Year 2 Retake: EOC Make Up for Geometry 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 Year 2 Retake (EOC Make Up for Geometry). 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. 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.

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Year 2 Retake: EOC Make Up for Geometry Study Guide

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Year 2 Retake: EOC Make Up for Geometry Study Guide

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Year 2 Retake: EOC Make Up for Geometry 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. If

then o

A.

a = 11, b = -3

o

B.

a = 11, b = 3

o

C.

a = 3, b = 11

o

D.

a = -11, b = 3

Additional Practice at www.interactmath.com Chapter 2 Section 2 Exercises: 17, 19 Chapter 2 Section 4 Exercises: 6, 11, 13, 15

Answer: A Used by permission from the Northshore School District

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Year 2 Retake: EOC Make Up for Geometry 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

Additional Practice at www.interactmath.com Chapter 1 Section 2 Exercises: 1, 4, 12, 15, 19, 27, 53

Answer: C

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?

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

Answer: 14 Used by permission from the Northshore School District

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Year 2 Retake: EOC Make Up for Geometry Study Guide 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

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

Additional Practice at www.interactmath.com Chapter 5 Section 4 Exercises: 10, 11, 15, 31 Chapter 5 Section 6 Exercises: 13, 15, 21, 27, 39

b) EC

Answers: a) 16.4 b) 17.4 Identify the sides of STU in order from shortest to longest.

o o o o

A. B. C. D.

UT, ST, SU SU, UT, ST SU, ST, UT ST, US, UT

Answer: C Used by permission from the Northshore School District

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Year 2 Retake: EOC Make Up for Geometry 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 O A.

SSS

O B.

SAS

O C.

ASA

O D.

HL

Answer: A

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

Which theorem or postulate can be used to prove that

Chapter 4 Section 6 Exercises: 1, 12

O A.

SSS

O B.

SAS

Chapter 7 Section 3 Exercises: 7, 9, 11, 15

O C.

ASA

O D.

AAS

Answer: D

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Year 2 Retake: EOC Make Up for Geometry 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 1. WY is the perpendicular bisector of

XZ .

Reasons 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

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Year 2 Retake: EOC Make Up for Geometry 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

.

Additional Practice at www.interactmath.com Chapter 8 Section 2 Exercises: 9, 11, 15, 17, 21, 23

Determine the exact length of side CD.

Answer: √ 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

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: √

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 Used by permission from the Northshore School District

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Year 2 Retake: EOC Make Up for Geometry Study Guide

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.

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

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)?

Chapter 10 Section 5 Exercises: 3, 6, 11, 25, 35

Answer: 12 feet

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

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

Answers: a) 25 b) 16 c) 137.6

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Year 2 Retake: EOC Make Up for Geometry 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:

√

or about 374.1

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Year 2 Retake: EOC Make Up for Geometry 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 ̅̅̅̅. 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 X (0, -3), Y (5, 3), Q (-3, -1), which of the following points is a location of P so that ̅̅̅̅ is parallel to ̅̅̅̅? 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

Additional Practice at www.interactmath.com Chapter 6 Section 7 Exercises: 1, 2, 9, 17, 33 Chapter 6 Section 8 Exercises: 27, 37

Answer: B

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 √

. 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 Used by permission from the Northshore School District

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Year 2 Retake: EOC Make Up for Geometry Study Guide

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

Additional Practice at www.interactmath.com Chapter 7 Section 1 Exercises: 13, 15, 37

Determine the volume of the calculator box to the nearest cubic centimeter. Answer: 475

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