Geometry Module 4 Unit 2 Practice Exam


 Ethel Peters
 1 years ago
 Views:
Transcription
1 Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning and accurate labeling of an isoscles trapezoid in the coordinate plane? a. c. b. d. 1
2 Name: ID: A 2. Which diagram shows the most useful positioning of a rectangle in the first quadrant of a coordinate plane? a. c. b. d. Short Answer 3. Is TVS scalene, isosceles, or equilateral? The vertices are T(1,1), V(4,0), and S(2,4). 4. A quadrilateral has vertices ( 3, 1), (4, 5), ( 1, 5), and ( 3, 3). What special quadrilateral is formed by connecting the midpoints of the sides? 5. In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C? 6. The vertices of the trapezoid are the origin along with A(4p, 4q), B(4r, 4q), and C(4s, 0). Find the midpoint of the midsegment of the trapezoid. 2
3 Name: ID: A 7. For the parallelogram, find coordinates for P without using any new variables. 8. For A( 1, 1), B(2, 1), and C(2, 1), find all locations of a fourth point, D, so that a parallelogram is formed using A, B, C, D in order as vertices. Plot each point D on a coordinate grid and draw the parallelogram. 9. The fact that the diagonals of a kite are perpendicular suggests a way to place a kite in the coordinate plane. Show this placement. Include labels for the kite vertices. 10. Show how to place a rhombus in the coordinate plane so that its diagonals lie along the axes. Label the vertices using as few variables as possible. 11. Find the lengths of the diagonals of this trapezoid. 12. In the coordinate plane, draw a square with sides 8n units long. Give coordinates for each vertex, and the coordinates of the point of intersection of the diagonals. 3
4 Name: ID: A Essay 13. Verify that parallelogram ABCD with vertices A( 5, 1), B( 9, 6), C( 1, 5), and D(3, 2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals. 14. Find the midpoint of each side of the kite. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the kite? 15. Prove using coordinate geometry: The midpoints of the sides of a rhombus determine a rectangle. 16. Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. 17. Write a coordinate proof of the following theorem: If a parallelogram is a rectangle, then its diagonals are congruent. 4
5 Name: ID: A Other 18. In the coordinate plane, draw JKL with J(2, 3), K(10, 4), and L(8, 9). Classify JKL. Explain. 19. In the coordinate plane, draw parallelogram ABCD with A( 5, 0), B(1, 7), C(8, 1), and D(2, 6).Then demonstrate that ABCD is a rectangle. 20. AC is a segment in the coordinate plane. Explain why sometimes it is a good idea to give points A and C the coordinates (2a, 2b) and (2c, 2d). 21. If you want to prove that the diagonals of a parallelogram bisect each other using coordinate geometry, how would you place the parallelogram on the coordinate plane? Give the coordinates of the vertices for the placement you choose. 22. Write the Given and Prove statements for a proof of the following theorem: If a quadrilateral is a square, then its diagonals are perpendicular. Square FGHK and its diagonals have been drawn for you. 23. Write a coordinate proof of the following theorem: If a quadrilateral is a kite, then its diagonals are perpendicular. 5
6 Geometry Module 4 Unit 2 Practice Exam Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 1 Naming Coordinates KEY: algebra coordinate plane isosceles trapezoid kite 2. ANS: A PTS: 1 DIF: L2 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 1 Naming Coordinates KEY: algebra coordinate plane rectangle square DOK: DOK 1 SHORT ANSWER 3. ANS: isosceles PTS: 1 DIF: L2 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 1 Classifying a Triangle KEY: triangle distance formula isosceles scalene 4. ANS: kite PTS: 1 DIF: L3 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 3 Classifying a Quadrilateral 5. ANS: (b, a) KEY: midpoint kite rectangle PTS: 1 DIF: L2 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 2 Using Variable Coordinates KEY: coordinate plane algebra rectangle 1
7 6. ANS: (p + r + s, 2q) PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 2 Using Variable Coordinates KEY: algebra coordinate plane isosceles trapezoid midsegment 7. ANS: (a + c, b) PTS: 1 DIF: L2 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 2 Using Variable Coordinates KEY: parallelogram coordinate plane algebra 2
8 8. ANS: PTS: 1 DIF: L4 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 3 Classifying a Quadrilateral KEY: coordinate plane graphing parallelogram opposite sides multipart question DOK: DOK 3 3
9 9. ANS: Answers may vary. Sample: PTS: 1 DIF: L2 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 1 Naming Coordinates KEY: kite algebra coordinate plane 10. ANS: Answers may vary. Sample: PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 1 Naming Coordinates KEY: rhombus algebra coordinate plane 11. ANS: Each diagonal has length (a b) 2 c 2. PTS: 1 DIF: L4 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 2 Using Variable Coordinates KEY: algebra coordinate plane isosceles trapezoid trapezoid diagonal 4
10 12. ANS: PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 2 Using Variable Coordinates KEY: algebra coordinate plane square ESSAY 13. ANS: [4] Shows ABCD is a parallelogram (by any of several methods); then shows diagonals are perpendicular by computing slopes to be 3 2 and 2. Includes meaningful commentary 3 on what is occurring. [3] Shows ABCD is a parallelogram and shows diagonals are perpendicular, but presentation is not clear. [2] work complete and shows correct ideas, but contains errors [1] work incomplete, but shows some understanding of what to do PTS: 1 DIF: L3 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 2 Classifying a Parallelogram KEY: extended response rubricbased question reasoning writing in math rhombus 5
11 14. ANS: [4] midpoint of AB ( 3, 3) midpoint of BC (3, 3) midpoint of CD (3, 1) midpoint of DA ( 3, 1) The figure is a rectangle. [3] Shows correct midpoints and shape, but presentation is not clear. [2] work complete and shows correct ideas, but contains errors [1] work incomplete, but shows some understanding of what to do PTS: 1 DIF: L3 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 3 Classifying a Quadrilateral KEY: extended response rubricbased question reasoning writing in math rhombus square rectangle 6
12 15. ANS: [4] Proofs may vary. Sample: For rhombus in the coordinate plane, as shown, the quadrilateral determined by the midpoints (a, b), ( a, b), (a, b), and ( a, b) has one pair of opposite sides vertical (no slope) and the other pair horizontal (slope 0), so the quadrilateral is a parallelogram with perpendicular sides, or a rectangle. [3] shows good setup and idea for proof, but has some small inaccuracies [2] shows reasonable setup and idea for proof, but has significant math difficulties [1] shows reasonable setup for proof PTS: 1 DIF: L4 REF: 69 Proofs Using Coordinate Geometry OBJ: Prove theorems using figures in the coordinate plane TOP: 69 Problem 1 Writing a Coordinate Proof KEY: rhombus midpoint rectangle extended response rubricbased question coordinate plane algebra writing in math reasoning DOK: DOK 3 7
13 16. ANS: [4] Proofs may vary. Sample: Given: Line l is the perpendicular bisector of CD. Prove: Point R(a, b) is equidistant from points C and D. By the Distance Formula, CR (a 0) 2 (b 0) 2 a 2 b 2 DR (a 2a) 2 (b 0) 2 a 2 b 2 Because CR DR, point R on the perpendicular bisector of the segment is equidistant from the endpoints of the segment. [3] shows good setup and idea for proof, but has some small inaccuracies [2] shows reasonable setup and idea for proof, but has significant math difficulties [1] shows reasonable setup for proof PTS: 1 DIF: L4 REF: 69 Proofs Using Coordinate Geometry OBJ: Prove theorems using figures in the coordinate plane TOP: 69 Problem 1 Writing a Coordinate Proof KEY: rhombus midpoint rectangle extended response rubricbased question coordinate plane algebra writing in math reasoning DOK: DOK 3 8
14 17. ANS: [4] Proofs may vary. Sample: Answers may vary. Sample: Given: WY and XZ are diagonals of rectangle WXYZ. Prove: WY XZ Distance of XZ (a 0) 2 (0 b) 2 a 2 b 2 WY (a 0) 2 (b 0) 2 a 2 b 2 By the definition of congruency, diagonals XZ and WY of rectangle WXYZ are congruent. [3] shows good setup and idea for proof, but has some small inaccuracies [2] shows reasonable setup and idea for proof, but has significant math difficulties [1] shows reasonable setup for proof PTS: 1 DIF: L4 REF: 69 Proofs Using Coordinate Geometry OBJ: Prove theorems using figures in the coordinate plane TOP: 69 Problem 2 Writing a Coordinate Proof KEY: rhombus midpoint rectangle extended response rubricbased question coordinate plane algebra writing in math reasoning DOK: DOK 3 9
15 OTHER 18. ANS: Answers may vary. Sample: JKL is scalene. All three sides have different lengths. PTS: 1 DIF: L3 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 1 Classifying a Triangle KEY: scalene isosceles triangle distance formula 10
16 19. ANS: Answers may vary. Sample: slope of AB is 7 6 slope of BC is 6 7 slope of CD is 7 6 slope of AD is 6 7 AB CD and BC AD, so ABCD is a parallelogram. AB BC, BC CD, CD AD, and AB AD. ABC, BCD, CDA, BAD are right angles. ABCD is a rectangle. PTS: 1 DIF: L4 REF: 67 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 TOP: 67 Problem 2 Classifying a Parallelogram KEY: coordinate plane proof reasoning rectangle slope multipart question 20. ANS: Answers may vary. Sample: Using a factor of 2 in each coordinate simplifies what you find for the coordinates of the midpoint of AB, namely (a + c, b + d). PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 1 Naming Coordinates KEY: algebra coordinate plane graphing reasoning writing in math 11
17 21. ANS: Answers may vary. Sample: PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 3 Planning a Coordinate Proof KEY: diagonal parallelogram algebra coordinate plane writing in math reasoning DOK: DOK ANS: Answers may vary. Sample: Given: FH and GK are diagonals of square FGHK. Prove: FH GK PTS: 1 DIF: L3 REF: 68 Applying Coordinate Geometry TOP: 68 Problem 3 Planning a Coordinate Proof KEY: diagonal parallelogram algebra coordinate plane writing in math reasoning DOK: DOK 3 12
18 23. ANS: 4] Proofs may vary. Sample: Given: AC and BD are diagonals of kite ABCD. Prove: AC BD Slope of DB 3b 3b 2a 0 0 Slope of AC 4b 0 a a 4b 0 = undefined A line with a zero slope is perpendicular to a line with an undefined slope, so the diagonals of the kite are perpendicular. [3] shows good setup and idea for proof, but has some small inaccuracies [2] shows reasonable setup and idea for proof, but has significant math difficulties [1] shows reasonable setup for proof PTS: 1 DIF: L3 REF: 69 Proofs Using Coordinate Geometry OBJ: Prove theorems using figures in the coordinate plane TOP: 69 Problem 2 Writing a Coordinate Proof KEY: diagonal kite algebra coordinate plane writing in math reasoning DOK: DOK 3 13
Quadrilaterals Unit Review
Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationQuadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid
Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,
More informationName: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work
Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work 1. An equilateral triangle always has three 60 interior angles. 2. A line segment
More informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationGeometry. Unit 6. Quadrilaterals. Unit 6
Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections
More information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More information63 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer.
1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before
More informationIsosceles triangles. Key Words: Isosceles triangle, midpoint, median, angle bisectors, perpendicular bisectors
Isosceles triangles Lesson Summary: Students will investigate the properties of isosceles triangles. Angle bisectors, perpendicular bisectors, midpoints, and medians are also examined in this lesson. A
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram
More informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
More informationYou can use the postulates below to prove several theorems.
Using Area Formulas You can use the postulates below to prove several theorems. AREA POSTULATES Postulate Area of a Square Postulate The area of a square is the square of the length of its side, or s.
More information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More information8.1 Find Angle Measures in Polygons
8.1 Find Angle Measures in Polygons Obj.: To find angle measures in polygons. Key Vocabulary Diagonal  A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon ABCDE has two
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More informationSTRAIGHT LINE COORDINATE GEOMETRY
STRAIGHT LINE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) The points P and Q have coordinates ( 7,3 ) and ( 5,0), respectively. a) Determine an equation for the straight line PQ, giving the answer
More information**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.
Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationCoordinate Coplanar Distance Formula Midpoint Formula
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to
More informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
More informationProperties of Special Parallelograms
Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then
More informationPolygons in the Coordinate Plane. isosceles 2. X 2 4
Name lass ate 67 Practice Form G Polgons in the oordinate Plane etermine whether k is scalene, isosceles, or equilateral. 1. isosceles. scalene 3. scalene. isosceles What is the most precise classification
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationLine. A straight path that continues forever in both directions.
Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 3. PROOF Write a twocolumn proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationHigher Geometry Problems
Higher Geometry Problems ( Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement
More informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More informationChapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More information5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle  A midsegment of a triangle is a segment that connects
More informationName Geometry Exam Review #1: Constructions and Vocab
Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make
More informationTABLE OF CONTENTS. Free resource from Commercial redistribution prohibited. Understanding Geometry Table of Contents
Understanding Geometry Table of Contents TABLE OF CONTENTS Why Use This Book...ii Teaching Suggestions...vi About the Author...vi Student Introduction...vii Dedication...viii Chapter 1 Fundamentals of
More informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More information112 Areas of Trapezoids, Rhombi, and Kites. Find the area of each trapezoid, rhombus, or kite. 1. SOLUTION: 2. SOLUTION: 3.
Find the area of each trapezoid, rhombus, or kite. 1. 2. 3. esolutions Manual  Powered by Cognero Page 1 4. OPEN ENDED Suki is doing fashion design at 4H Club. Her first project is to make a simple Aline
More informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationOverview Mathematical Practices Congruence
Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason
More informationhttp://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4
of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationWinter 2016 Math 213 Final Exam. Points Possible. Subtotal 100. Total 100
Winter 2016 Math 213 Final Exam Name Instructions: Show ALL work. Simplify wherever possible. Clearly indicate your final answer. Problem Number Points Possible Score 1 25 2 25 3 25 4 25 Subtotal 100 Extra
More information116 Chapter 6 Transformations and the Coordinate Plane
116 Chapter 6 Transformations and the Coordinate Plane Chapter 61 The Coordinates of a Point in a Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationContent Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade
Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources
More informationEstimating Angle Measures
1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle
More informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
More informationQuadrilaterals GETTING READY FOR INSTRUCTION
Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper
More informationTIgeometry.com. Geometry. Angle Bisectors in a Triangle
Angle Bisectors in a Triangle ID: 8892 Time required 40 minutes Topic: Triangles and Their Centers Use inductive reasoning to postulate a relationship between an angle bisector and the arms of the angle.
More information11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
More informationC1: Coordinate geometry of straight lines
B_Chap0_0805.qd 5/6/04 0:4 am Page 8 CHAPTER C: Coordinate geometr of straight lines Learning objectives After studing this chapter, ou should be able to: use the language of coordinate geometr find the
More informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationChapters 4 and 5 Notes: Quadrilaterals and Similar Triangles
Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is
More informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
More information(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationGeometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationA. 3y = 2x + 1. y = x + 3. y = x  3. D. 2y = 3x + 3
Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x  1 D. y = 3x + 1
More informationPROPERTIES OF TRIANGLES AND QUADRILATERALS
Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 21 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS
More informationGEOMETRY WHAT S INSIDE: CASIO Education Workbook Series. with the CASIO fx9750gii
CASIO Education Workbook Series GEOMETRY with the CASIO fx9750gii WHAT S INSIDE: Distance Slope Pythagorean Theorem Properties of Triangles Reflections Rotations Translations Properties of Parallelogramsams
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More information37 Basic Geometric Shapes and Figures
37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars
More information41 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationMath 311 Test III, Spring 2013 (with solutions)
Math 311 Test III, Spring 2013 (with solutions) Dr Holmes April 25, 2013 It is extremely likely that there are mistakes in the solutions given! Please call them to my attention if you find them. This exam
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More information1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED
CONDENSED LESSON 1.1 Building Blocks of Geometry In this lesson you will Learn about points, lines, and planes and how to represent them Learn definitions of collinear, coplanar, line segment, congruent
More informationGeometry, Final Review Packet
Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a
More informationLesson 13: Proofs in Geometry
211 Lesson 13: Proofs in Geometry Beginning with this lesson and continuing for the next few lessons, we will explore the role of proofs and counterexamples in geometry. To begin, recall the Pythagorean
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationSu.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)
MA.912.G.2 Geometry: Standard 2: Polygons  Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures
More informationUNCORRECTED PROOF. Unit objectives. Website links Opener Online angle puzzles 2.5 Geometry resources, including interactive explanations
21.1 Sequences Get in line Unit objectives Understand a proof that the angle sum of a triangle is 180 and of a quadrilateral is 360 ; and the exterior angle of a triangle is equal to the sum of the two
More informationMost popular response to
Class #33 Most popular response to What did the students want to prove? The angle bisectors of a square meet at a point. A square is a convex quadrilateral in which all sides are congruent and all angles
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More informationMathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More informationGeometry 81 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 81 ngles of Polygons 1. Interior angles  The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
More informationFinding Parallelogram Vertices
About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection
More information7. 6 Justifying Constructions
31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
More informationacute angle acute triangle Cartesian coordinate system concave polygon congruent figures
acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles
More informationM 1312 Section Trapezoids
M 1312 Section 4.4 1 Trapezoids Definition: trapezoid is a quadrilateral with exactly two parallel sides. Parts of a trapezoid: Base Leg Leg Leg Base Base Base Leg Isosceles Trapezoid: Every trapezoid
More informationClassify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a
More informationGeometry. Kellenberg Memorial High School
20152016 Geometry Kellenberg Memorial High School Undefined Terms and Basic Definitions 1 Click here for Chapter 1 Student Notes Section 1 Undefined Terms 1.1: Undefined Terms (we accept these as true)
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationGeometry  Chapter 5 Review
Class: Date: Geometry  Chapter 5 Review 1. Points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 17. Find AC. The diagram is not to scale. 3. Find the value of x. The diagram is not to
More information