# SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore,

Save this PDF as:

Size: px
Start display at page:

Download "SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore," ## Transcription

1 Find each measure. 1. The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, 2. WT, if ZX = 20 and TY = 15 The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent. Therefore, WY = ZX. WT + TY = ZX WT + 15 = 20 WT = 5 esolutions Manual - Powered by Cognero Page 1

2 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A ( 4, 1), B( 2, 3), C(3, 3), and D(5, 1). 3. Verify that ABCD is a trapezoid. First graph the points on a coordinate grid and draw the trapezoid. Use the slope formula to find the slope of the sides of the trapezoid. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral ABCD is a trapezoid. esolutions Manual - Powered by Cognero Page 2

3 4. Determine whether ABCD is an isosceles trapezoid. Explain. Refer to the graph of the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral ABCD is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are equal. Therefore, ABCD is an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 3

4 CCSS SENSE-MAKING If ABCD is a kite, find each measure. 7. A is an obtuse angle and C is an acute angle. Since a kite can only have one pair of opposite congruent angles and The sum of the measures of the angles of a quadrilateral is 360. Find each measure. 9. The trapezoid QRST is an isosceles trapezoid so each pair of base angles is congruent. So, The sum of the measures of the angles of a quadrilateral is 360. Let m Q = m T = x. So, esolutions Manual - Powered by Cognero Page 4

5 11. PW, if XZ = 18 and PY = 3 The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent. Therefore, YW = XZ. YP + PW = XZ. 3 + PW = 18 PW = 15 esolutions Manual - Powered by Cognero Page 5

6 COORDINATE GEOMETRY For each quadrilateral with the given vertices, verify that the quadrilateral is a trapezoid and determine whether the figure is an isosceles trapezoid. 13. J( 4, 6), K(6, 2), L(1, 3), M( 4, 1) First graph the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral JKLM is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are not equal. Therefore, JKLM is not an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 6

7 15. W( 5, 1), X( 2, 2), Y(3, 1), Z(5, 3) First graph the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral WXYZ is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are not equal. Therefore, WXYZ is not an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 7

8 For trapezoid QRTU, V and S are midpoints of the legs. 17. If QR = 4 and UT = 16, find VS. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, 19. If TU = 26 and SV = 17, find QR. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, 21. If RQ = 5 and VS = 11, find UT. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, esolutions Manual - Powered by Cognero Page 8

### 6-6 Trapezoids and Kites. CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP By the Pythagorean Theorem, WP 2 = WX 2 XP 2 = 6 2 4 2 = 20 27. A kite can only have one pair of opposite congruent angles and Let m X = m

### Geometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES Geometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES Use Properties of Trapezoids and Kites Objective: Students will be able to identify and use properties to solve trapezoids and kites. Agenda

### 6-1. Angles of Polygons. Lesson 6-1. What You ll Learn. Active Vocabulary 6-1 Angles of Polygons What You ll Learn Skim Lesson 6-1. Predict two things that you expect to learn based on the headings and figures in the lesson. 1. 2. Lesson 6-1 Active Vocabulary diagonal New Vocabulary

### Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 www.jmap.org Name: G.G.69: Quadrilaterals in the Coordinate Plane 2: Investigate the properties of quadrilaterals in the coordinate Unit 6 Quadrilaterals ay lasswork ay Homework Monday Properties of a Parallelogram 1 HW 6.1 11/13 Tuesday 11/14 Proving a Parallelogram 2 HW 6.2 Wednesday 11/15 Thursday 11/16 Friday 11/17 Monday 11/20

### Geometry Tutor Worksheet 9 Quadrilaterals Geometry Tutor Worksheet 9 Quadrilaterals 1 Geometry Tutor - Worksheet 9 - Quadrilaterals 1. Which name best describes quadrilateral DEFG? 2. Which name best describes quadrilateral ABCD? 3. Which name

### The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2. ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid

### Warm-Up Exercises. Find the value of x. 1. ANSWER 65 ANSWER 120 Warm-Up Exercises Find the value of x. 1. 65 2. 120 Warm-Up Exercises Find the value of x. 3. 70 EXAMPLE Warm-Up 1Exercises Identify quadrilaterals Quadrilateral ABCD has at least one pair of opposite

### Secondary 2 Unit 7 Test Study Guide Class: Date: Secondary 2 Unit 7 Test Study Guide 2014-2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement can you use to conclude that

### Geometry - Chapter 6 Review Class: Date: Geometry - Chapter 6 Review 1. Find the sum of the measures of the angles of the figure. 4. Find the value of x. The diagram is not to scale. A. 1260 B. 900 C. 540 D. 720 2. The sum of the

### Geometry Unit 5 Practice Test Name: Class: Date: ID: X Geometry Unit 5 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x in the rectangle? Hint: use

### Indicate whether the statement is true or false. MATH 121 SPRING 2017 - PRACTICE FINAL EXAM Indicate whether the statement is true or false. 1. Given that point P is the midpoint of both and, it follows that. 2. If, then. 3. In a circle (or congruent

### 16. DOK 1, I will succeed." In this conditional statement, the underlined portion is Geometry Semester 1 REVIEW 1. DOK 1 The point that divides a line segment into two congruent segments. 2. DOK 1 lines have the same slope. 3. DOK 1 If you have two parallel lines and a transversal, then

### Geometry Unit 6 Note Sheets. Name of Lesson. 6.1 Angles of Polygons 1.5 days. 6.2 Parallelograms 1 day. 6.3 Tests for Parallelograms 1. Date Name of Lesson 6.1 Angles of Polygons 1.5 days 6.2 Parallelograms 1 day 6.3 Tests for Parallelograms 1.5 days Quiz 6.1-6.3 0.5 days 6.4 Rectangles 1 day 6.5 Rhombi and Squares 1 day 6.6 Trapezoids

### Geometry Topic 4 Quadrilaterals and Coordinate Proof Geometry Topic 4 Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 In the diagram below, parallelogram has diagonals and that intersect at point. Which expression is NOT always true? A. B. C. D. C

### Areas of Tropezoids, Rhombuses, and Kites 102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective

### All in the Family. b. Use your paper tracing to compare the side lengths of the parallelogram. What appears to be true? Summarize your findings below. The quadrilateral family is organized according to the number pairs of sides parallel in a particular quadrilateral. Given a quadrilateral, there are three distinct possibilities: both pairs of opposite 1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal

### Date: Period: Quadrilateral Word Problems: Review Sheet Name: Quadrilateral Word Problems: Review Sheet Date: Period: Geometry Honors Directions: Please answer the following on a separate sheet of paper. Completing this review sheet will help you to do well

### Plot the points. Then connect the vertices, X', Y', and Z' to form the reflected image. Graph each figure and its image under the given reflection. 11. rectangle ABCD with A(2, 4), B(4, 6), C(7, 3), and D(5, 1) in the x-axis. To reflect over the x-axis, multiply the y-coordinate of each vertex

### Geometry 1 FINAL REVIEW 2011 Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. Name: Period: Unit 6: Quadrilaterals Geometry Honors Homework Section 6.1: Classifying Quadrilaterals State whether each statement is true or false. Justify your response. 1. All squares are rectangles.

### Midsegment of a Trapezoid Technology ctivity 6.5 idsegment of a Trapezoid Question What are some properties of the midsegment of a trapezoid? Explore 1 raw. raw a point not on and construct a line parallel to through point. onstruct

### 6-3 Conditions for Parallelograms Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and y = 8.5. 3. 2x + 7 4. 16x 9 31 183 5. (8y + 5) 73 Objective Prove that a given quadrilateral

### 9.5 Properties and Conditions for Kites and Trapezoids Name lass ate 9.5 Properties and onditions for Kites and Trapezoids ssential uestion: What are the properties of kites and trapezoids? Resource Locker xplore xploring Properties of Kites kite is a quadrilateral

### 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section

### Geometry Vocabulary Book Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one

### FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true. FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth The Quadrilateral Detective a Coordinate Geometry Activity An object might certainly LOOK like a square, but how much information do you really need before you can be absolutely sure that it IS a square?

### Fair Game Review. Chapter 7. Name Date Name Date Chapter 7 Fair Game Review Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. 1. 2. 3. 4. 5. 6. 141 Name Date Chapter 7 Fair Game

### 8.3 Prove It! A Practice Understanding Task 15 8.3 Prove It! A Practice Understanding Task In this task you need to use all the things you know about quadrilaterals, distance, and slope to prove that the shapes are parallelograms, rectangles, rhombi,

### 6. Which angles in the diagram are congruent to 1? Choose all that apply. 2. m YKZ PRYZ is a rhombus. If RK = 5, RY = 13 and m YRZ = 67, find each measure. Quadrilateral GHJK is a rectangle and m 1 = 37. 1. KY 6. Which angles in the diagram are congruent to 1? Choose all that apply.

### Unit 7 Scale Drawings and Dilations Unit 7 Scale Drawings and Dilations Day Classwork Day Homework Friday 12/1 Unit 6 Test Monday 12/4 Tuesday 12/5 Properties of Scale Drawings Scale Drawings Using Constructions Dilations and Scale Drawings

### 6.2 Slopes of Parallel and Perpendicular Lines . Slopes of Parallel and Perpendicular Lines FOCUS Use slope to find out if two lines are parallel or perpendicular. These two lines are parallel. Slope of line AB Slope of line CD These two lines have

### Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1 Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once

### Properties of Special Parallelograms Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a trapezoid. Students then explore the shapes, making conclusions about

### 8 th Grade Domain 3: Geometry (28%) 8 th Grade Domain 3: Geometry (28%) 1. XYZ was obtained from ABC by a rotation about the point P. (MGSE8.G.1) Which indicates the correspondence of the vertices? A. B. C. A X, B Y, C Z A Y, B Z, C X A

### Title: Quadrilaterals Aren t Just Squares Title: Quadrilaterals ren t Just Squares Brief Overview: This is a collection of the first three lessons in a series of seven lessons studying characteristics of quadrilaterals, including trapezoids, parallelograms,

### Trapezoids and Kites. isosceles trapezoid. You are asked to prove the following theorems in the exercises. Page 1 of 8 6.5 Trapezoids and ites What you should learn O 1 Use properties of trapezoids. O 2 Use properties of kites. Why you should learn it To solve real-life problems, such as planning the layers

### Unit 6 Guided Notes. Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle. Unit 6 Guided Notes Geometry Name: Period: Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle. Materials: This paper, compass, ruler

### 3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine

### Parallels and Euclidean Geometry Parallels and Euclidean Geometry Lines l and m which are coplanar but do not meet are said to be parallel; we denote this by writing l m. Likewise, segments or rays are parallel if they are subsets of

### Geometry 2001 part 1 Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?

### June 2016 Regents GEOMETRY COMMON CORE 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2

### Trapezoids. are the bases. TP. / are the legs. 8 5 What You ll Learn You ll learn to identify and use the properties of trapezoids and isosceles trapezoids. rapezoids any state flags use geometric shapes in their designs. an you find a quadrilateral

### Polygon Unit Test Review Name Hour Polygon Unit Test Review Directions: You must show all work for all problems below. For the problems where you have a quadrilateral and use their properties, justify the set up, and provide the

### 11.2 Areas of Trapezoids, 11. Areas of Trapezoids, Rhombuses, and Kites Goal p Find areas of other types of quadrilaterals. Your Notes VOCABULARY Height of a trapezoid THEOREM 11.4: AREA OF A TRAPEZOID b 1 The area of a trapezoid

### Honors Geometry Chapter 6 Supplement. Q (4x) (5x) Honors Geometry hapter 6 upplement Name: 1. Given: Q m Q = (4x) m Q = (5x) m Q = 40 m Q = 32 Find the value of x, m Q, m Q, m Q Q (4x) (5x) 40 32 2. Given: m = (8x + 20) m = (150 6x) m = (12x + 60) a)

### 4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and 4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge

### Find the area and perimeter of each figure. Round to the nearest tenth if necessary. Find the area and perimeter of each figure. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite sides of a parallelogram

### 11.2 Areas of Trapezoids and Kites Investigating g Geometry ACTIVITY Use before Lesson 11.2 11.2 Areas of Trapezoids and Kites MATERIALS grap paper straigtedge scissors tape Q U E S T I O N How can you use a parallelogram to find oter areas?

### AW Math 10 UNIT 6 SIMILARITY OF FIGURES AW Math 10 UNIT 6 SIMILARITY OF FIGURES Assignment Title Work to complete Complete 1 Review Proportional Reasoning Cross Multiply and Divide 2 Similar Figures Similar Figures 3 4 Determining Sides in Similar

### Name Date. Chapter 15 Final Review Name Date Chapter 15 Final Review Tell whether the events are independent or dependent. Explain. 9) You spin a spinner twice. First Spin: You spin a 2. Second Spin: You spin an odd number. 10) Your committee

### LAB 9.2 The Pythagorean Theorem LAB 9.2 The Pythagorean Theorem Equipment: Geoboards, dot paper 1. The figure above shows a right triangle with a square on each side. Find the areas of the squares. 2. Make your own right triangles on

### Book 2. The wee Maths Book. Growth. Grow your brain. N4 Relationships. of Big Brain Grow your brain N4 Relationships Book 2 Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! The wee Maths Book of Big Brain Growth

### Mathematics 43601F. Geometry. In the style of General Certificate of Secondary Education Foundation Tier. Past Paper Questions by Topic TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials In the style of General Certificate of Secondary Education Foundation Tier Pages 2 3 4 5 Mark

### Investigation. Triangle, Triangle, Triangle. Work with a partner. Investigation Triangle, Triangle, Triangle Work with a partner. Materials: centimetre ruler 1-cm grid paper scissors Part 1 On grid paper, draw a large right triangle. Make sure its base is along a grid

### Foundations of Math II Unit 3: Similarity and Congruence Foundations of Math II Unit 3: Similarity and Congruence Academics High School Mathematics 3.1 Warm Up 1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch your

### 1. Convert 60 mi per hour into km per sec. 2. Convert 3000 square inches into square yards. ACT Practice Name Geo Unit 3 Review Hour Date Topics: Unit Conversions Length and Area Compound shapes Removing Area Area and Perimeter with radicals Isosceles and Equilateral triangles Pythagorean Theorem

### 2.1 Slope and Parallel Lines Name Class ate.1 Slope and Parallel Lines Essential Question: How can ou use slope to solve problems involving parallel lines? Eplore Proving the Slope Criteria for Parallel Lines Resource Locker The following

### Discussion: With a partner, discuss what you believe a parallelogram is? Parallelogram Definition: Name: Ms. Ayinde Date: Geometry CC 4.2: Properties of Parallelograms Objective: To recognize and apply properties of sides, angles, and diagonals of parallelograms. To determine the area and perimeter

### Lesson 3.1 Duplicating Segments and Angles Lesson 3.1 Duplicating Segments and ngles Name eriod Date In Exercises 1 3, use the segments and angles below. omplete the constructions on a separate piece of paper. S 1. Using only a compass and straightedge,

### CTB/McGraw-Hill. Math Quarter 2: Week 5: Mixed Review Test ID: Page 1 of 35 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703. All rights reserved. Only authorized customers

### Catty Corner. Side Lengths in Two and. Three Dimensions Catty Corner Side Lengths in Two and 4 Three Dimensions WARM UP A 1. Imagine that the rectangular solid is a room. An ant is on the floor situated at point A. Describe the shortest path the ant can crawl

### GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance

### Good Luck To. DIRECTIONS: Answer each question and show all work in the space provided. The next two terms of the sequence are, Good Luck To Period Date DIRECTIONS: Answer each question and show all work in the space provided. 1. Find the next two terms of the sequence. 6, 36, 216, 1296, _?_, _?_ The next two terms of the sequence

### Geometry Mrs. Crocker Spring 2014 Final Exam Review Name: Mod: Geometry Mrs. Crocker Spring 2014 Final Exam Review Use this exam review to complete your flip book and to study for your upcoming exam. You must bring with you to the exam: 1. Pencil, eraser,

### E G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.

### Slopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1 5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz Bell Quiz 5-8 Find the reciprocal. 1. 2 2. 1 pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through

### 6.3 proving parallelograms day ink.notebook. January 17, Page 20 Page Prove Parallelogram Using Coordinate Geometry. 6.3 proving parallelograms da 2 2016 ink.notebook Januar 17, 2017 Page 20 Page 21 6.3 Prove Using oordinate Geometr Lesson Objectives Standards Lesson Notes 6.3 Proving s Lesson Objectives Standards Lesson

### Geometry. a) Rhombus b) Square c) Trapezium d) Rectangle Geometry A polygon is a many sided closed shape. Four sided polygons are called quadrilaterals. Sum of angles in a quadrilateral equals 360. Parallelogram is a quadrilateral where opposite sides are parallel.

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications

### Find the coordinates of the midpoint of a segment having the given endpoints. G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to

### 4-4 Graphing Sine and Cosine Functions Describe how the graphs of f (x) and g(x) are related. Then find the amplitude of g(x), and sketch two periods of both functions on the same coordinate axes. 1. f (x) = sin x; g(x) = sin x The graph of

### A portfolio of counter-examples A portfolio of counter-examples With answers Consider each of the following claims. All of them are false, and most are based on common misconceptions. Devise a counter example to show the claim is false.

### 9.1 Properties of Parallelograms Name lass ate 9.1 Properties of Parallelograms Essential Question: What can you conclude about the sides, angles, and diagonals of a parallelogram? Explore Investigating Parallelograms quadrilateral is

### UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet Name Period Date UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet 24.1 The Pythagorean Theorem Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof

### Since each element is paired with unique element in the range, it is a function. 1. State the domain and range of the relation {( 3, 2), (4, 1), (0, 3), (5, 2), (2, 7)}. Then determine whether the relation is a function. The domain is the set of x-coordinates. The range is the set

### 1 st Subject: 2D Geometric Shape Construction and Division Joint Beginning and Intermediate Engineering Graphics 2 nd Week 1st Meeting Lecture Notes Instructor: Edward N. Locke Topic: Geometric Construction 1 st Subject: 2D Geometric Shape Construction and Division

### FSA Geometry EOC Getting ready for. Circles, Geometric Measurement, and Geometric Properties with Equations. Getting ready for. FSA Geometry EOC Circles, Geometric Measurement, and Geometric Properties with Equations 2014-2015 Teacher Packet Shared by Miami-Dade Schools Shared by Miami-Dade Schools MAFS.912.G-C.1.1 Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

### Constructing Perpendiculars to a Line. Finding the Right Line. Draw a line and a point labeled P not on the line, as shown above. Page 1 of 5 3.3 Intelligence plus character that is the goal of true education. MARTIN LUTHER KING, JR. Constructing Perpendiculars to a Line If you are in a room, look over at one of the walls. What is

### 6.1 Ratios, Proportions, and the Geometric Mean 6.1 Ratios, Proportions, and the Geometric Mean VOCABULARY Ratio of a to b Proportion Means and Extremes Geometric Mean EX1: Simplify Ratios Simplify the ratio. (See Table of Measures, p. 921) a. 76 cm:

### Book 17. The wee Maths Book. Growth. Grow your brain. Green. of Big Brain. Guaranteed to make your brain grow, just add some effort and hard work Grow your brain Green Book 17 Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! The wee Maths Book of Big Brain Growth Enlargement

### b = 7 The y-intercept is 7. State the x- and y-intercepts of each equation. Then use the intercepts to graph the equation. 1. y = 2x + 7 To find the x-intercept, substitute 0 for y and solve for x. y = 2x + 7 0 = 2x + 7 7 = 2x 3.5

### CHAPTER 3. Parallel & Perpendicular lines CHAPTER 3 Parallel & Perpendicular lines 3.1- Identify Pairs of Lines and Angles Parallel Lines: two lines are parallel if they do not intersect and are coplaner Skew lines: Two lines are skew if they

### ISBN Copyright 2015 The Continental Press, Inc. Table of COntents Introduction 3 Format of Books 4 Suggestions for Use 7 Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 175 ISBN 978-0-8454-8768-6 Copyright 2015 The Continental Study Island Copyright 2014 Edmentum - All rights reserved. Generation Date: 03/05/2014 Generated By: Brian Leslie Unit Rates 1. Tanya is training a turtle for a turtle race. For every of an hour that

### Methods in Mathematics (Linked Pair Pilot) Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Methods in Mathematics (Linked Pair Pilot) Unit 2 Geometry and Algebra Monday 11 November 2013

### 1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling: Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Geometry Target E [a]: Draw, construct,

### KCATM Geometry Name School KCATM Geometry 9 10 2013 1) Find the minimum perimeter of a rectangle whose area is 169 square meters. a) 42 meters b) 13 meters c) 26 meters d) 52 meters 2) Find the coordinates of the midpoint

### Foundations of Math II Unit 3: Similarity and Congruence Foundations of Math II Unit 3: Similarity and Congruence Academics High School Mathematics 3.1 Warm Up 1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch your

### Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example

### Angle Measure and Plane Figures Grade 4 Module 4 Angle Measure and Plane Figures OVERVIEW This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, 3.1 Number Operations and Equality Algebraic Postulates of Equality: Reflexive Property: a=a (Any number is equal to itself.) Substitution Property: If a=b, then a can be substituted for b in any expression. Find the x-intercept and y-intercept of the graph of each linear function. 11. The x-intercept is the point at which the y-coordinate is 0, or the line crosses the x-axis. So, the x-intercept is 8. The