
x
30. If the m ACB  250 . Find x.
A
C
x
B
31. Which of the following statements about equilateral triangles is
correct?
a.
b.
c.
d.
Two angles are congruent.
No sides are congruent.
All angles are congruent.
All sides are congruent.
32. Which of the following statements about rhombuses is correct?
a.
b.
c.
d.
The diagonals are congruent.
All sides are congruent.
All angles are congruent.
Opposite angles are congruent
33. Find the value of x.
A
17
2º
C
x
B
34. For the trapezoid shown, find the measure of the midsegment.
15
32
35. The polygons are similar as indicated. Find the value of x.
Δ STU ~ ΔPQR
36. Find the value of x.
Hint: find the sum of the interior angles first and then write an equation to
solve for x.
Interior Angle Formula: (n – 2 ) x 180
x
x
+
2
x3
13
0
11
2
12
0
37. Find the measure of each exterior and interior angle of a regular pentagon.
38. Find the sum of the measures of the interior angles of a nonagon.
39. Find x.
6
x
4
x = _________
40. Find x and y.
1
0
41. Find x.
(x + 40)º
xº
112º
94º
42. Use the distance formula to find the distance between (-3, 4) and (5, 9)
43. Find the midpoint of the two ordered pairs: (-6, 1) and (4, -9)
44. A meter stick is held perpendicular to the ground. It casts a shadow 2.5m long.
At the same time, a telephone pole casts a shadow that is 10m long. How tall is
the telephone pole?
45. Find the value of x and y.
x
8 3
6
0º
y
46. For C find the value of x. Assume that segments that appear to be tangent are
tangent.
x
C
2
4
1
6
x
47. Solve the right triangle.
A
x = ______
y = ______
1
0
x
B
A  ______
4
2
°
y
C
Problems 48-52, use circle P below, given the following information:
A and B are points of tangency, BC = 80°, DC = 50°, DE = 60°
48.
m
1 = ___________
A
E
1
49.
50.
m
2 = ___________
m
3
G
4P
2
3 = ___________
51.
m
4 = ___________
52.
m
5 = ___________
5
B
F
D
C
Find the values of x, y, and z. The center of the circle is marked.
53. x = ____ y = ____ z = ____
54. x = ____ y =____ z = ____
55. x = ____ y = ____ z = ____
z°
z°
1
1
0
°
y
°
z°
x
°
3
0
°
56. x = ____ y = ____ z = ____
2
5
8°
0
° y
°
57.
x
°
8
5
8 °
0
°
x = ____ y = ____ z = ____
x
y° 4
° 0
°
x
°
y
°
1
1
0
°
x
°
z°
5
0
°
58. UT = 150◦, VT = 20◦,
x
°
3
5
°
y
z° °
U
S = ____________(3 points)
V
59.
S = 42◦, UT = 120◦, VT = ____________(3 points)
S
T
60. It is given that ABDC is a parallelogram. Graph A(–2, 0) B(5,7) C(1, –3) D(8,4)
Decide whether it is a rectangle, a rhombus or a square or none of the above.
Explain your answer. Include in your explanation why it is not the other figures,
showing work to support your answer.
d=
( x 2  x1) 2  ( y 2  y1) 2
slope= m =
y 2  y1
x 2  x1