Download geometry summer assignment

GEOMETRY
SUMMER ASSIGNMENT
NAME ______________________________
Throughout the summer months, please work on this assignment to stay refreshed
with the basic math concepts we will start with in August. You are expected to have
this assignment complete on the first day of school to turn in for your first grade.
It would be beneficial to begin the semester with a good grade.
You can do your work on these pages or on loose-leaf. You may use graph paper for
some problems, if necessary. Any additional work (not on these pages) must be
stapled to the back of this packet to turn in.
Name: ____________________________________
Geometry Summer Work
Date: _________________
A. Ordered Pairs
Write the ordered pair for each point shown at the
right.
1.
A
2. C
3. D
4. F
5. G
6. H
7. L
8. M
B. Perimeter and Area
Find the perimeter and area of each figure.
9. a rectangle with length
10. a square with length 6 inches
7 meters and width 11 meters
11. James purchased a lot that was 121 feet in width and 360 feet in length. If he wants
to build a fence around the entire lot, how many feet of fence does he need?
C. Pythagorean Theorem
Find the missing side of each right triangle. Round to the nearest tenth, if necessary.
12.
13.
.
D. Evaluating Algebraic Expressions
Evaluate each expression if a = 2, b = -3, c = -1, and d = 4.
𝑏𝑑
2𝑑−𝑎
14. 2a + c
15. 2𝑐
16. 𝑏
17. 3d – c
E. Solving Linear Equations
18. x + 11 = 3
20. – 12 = 6
21.
12
5
f = -18
24. b + 2 = -5
27.
𝑚
10
+ 15 = 21
𝑝
19. d – 7 = 8
22.
6
y=3
23. t – 14 = -29
7
25. -12q = 84
26. 5c – 7 = 8c – 4
28. 8t + 1 = 3t – 19
29. 5c – 24 = -4
2
2
30. -2y + 17 = -13
31.
33. -2(n – 7) = 15
34. -8a – 11 = 37
9
𝑥−4=
3
32. 9 – 4g = -15
35. 2(5 – n) = 8
F. Slope
Find the slope of the line that contains each pair of points. Then find the slope of a line
parallel to that line, and perpendicular to that line.
36. (4, 2) and (8, 6)
37. (0, -3) and (10, 1)
38. (7, 2) and (-2, 1)
G. Writing Equations of Lines
Write an equation in slope-intercept form of each line with the given slope and yintercept.
39. slope = 4
40. slope = -½
41. Slope = 0
y-intercept = -3
y-intercept = 5
y-intercept = 12
H. Simplifying Radicals
Simplify each radical. (Example: √20 = 2√5 )
42. √32
43. √75
44. √80
45. √40
I. Midpoint
Find the coordinates of the midpoint of a segment having the given endpoints.
46. (-4, 3) and (-1, 5)
47. (2, 8) and (-2, 2)
J. Distance
Use the number line to find each measure.
48. AC
49. CD
50. BF
Find the distance between each pair of points.
53. (5, 1) and (-3, -3)
54. (7, 1) and (-1, 5)
K. Area
Find the area of each figure.
56.
58.
57.
59.
51. DF
52. AD
55. (2, 0) and (8, 6)
60.
61.
Terms to Know:
TERM
1. Point
2. Line
3. Plane
4. Collinear Points
5. Coplanar Points
DEFINITION
●A point is a location.
●In a figure, points are represented by a
dot.
●Points are named by capital letters.
●A line is made up of points and has no
thickness or width.
●In a figure, a line is shown with an
arrowhead at each end.
●Lines are usually named by lowercase
script
letters or by writing capical letters for
two
points on the line, with a double arrow
over
the pair of letters.
A plane is a flat surface made up of points
that has no depth and extends indefinitely
in all directions. In a figure, a plane is
often represented by a shaded, slanted 4sided figure. Planes are usually named by a
capital script letter or by three
noncollinear points on the plane.
Points that lie on the same line.
(Noncollinear points do not lie on the same
line.)
Points that lie on the same plane.
(Noncoplanar points do not lie on the same
plane.)
PICTURE
●A
Point A
⃡𝐴𝐵
plane ABC
A, B, and C are collinear points
A, B, C, and D are coplanar
points.
6. Line Segment
A measurable part of a line that consists of
two points, called endpoints, and all of the
points between them.
7. Congruent
Having the same measure (Symbol: )
̅̅̅̅
𝐴𝐵
A
B
C
D
̅̅̅̅
𝐴𝐵  ̅̅̅̅
𝐶𝐷
8. Midpoint
The point halfway between the endpoints
of a segment.
9. Degree
A unit of measure used in measuring angles
and arcs.
10. Ray
𝑃𝑄 is a ray if it is the set of points
consisting of PQ and all points S for which
Q is between P and S.
11. Angle
12. Right Angle
●The intersection of two noncollinear rays
at
a common endpoint.
●The rays are called sides and the common
endpoint is called the vertex.
An angle with a degree measure of 90.
13. Acute Angle
An angle with a degree measure than 90.
14. Obtuse Angle
An angle with a degree measure greater
than 90 and less than 180.
ABC
15. Adjacent
Angles
Two angles that lie in the same plane, have
a common vertex and a common side, but no
common interior points.
16. Vertical Angles
Two nonadjacent angles formed by two
intersecting lines.
17. Complementary
Angles
Two angles with measures that have a sum
of 90.
18. Supplementary
Angles
Two angles with measures that have a sum
of 180.
19. Parallel Lines
Coplanar Lines that do not intersect.
(symbol: )
m  n
20. Perpendicular
Lines
Lines that intersect to form right angles.
(symbol: )
AB
21. Polygons
A polygon is a closed figure formed by segments, called sides.
# of sides in polygon
Name
3
4
5
6
7
8
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
9
10
FORMULAS
Slope
m=
𝑦2 − 𝑦1
𝑥2 −𝑥1
Distance
d = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
AREA FORMULAS
Rectangle
A = l●w
Trapezoid
A = ½ h(b1 + b2)
Nonagon
Decagon
Midpoint
𝑥1 +𝑥2 𝑦1 + 𝑦2
(
2
,
2
Pythagorean Theorem
)
Slope-intercept Form
y = mx + b
Triangle
A = ½bh
Circle
A = πr2
a2 + b2 = c2
Vocabulary Practice:
Match the geometry term with the most correct picture. Each term will only be used once.
Write the term under the picture.
Acute angle
Adjacent angles
Angle
Complementary angles
Line
Line segment
Midpoint
Obtuse angle
Parallel lines
Perpendicular lines
Plane
Point
Ray
Right angle
Supplementary angles
Vertical angles
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
13.
11.
14.
12.
15.
Name each figure using the correct symbols and letters. (Ex: ABC)
16.
17.
18.
19.
20.
21.
22.
Fill in the blanks:
Congruent
Collinear points
Coplanar points
degree
23. ___________________________ are points that are on the same line.
24. The unit of measure used in measuring angles and arcs is ___________________.
25. Points that are on the same plane are called ________________________.
26. ______________________ figures have the same measure.
Name each polygon:
decagon
heptagon
27.
30.
33.
hexagon
nonagon
28.
octagon
pentagon
quadrilateral
triangle
29.
31.
34.
32.