Geometry Summer Packet
Robbinsville High School
Mathematics Department
155 Robbinsville-Edinburg Road
Robbinsville NJ 08691
Dear Parents and Guardians,
We would like to take this opportunity to thank you for your support this year. Attached you will find a
packet for math reinforcement for your student’s use over the summer. This packet should be completed and
returned to school with your student on the first full day of school. September is filled with review, but with
completion of this packet, the review will come very naturally. The packet will be collected and graded as a 20point homework grade based on completion and effort.
In addition to this packet, we have provided for your student some resources for extra help. Below, you
will find a variety of websites your student may want to visit over the summer to refresh their memory about the
topics discussed in this packet.

Math Forum at Drexel University: http://mathforum.org/dr.math/

Purple Math: http://www.purplemath.com/

Math Is Fun?: http://www.mathsisfun.com/

Cut the Knot: http://www.cut-the-knot.org/MathHelp.shtml

Cool Math (Algebra I): http://coolmath.com/algebra/Algebra1/index.html

Math League (Geometry): http://www.mathleague.com/help/geometry/geometry.htm
Thank you again for your support throughout the year and we wish you a happy and safe summer vacation.
Happy Summer!
Robbinsville High School Mathematics Department
Name__________________________________
Due Date: The first full day of Geometry Class!
Geometry Summer Packet
Directions: You must show all work in the space provided to receive credit. Write your final answer on the
line.
Part 1: Algebra 1 Skills
Solve. Show all work!
1.
–3(x + 5) = 8x + 18
1._______________
2.
5( x  4)  1  7 x  3
2._______________
3.
5
7

x 1 x
3._______________

4.
x 1
x4
=
3
5
4._______________
5.
x 2  x  56=0
5._______________
6.
x2 – 16x + 64 = 0
6._______________

Geometry Summer Packet
7.
2x2 = 9x +5
7._______________
8.
25y2 – 49 = 0
8. ________________
9.
2x 4 12x 2 =0
9.
______

Simplify.
2x
2
10.
 11xy  10 3x 2  4 x  2  x 2 y  4 
10.
______
2x
2
11.
 5x  x 3  1 9x 2  8x  x 3  7
11.
______
12.
4a  5c 4a  5c 
12.
______
13.
w  22
13.
______




Geometry Summer Packet
Solve each system.
14.
2x  y  5
4 x  2 y  10
14.
______
15.
xy 0
xy 2
15.
______


16. Graph the function: y  3x  5

17. Find the slope of the line containing points: (9, 4) and (5, 2)
17.
______
Geometry Summer Packet
Part 2: Geometry Skills
18.
The measures of two supplementary angles are x + 10 and 4x+ 85. Find the value of x. What is the
degree measure of the smaller angle?
x=
Smaller angle =
19.
°
The measure of an angle is 3 times the measure of its supplement. Find the measure of each angle.
x=
Angles =______° and ______°
20.
The measure of an angle is six more than twice the measure of its complement. Find the measure of both
angles.
x=
Angles =______° and ______°
21.
A tree casts a 20-m shadow at the same time that a 6-m pole casts an 8-m shadow. Find the height of the
tree. Label the triangles below based on the information in the word problem to help you solve.
Height =
Geometry Summer Packet
Find the value of x in each figure.
22.
x=
23.
x=
24.
x=
25.
x=
Geometry Summer Packet
Use the rectangle shown below (rectangle PQRS) to answer questions 26 and 27.
P
Q
(3x+3) in
S
26.
(7x-3) in
R
Rectangle PQRS has a perimeter of 40 inches. Find the value of x.
P = 2 ( l + w)
x=
27.
Find the area of the rectangle PQRS.
A = lw
Area =
28.
Joe Bean regularly takes a short-cut across Mr. Wilson's lawn instead of walking on the sidewalk on his
way home from school. How much distance is saved by Joe cutting across the lawn?
Total Distance Saved =
Geometry Summer Packet
Use the figure shown below in which AB and CD intersect at point X and m5 = 90° to answer
questions 29-34. Refer to the angles by their numbers when answering.
29.
A
Name a pair of vertical angles.
D
2
4
X
5
30.
3
Is 1 vertical to 2? Explain.
1
C
E
B
31.
Name an angle adjacent to 2.
32.
Are 3 and 5 supplementary? Explain.
33.
Are 2 and 4 supplementary? Explain.
34.
Are 3 and 1 complementary? Explain.