Download Geometry_Honors_2016_Summer_Assignment

GEOMETRY HONORS
SUMMER ASSIGNMENT
June 2016
Dear Geometry Honors Students,
Welcome to the beginning of your journey through the Honors Mathematics Program at Randolph
High School. Geometry is the beginning of this exciting adventure. This coming school year, you will
build a solid foundation that focuses on your ability to use critical thinking and reasoning skills.
This assignment is designed to prepare you for an easy transition into our program. Although the
Homework Administrative Regulations of the Randolph Township Schools do not permit us to “grade”
your work on this summer assignment, the material in this packet will be the focus of instruction
during the first few days of school and you will be tested on this material within the first week of
school. The material contained in this packet is not new - it is preparatory and review for the ensuing
school year.
There are three parts to this assignment. The first and second parts ask you to build on your
Geometry vocabulary and apply your knowledge. The third part is a review of the Algebra One
concepts you will be expected to know and be able to use when you solve Geometry problems. As
you work through this assignment, feel free to contact me with any questions or concerns via email at
[email protected].
I look forward to meeting all of you in September.
Teresa Schuele
Mathematics Teacher
Class of 2018 Advisor
Randolph High School
PART l: Basic Terminology
Directions: Find the term that best represents the definition given below.
1.
GEOMETRY
The study of the properties and the relationships of points, lines, planes, and solids
2.
An unidentified term represented as a dot on a piece of paper; usually named by a capital
letter; has no length, width, of thickness; merely indicates a position.
3.
A set of points that may form a straight or curved line
4.
A set of points that forms a completely flat surface extending indefinitely in all directions.
LINES AND LINE SEGMENTS
5.
A set of points all of which lie on the same straight line
6.
A set of three or more points that are not found on the same straight line
7.
A set points consisting of two points on a line, called endpoints, and all points on the line
between the endpoints.
8.
Segments that have the same length
9.
The point of that line segment that divides the segment into two congruent segments
10.
Any line or subset of a line that intersects the segment at its midpoint
11.
A part of a line that consist of a point on the line, called an endpoint, and all the points on one
side of the endpoint.
12.
Two rays of the same line with a common endpoint and no other points in common
ANGLES
13.
A set of points that is the union of the two rays having the same endpoints
14.
An angle that is the union of opposite rays whose measure is 180
15.
An angle whose measure is 90
16.
An angle whose measure is greater than 0 and less than 90
17.
An angle whose measure is greater than 90 and less than 180
18.
An angle whose measure is greater than 180 and less than 360
19.
Angles that have the same measure
20.
A ray whose endpoint is the vertex of the angle and which divides the angle into two congruent
angles
PAIRS OF ANGLES
21.
Two angles in the same plane that have a common vertex and a common side, but do not
have any interior points in common
22. Two angles in which the sides of one angle are opposite rays to the sides of the second angle
23. Two angles the sum of whose measure is 90 degrees
24. Two angles the sum of whose measure is 180 degrees
25. Two angles that have a common side and their remaining sides are opposite rays
LINES
26. Two lines that intersect to form right angles
27. Two lines that never intersect
28. A line, line segment, or ray that is perpendicular to a line segment and bisects that line segment
TRIANGLES AND LINE SEGMENTS ASSOCIATED WITH TRIANGLES
29. A closed figure in a plane that is the union of line segments such that the segments intersect only
at their endpoints and no segments sharing a common endpoint are collinear
30. A polygon that has exactly three sides
31. A triangle that has two congruent sides
32. A triangle that has three congruent sides
33. A triangle that has three acute angles
34. A triangle that has three congruent angles
35. A triangle that has a right angle
36. A triangle that has an obtuse angle
37. A triangle that has no congruent sides
38. A line segment drawn from any vertex of the triangle, perpendicular to and ending in the line that
contains the opposite side
39. A line segment drawn from any vertex of the triangle, ending at the midpoint of the opposite side
PART ll: Application
1. BD divides the right <ABC into two parts. The ratio of
the measures of <ABD to the measure of <DBC is 3:2.
Find the measure of <ABD.
A
D
C
B
A
2. AB  AC , and AB is 3 times as long as BC. If the perimeter
of triangle ABC is 28, find AB.
B
C
S
3. Solve for y in terms of x.
m<PQS = x + y
m<SQR = 3x – 8
P
Q
R
4. A point P is randomly chosen on AB. What is the probability
that it is within 5 units of C?
A
C
B
-6
-3
10
5. The measure of the supplement of an angle is 30 more than four times the measure of the
complement of the angle. Find the measure of the complement.
A
C
6. If the m<1 = 6x2 + 15x and the m<2 = 4x + 10, find the m<EBD.
1
B
2
E
D
7. m<K = 3x – 42 and <K is obtuse. Find the restriction(s) on the value of x.
8. Given points F, G, and H. FG = 18, FH = 7, and GH = 11. Describe the relative positions of F, G,
and H. Justify your conclusion.
9. Find the sum of x and y.
4y+14
3x+7y
F
10. The perimeter of triangle PQR is at least 50. If y > 7,
what do you know about the value of x?
22
4x-2y
G
18
H
11. Answer each of the following questions. Be sure to completely justify your answer.
a. If AB  BC, does this imply B is the midpoint of AC?
b. Is it possible for an obtuse angle to be complementary to an acute angle?
c. Can a right angle be one of two supplementary angles?
12. <ABC is a right angle. BD and BE trisect <ABC.
3
m<ABD = 3x  y
Solve for x and y.
2
8x  y  2
m<DBE =
3
9 y  2x
m<EBC =
2
A
D
E
B
C
Part lll: Algebra Review
1. Solve the following word problems by:
a. drawing a diagram
b. writing an equation
c. solving the equation.
a. Separate 150 into two parts such that four times the larger exceeds five times the smaller by
60.
b. The length of a rectangle exceeds its width by four feet. If the width is doubled and the length
is diminished by two feet, a new rectangle is formed whose perimeter is eight feet more than the
perimeter of the original rectangle. Find the dimensions of the original rectangle.
2. Simplify:
x y
x
( x  y )2
a. 2


x  y2 x  y x4  y4
b.
x 2  2 xy  8 y 2 5x  10 y

x 2  16 y 2
3x  12 y
3. Solve for x.
a. ax  bx  4a  4b
b.
4. Simplify the radicals.
a. 5 18 y 3 w 6 z 8
b. x 8 y  3 2 x 2 y
c.

a b
5. Solve the inequality:
a. 90 < 5x + 5 < 180
6. Solve for x.
a. 5y2 – 1 = 2y
1 1 1
 
x c d
b.

a b

d.
60
3 8
3t  4 2t  4 5t  1


3
6
9
b. (x + 4)2 = (x – 4)2 + 96
7. Review all methods of factoring & solving – simple, AC method, completing the square, quadratic
formula, special patterns – difference of squares and perfect square trinomials. Write and solve an
example of each.
8. Review solving systems of linear equations – graphing, elimination, substitution. Write and solve
an example of each.