Download Geometry EOC Study Guide - Northshore School District

Geometry EOC Study Guide
Study Guide
General Notes
This document is not state (OSPI) created or approved. This was developed using resources created by OSPI, the
Seattle School District, the Bainbridge Island School district, and NSD. It has been designed to help students
prepare for taking the Geometry EOC.
This is not an exhaustive sampling of EOC Exam test items. Rather it is intended to give students an idea of what
their level understanding is for the Performance Expectations assessed on the state EOC.
Information about the EOC Assessment
o
o
o
o
o
o
The format of the exam questions will be: 29 multiple choice, 5 completion items, and 3 short answers.
A graphing calculator can be used for all questions and will be cleared at the start of the exam.
You may use a straightedge and compass while taking the exam.
A formula sheet and graph paper will be provided in the test booklet.
The formula sheet is provided on the next two pages of this document.
There will be a total of 37 questions on the Year 2 Retake Exam.
The following gives the strands to be assessed along with the estimated number of questions for each strand.
End-of-Course Exam Items
Estimated Number of Questions (37 questions)
Logical Arguments and Proof
Proving and Applying Properties of 2-dimensional figures
Figures in a Coordinate Plane & Measurement
6-8
21 - 24
7-9
Organization of the Study Guide
The study guide has been organized by using the strands given in the previous table. The number of test items for
each strand is shown to help guide your study priorities.
For each strand, you will find the specific state Performance Expectations that will be assessed for graduation. You
will find the following information for each Performance Expectation:
o The problem number(s) from the companion Practice Test that is aligned with this particular Performance
Expectation
o Sample Questions for each objective
o Additional Practice Problems that can be found at www.interactmath.com
Using the Interact Math Website:
This website has practice problems that match our curriculum. To use this site, you need to
1. Go to www.interactmath.com
2. Select Enter at the top of the page.
3. Select “Prentice Hall Geometry© 2011 from the drop down menu
4. Select Submit
5. You will then be able to select the chapter and exercises that match those listed on this guide.
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Logical Arguments and Proof
Performance Expectation G.1.D
Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.
Practice Exam
Problem(s)
#1
Sample Question(s)
The given statement is a valid geometric proposition.
If a quadrilateral is a kite, then its diagonals are
perpendicular.
Which of the following is the inverse statement?
o A. If a quadrilateral has diagonals that are
perpendicular, then it is a kite.
o B. If a quadrilateral is not a kite, then its diagonals are
not perpendicular.
o C. If a quadrilateral has diagonals that are not
perpendicular, then it is not a kite.
o D. If a quadrilateral is a kite, then its diagonals are not
perpendicular.
Answer: B
Additional Practice at
www.interactmath.com
Chapter 2 Section 2
Exercises: 20, 23
Chapter 2 Section 3
Exercises: 7, 9
Determine the converse of the given statement.
If the tabletop is rectangular, then its diagonals are
congruent.
o A. If a tabletop is rectangular, then its diagonals are
not congruent.
o B. If the diagonals of a tabletop are congruent, then it
is rectangular.
o C. If a tabletop is not rectangular, then its diagonals
are not congruent.
o D. If the diagonals of a tabletop are not congruent, then
it is not rectangular.
Answer: B
Performance Expectation G.1.E
Identify errors or gaps in a mathematical argument and develop counterexamples to refute
invalid statements about geometric relationships.
Practice Exam
Problem(s)
#2, 3
Sample Question(s)
Show that the conjecture is false by finding a counterexample.
𝑎
If 𝑎 > 𝑏, then 𝑏 > 0
o
A.
a = 11, b = -3
o
B.
a = 11, b = 3
o
C.
a = 3, b = 11
o
D.
a = -11, b = 3
Answer: A
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 2 Section 2
Exercises: 17, 19
Chapter 2 Section 4
Exercises: 6, 11, 13, 15
Geometry EOC Study Guide
Study Guide
Performance Expectation G.1.F
Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined
terms, postulates (axioms), and theorems.
Practice Exam
Problem(s)
#4
Sample Question(s)
Although the statement “if two points lie in a plane, then the lines
containing those points lie in a plane” cannot be proven, it is
agreed to be true. Which type of statement is this an example
of?
O A.
Undefined term
O B.
Definition
O C.
Postulate (or axiom)
O D.
Theorem
Answer: C
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 1 Section 2
Exercises: 1, 4, 12, 15, 19, 27, 53
Geometry EOC Study Guide
Study Guide
Proving and Applying Properties of 2-Dimensional Figures
Performance Expectation G.3.A
Know, explain, and apply basic postulates and theorems about triangles and the special lines, line
segments, and rays associated with a triangle.
Practice Exam
Problem(s)
#5, 6, 7
Sample Question(s)
Triangle JKE is an obtuse isosceles triangle with m∠E = 10°
and KE > JK. What is the measure of ∠ J?
O A.
170
O B.
160
O C.
85
O D.
10
Answer: B
Triangle XYZ is the midsegment triangle of ∆WUV. What is the
perimeter of ∆XYZ?
Answer: 14
Which construction represents the center of a circle that is
inscribed in a triangle?
o
o
o
o
A. The intersection of the three altitudes of the triangle.
B. The intersection of the three medians of the triangle.
C. The intersection of the angle bisectors of each angle
of the triangle.
D. The intersection of the perpendicular bisectors of
each side of the triangle.
Answer: C
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 3 Section 5
Exercises: 17, 19, 29, 31
Chapter 4 Section 5
Exercises: 11, 13, 21, 31
Chapter 5 Section 1
Exercises: 3, 21, 31
Chapter 5 Section 2
Exercises: 7, 9, 14, 17
Chapter 5 Section 3
Exercises: 2, 7, 11, 17
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.A Continued
Know, explain, and apply basic postulates and theorems about triangles and the special lines, line
segments, and rays associated with a triangle.
Practice Exam
Problem(s)
#8, 9
Sample Question(s)
In ∆DEB, DB = 24. 6 and EZ = 11.6. Find each length:
a) DZ
Answers: a) 16.4 b) 17.4
Identify the sides of ∆STU in order from shortest to longest.
A.
B.
C.
D.
Chapter 5 Section 4
Exercises: 10, 11, 15, 31
Chapter 5 Section 6
Exercises: 13, 15, 21, 27, 39
b) EC
o
o
o
o
Additional Practice at
www.interactmath.com
UT, ST, SU
SU, UT, ST
SU, ST, UT
ST, US, UT
Answer: C
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.B
Determine and prove triangle congruence, triangle similarity, and other properties of triangles.
Practice Exam
Problem(s)
#10, 11, 12
Sample Question(s)
Which theorem or postulate can be used to prove that
∆𝐴𝐵𝐶 ≅ ∆𝐷𝐵𝐶?
O A.
SSS
O B.
SAS
O C.
ASA
O D.
HL
Answer: A
Which theorem or postulate can be used to prove that
∆𝐽𝐾𝐿 ≅
∆𝐽𝑀𝐿?
O A.
SSS
O B.
SAS
O C.
ASA
O D.
AAS
Answer: D
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 4 Section 2
Exercises: 8, 11, 14, 24, 26
Chapter 4 Section 3
Exercises: 3, 9, 13, 16
Chapter 4 Section 4
Exercises: 1, 5
Chapter 4 Section 6
Exercises: 1, 12
Chapter 7 Section 3
Exercises: 7, 9, 11, 15
Geometry EOC Study Guide
Study Guide
A sample proof for Performance Expectation G.3.B
A proof is shown.
Fill in the blanks for steps 4 and 5 to complete the proof.
Given: WY is the perpendicular bisector of XZ
Prove: WXY  WZY
Statements
Reasons
1. WY is the perpendicular bisector of
XZ .
1. Given
2. WYX  WYZ
2. Perpendicular lines form 90 degree
angles
3. WY  WY
3. Reflexive property of congruence
4.
4. A bisector divides a segment into
two equal halves
5. WXY  WZY
5.
2-point response: The student shows understanding of proving triangle congruence by doing the
following:
 Writes XY  YZ , or equivalent, for statement 4
 Writes Side-Angle-Side, or equivalent, for reason 5
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.C
Use the proportions of special right triangles (300-600-900 and 450-900) to solve problems.
Practice Exam
Problem(s)
#13
Sample Question(s)
In rectangle ABCD, the length of AC is 4 and 𝑚∠𝐵𝐴𝐶 = 30°.
Determine the exact length of side CD.
Answer: 𝟐√𝟑
Square ABCD is shown. Diagonal BD has a length of 10 inches.
Determine the exact length of a side of the square.
Answer:
50 or 5 2
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 8 Section 2
Exercises: 9, 11, 15, 17, 21, 23
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.D
Know, prove, and apply the Pythagorean Theorem and its converse.
Practice Exam
Problem(s)
#14
Sample Question(s)
ΔABC has a right angle C. AC = 6 m, and altitude CD from
to AB is 5 m. Find the exact length of AD.
C
Additional Practice at
www.interactmath.com
Chapter 8 Section 1
Exercises: 17, 19, 22, 24, 27, 37
Answer: √𝟏𝟏
The length of one diagonal of a rectangle is 17 feet. The
length of the rectangle is 7 feet greater than its width.
Determine the perimeter of the rectangle.
Answer: 46
Performance Expectation G.3.E
Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.
Practice Exam
Problem(s)
#15, 16
Sample Question(s)
Find the length of the hypotenuse, to the nearest tenth of a centimeter,
of a right triangle if one angle measures 70° and the adjacent leg
measures 8 cm.
Answer: 23.4 cm
A ladder leans against a wall to form a 62 angle with the
ground. If we know the top of the ladder touches the wall at 11
feet, how many feet long is this ladder (round to the nearest
whole foot)?
Answer: 12 feet
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 8 Section 3
Exercises: 11, 14, 15, 16, 17, 22, 23,
25
Chapter 8 Section 4
Exercises: 19, 22, 23, 33
Chapter 10 Section 5
Exercises: 3, 6, 11, 25, 35
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.F
Know, prove, and apply basic theorems about parallelograms.
Practice Exam
Problem(s)
#17, 18
Sample Question(s)
In parallelogram RSTU, UR = 25, RX = 16, and m∠STU=42.4.
Find:
a) ST =
b) XT =
c) m∠RST
Answers: a) 25 b) 16 c) 137.6
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 6 Section 2
Exercises: 1, 3, 9, 16, 26, 29
Chapter 6 Section 3
Exercises: 1, 7, 11
Geometry EOC Study Guide
Study Guide
Performance Expectation G.3.G
Know, prove, and apply theorems about properties of quadrilaterals and other polygons.
Practice Exam
Problem(s)
#19, 20, 21
Sample Question(s)
PQRS is a rhombus. Find QR.
O A.
QR = 28
O B.
QR = 26
O C.
QR = 14
O D.
QR = 7
Additional Practice at
www.interactmath.com
Chapter 6 Section 1
Exercises: 1, 3, 17, 19, 23, 29, 33
Chapter 6 Section 4
Exercises: 1, 13, 23, 25, 35, 39, 43
Chapter 6 Section 5
Exercises: 3, 9, 11, 19
Chapter 6 Section 6
Exercises: 11, 13, 23, 29, 31, 35
Answer: A
Chapter 10 Section 3
Exercises: 3, 17, 21
In kite EFGH, m∠ JFE = 72. What is the m∠HEF?
O A.
m∠HEF = 18
O B.
m∠HEF 22
O C.
m∠HEF = 36
O D.
m∠HEF = 52
Answer: C
Find the area of the regular hexagon,
Answer: 𝟐𝟏𝟔√𝟑 or about 374.1
Northshore School District January 2012
Geometry EOC Study Guide
Study Guide
Performance Expectation G.4.B
Determine the coordinates of a point that is described geometrically.
Practice Exam
Problem(s)
#22, 23
Sample Question(s)
Points X, Y and Z are collinear. Y is the midpoint of ̅̅̅̅
𝑋𝑍.
The coordinates of point X are (-4, 5). The coordinates of
point Z are (8, -3). Determine the coordinates of point Y.
Additional Practice at
www.interactmath.com
Chapter 1 Section 7
Exercises: 11, 17, 19, 23, 31, 51
Answer: (2, 1)
Given points A (0, -3), B (5, 3), Q (-3, -1), which of the following
̅̅̅̅ is parallel to 𝐴𝐵
̅̅̅̅?
points is a location of P so that 𝑃𝑄
o A. (0,3)
o B. (12,5)
o C. (-7,11)
o D. (2,5)
Answer: D
Performance Expectation G.4.C
Verify and apply properties of triangles and quadrilaterals in the coordinate plane.
Practice Exam
Problem(s)
#24, 25
Sample Question(s)
The vertices for quadrilateral EFGH are E(-2, 5), F(7, 8), G(4, 0)
and H(-5, -3). What type of quadrilateral is EFGH?
o
o
o
o
A.
B.
C.
D.
rhombus
parallelogram
kite
trapezoid
Answer: B
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 6 Section 7
Exercises: 1, 2, 9, 17, 33
Chapter 6 Section 8
Exercises: 27, 37
Geometry EOC Study Guide
Study Guide
Performance Expectation G.6.E
Use different degrees of precision in measurement, explain the reason for using a certain degree of precision,
and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given
purpose.
Practice Exam
Problem(s)
#14, 15, 16,
Sample Question(s)
A golden rectangle has a length and width in the golden ratio
1+ √5
.
2
Give a decimal approximation for the golden ratio that is
accurate to six decimal places.
o
o
o
o
A.
B.
C.
D.
2.118033
1.618034
2.581138
2.581139
Additional Practice at
www.interactmath.com
This standard is not in a specific
chapter. Pay attention to the
instructions on questions indicating
whether to express your answer as
an exact value or as specific decimal
value.
Answer: B
Performance Expectation G.6.F
Solve problems involving measurement conversions within and between systems, including those involving
derive units, and analyze solutions in terms of reasonableness of solutions and appropriate units.
Practice Exam
Problem(s)
#26, 27
Sample Question(s)
Martina has a calculator box that has a volume of 29 inches.
1 inch = 2.54 centimeters
Determine the volume of the calculator box to the nearest cubic
centimeter.
Answer: 475
Northshore School District January 2012
Additional Practice at
www.interactmath.com
Chapter 7 Section 1
Exercises: 13, 15, 37