6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date
|
|
- Allan Campbell
- 5 years ago
- Views:
Transcription
1 6.00 Trigonometry Geometry/Circles Basics for the ACT Name Period Date Perimeter and Area of Triangles and Rectangles The perimeter is the continuous line forming the boundary of a closed geometric figure. The area is the number of square units that covers a closed geometric figure. Ex: Find the perimeter and the area of the geometric figures. Square: Perimeter: Because all the sides are the same, the perimeter will be 4 times the length of one side. P 4(6.3) 5.km Area: The area will a side times a side, or a side. A (6.3) 39.69km Rectangle and Parallelogram: P (3) (0) 6cm Perimeter: Add the lengths of all four sides. A cm Because opposite sides of a rectangle and a parallelogram are equal, you can use the formula: P = l +w, where l is the length and w is the width. Area: In a rectangle, to find area you just multiply the length and the width: A = lw. It is a little trickier with a parallelogram, because to find area, the length and width must be perpendicular to one another (form a right P (3.7) angle.) The sides of a parallelogram are not necessarily perpendicular. Therefore you must take the base x height, A 7. where the height is the perpendicular distance between the bases. (7.).6yd 4.yd Triangle: Perimeter: Add the three sides. No special formula. Area: Once again you must use the perpendicular base and height. But you also must remember P 7 9 8km to multiply by ½! A 5. 3.km
2 Trapezoid: Perimeter: Add the four sides. No special formula. Area: A trapezoid has TWO bases the parallel sides. Therefore, you must add the bases together, then multiply by ½, and then multiply by the height, which is the perpendicular distance between the two parallel bases. P cm A (3.5.9) cm To find the missing value when you know the area, use the formula, plug in the values you know, and follow the rules of algebra to solve for the missing value. Ex: Find the missing value with the given information. A bh 5.8 ( b)(6) 5.8 3b 8.6 b A 64.8 ( b ( b 3.4) b 3.4 b ( b b ) h 3.4) 9 Compute Circumference and Area of Circles Perimeter: The perimeter of a circle is called the circumference. Use the formula: C = π diameter, or if you know the radius, use C = π radius Area: Use the formula: A = π radius. **On the ACT, you will usually leave your answers in terms of π because the test was actually designed to be completed without a calculator! Ex: Find the circumference and area of the circle: C r C () A r A () C ft A ft
3 Perimeter and Area of Simple Composite Geometric Figures The perimeter of an irregular shape is equal to the sum of the segments and semi-circles around the outside of the figure. A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles. To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together. Example: Find the perimeter and area of the composite figure: Perimeter: the outside is made up of two 60 yard segments, and two semi-circles who diameters are 60. If put together, they would form a circle with radius 30 yds. Find the circumference P of the circle and add it to the two 60 yd. sides. P 0 60 yds Area: Find the area of the 60 yd. square, and the area of the circle with a diameter of 60. Add them together. A s A 60 r (30) A yds Arc Length & Sector Area in Circles The arc length is the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints (which would be a chord). A minor arc is named by its two endpoints, such as AB. An arc > 80 o is a major arc and is named by its endpoints and one point inbetween, such as ADB. An arc = 80 o is a semi-circle. A circular sector or circle sector (symbol: ), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. Ex: Find the exact arc length. 05 Solution: the length of the arc is of the circumference of the 360 circle. Use this information to write an equation and solve. Arc length mi
4 Ex: Find the exact sector area. 5 Solution: the area of the sector is of the area of the entire 360 circle. Use this information to write an equation and solve. Angles in Circles Sector Area km There are many relationships between the angles, chords, secants, and tangents of a circle. The most commonly used on the ACT are: Central Angles central angles have their vertex at the center of the circle. A central angle s measure is equal to the arc it subtends (cuts through.) 88 o Arc FD = 8 o Inscribed Angles inscribed angles have their vertex ON the circle. An inscribed angle is ½ of the arc it subtends. Tangents any tangent to a circle meets the radius at the point of tangency at a 90 o angle. Because of the right angle, right triangles can be formed, which means the Pythagorean Theorem can be used to find missing measurements. Vertical angles formed in circles are still congruent; Linear Pairs are still supplementary. Pythagorean Theorem/Pythagorean Triples For any right triangle, the length of the hypotenuse squared (the longest side, opposite the right angle) is equal to the sum of the squares of the two legs of the right triangle. Pythagorean Theorem: a + b = c The converse of the Pythagorean Theorem is also true: If three sides of a triangle work in the Pythagorean Theorem, then they are the sides of a right triangle. If the side lengths are integers, it is said they form a Pythagorean Triple.
5 Examples: Use the properties of the angles of a circle and the Pythagorean Theorem to find the exact (in terms of π) answers to the following: Solution: The arcs are the same as the central angles. Because the central angles are vertical, they are congruent. Therefore the arcs are also congruent. Set up an equation and solve. x x 6 x 6 x 6 The angle is an inscribed angle, therefore it is ½ of the arc LM. Set up an equation and solve. 7x 4 (3x ) 7x 4 6x x 5 m LKM 7(5) 4 m LKM 8 o The line in question is tangent to the circle, which means it forms a right angle with the radius at that point. Since we have a right triangle and know sides, we can use the Pythagorean Theorem to find the missing side. (Careful the one side is a diameter of the circle, so it is 6, not 8!!) a a a a a b a c 0 44
6
7
8
9 Find the perimeter and area of each composite figure.
10
11
12
h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.
ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this
More informationE 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.
More information9.1 and 9.2 Introduction to Circles
Date: Secondary Math 2 Vocabulary 9.1 and 9.2 Introduction to Circles Define the following terms and identify them on the circle: Circle: The set of all points in a plane that are equidistant from a given
More informationGeometry 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
More information(1) Page 482 #1 20. (2) Page 488 #1 14. (3) Page # (4) Page 495 #1 10. (5) Page #12 30,
Geometry/Trigonometry Unit 8: Circles Notes Name: Date: Period: # (1) Page 482 #1 20 (2) Page 488 #1 14 (3) Page 488 489 #15 26 (4) Page 495 #1 10 (5) Page 495 496 #12 30, 37 39 (6) Page 502 #1 7 (7) Page
More informationGeometry. Practice Pack
Geometry Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Lines and Angles Practice 1.1 What Is Geometry?........................ 1 Practice 1.2 What Is Geometry?........................ 2 Practice
More informationProject Maths Geometry Notes
The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam
More information9-1: Circle Basics GEOMETRY UNIT 9. And. 9-2: Tangent Properties
9-1: Circle Basics GEOMETRY UNIT 9 And 9-2: Tangent Properties CIRCLES Content Objective: Students will be able to solve for missing lengths in circles. Language Objective: Students will be able to identify
More information1. 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
More informationStudent Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Form: 501
Student Name: Teacher: Date: District: Rowan Assessment: 9_12 T and I IC61 - Drafting I Test 1 Description: Test 4 A (Diagrams) Form: 501 Please use the following figure for this question. 1. In the GEOMETRIC
More informationWe will study all three methods, but first let's review a few basic points about units of measurement.
WELCOME Many pay items are computed on the basis of area measurements, items such as base, surfacing, sidewalks, ditch pavement, slope pavement, and Performance turf. This chapter will describe methods
More informationFind 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
More informationGeometer s Skethchpad 8th Grade Guide to Learning Geometry
Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
More informationWS Stilwell Practice 11-1
Name: Date: Period: WS Stilwell Practice 11-1 Find the area of each figure. Show your formula, work, and answer. Be sure to label! 1) 2) A calculator is allowed 3) 4) 5) 6) 7) Rectangle: 8) Parallelogram:
More informationDaily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC.
Daily Warmup Questions from HW?? B 1. BD bisects ABC. Find the m ABC. (3x + 17) (7x - 39) C 2. The figure below is a regular polygon. Find the value of x. - x 2 + x + 43 A D 4x 2 + x - 37 3. The measure
More informationTangents to Circles. The distance across the circle, through its center, is the diameter of the circle. The diameter is twice the radius.
ircles Tangents to ircles circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. circle with center P is called circle P. The distance from
More information1 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
More informationUNIT 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
More informationFINAL 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
More informationGEO: 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
More informationWhat role does the central angle play in helping us find lengths of arcs and areas of regions within the circle?
Middletown Public Schools Mathematics Unit Planning Organizer Subject Geometry Grade/Course 10 Unit 5 Circles and other Conic Sections Duration 16 instructional + 4 days for reteaching/enrichment Big Idea
More informationName No. Geometry 9-3 1) Complete the table: Name No. Geometry 9-1 1) Name a secant. Name a diameter. Name a tangent. Name No. Geometry 9-2 1) Find JK
Geometry 9-1 1) Name a secant 1) Complete the table: Name a diameter Name a tangent Geometry 9-2 1) Find JK 2) Find the measure of 1 Geometry 9-2 2) 3) At 2:00 the hands of a clock form an angle of 2)
More informationSquare Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest
More informationDroodle for Geometry Final Exam
Droodle for Geometry Final Exam Answer Key by David Pleacher Can you name this droodle? Back in 1953, Roger Price invented a minor art form called the Droodle, which he described as "a borkley-looking
More informationArea of Composite Figures. ESSENTIAL QUESTION do you find the area of composite figures? 7.9.C
? LESSON 9.4 Area of Composite Figures ESSENTIAL QUESTION How do you find the area of composite figures? Equations, expressions, and relationships Determine the area of composite figures containing combinations
More informationCHAPTER 10 PROPERTIES OF CIRCLES
HT 0 OTIS OF ILS In this chapter we address ig IS: ) Using properties of segments that intersect circles ) pplying angle relationships in circles 3) Using circles in the coordinate plane Section: ssential
More informationGeometry 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.
More informationGeometry 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?
More informationThe problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in
The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Totally Unusual The dice
More informationClass 5 Geometry O B A C. Answer the questions. For more such worksheets visit
ID : in-5-geometry [1] Class 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) The set square is in the shape of. (2) Identify the semicircle that contains 'C'. A C O B
More informationChapter 1. Trigonometry Week 6 pp
Fall, Triginometry 5-, Week -7 Chapter. Trigonometry Week pp.-8 What is the TRIGONOMETRY o TrigonometryAngle+ Three sides + triangle + circle. Trigonometry: Measurement of Triangles (derived form Greek
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More information3 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.
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 informationLesson 20T ~ Parts of Circles
Lesson 20T ~ Parts of Circles Name Period Date 1. Draw a diameter. 2. Draw a chord. 3. Draw a central angle. 4. Draw a radius. 5. Give two names for the line drawn in the circle. Given the radius, find
More informationINTERMEDIATE LEVEL MEASUREMENT
INTERMEDIATE LEVEL MEASUREMENT TABLE OF CONTENTS Format & Background Information...3-6 Learning Experience 1- Getting Started...6-7 Learning Experience 2 - Cube and Rectangular Prisms...8 Learning Experience
More informationArea of Composite Figures. ESSENTIAL QUESTION How do you find the area of composite figures? 7.G.2.6
LESSON 9.3 Area of Composite Figures Solve real-world and mathematical problems involving area, of objects composed of triangles, quadrilaterals, polygons,. ESSENTIAL QUESTION How do you find the area
More informationSec Geometry - Constructions
Sec 2.2 - Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have
More informationDownloaded from
Understanding Elementary Shapes 1 1.In the given figure, lines l and m are.. to each other. (A) perpendicular (B) parallel (C) intersect (D) None of them. 2.a) If a clock hand starts from 12 and stops
More informationMATH MEASUREMENT AND GEOMETRY
Students: 1. Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. 1. Compare weights, capacities, geometric measures, time, and
More informationThe 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
More information3.3. 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
More informationPerimeters of Composite Figures
8. Perimeters of Composite Figures How can you find the perimeter of a composite figure? ACTIVITY: Finding a Pattern Work with a partner. Describe the pattern of the perimeters. Use your pattern to find
More information1999 Mathcounts National Sprint Round Solutions
999 Mathcounts National Sprint Round Solutions. Solution: 5. A -digit number is divisible by if the sum of its digits is divisible by. The first digit cannot be 0, so we have the following four groups
More information2016 Geometry Honors Summer Packet
Name: 2016 Geometry Honors Summer Packet This packet is due the first day of school. It will be graded for completion and effort shown. There will be an assessment on these concepts the first week of school.
More informationUnit 6 Lesson 1 Circle Geometry Properties Project
Unit 6 Lesson 1 Circle Geometry Properties Project Name Part A Look up and define the following vocabulary words. Use an illustration where appropriate. Some of this vocabulary can be found in the glossary
More informationUnit C Homework Helper Answer Key
Lesson 3-1 Measuring Angles 1. 30 2. 140 3. acute 4. IV 5. x 35 6. x 5 7. 20 ; acute; NAK 8. x 15; answers will vary. 9. x 50 10. a. x 15 11. x 23 12. 3 13. a. 65 b. Read the inner scale of the protractor.
More informationName. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0
Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume
More informationHow to Do Trigonometry Without Memorizing (Almost) Anything
How to Do Trigonometry Without Memorizing (Almost) Anything Moti en-ari Weizmann Institute of Science http://www.weizmann.ac.il/sci-tea/benari/ c 07 by Moti en-ari. This work is licensed under the reative
More informationAll About That Base... and Height
All About That Base... and Height Area of Triangles and Quadrilaterals 2 WARM UP Write 3 different expressions to describe the total area of this rectangle. LEARNING GOALS State and compare the attributes
More informationGeometry. Warm Ups. Chapter 11
Geometry Warm Ups Chapter 11 Name Period Teacher 1 1.) Find h. Show all work. (Hint: Remember special right triangles.) a.) b.) c.) 2.) Triangle RST is a right triangle. Find the measure of angle R. Show
More informationIndicate 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
More informationGeometry 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,
More informationUNIT 10 PERIMETER AND AREA
UNIT 10 PERIMETER AND AREA INTRODUCTION In this Unit, we will define basic geometric shapes and use definitions to categorize geometric figures. Then we will use the ideas of measuring length and area
More informationSquares and Square Roots Algebra 11.1
Squares and Square Roots Algebra 11.1 To square a number, multiply the number by itself. Practice: Solve. 1. 1. 0.6. (9) 4. 10 11 Squares and Square Roots are Inverse Operations. If =y then is a square
More informationUnit 10 Arcs and Angles of Circles
Lesson 1: Thales Theorem Opening Exercise Vocabulary Unit 10 Arcs and Angles of Circles Draw a diagram for each of the vocabulary words. Definition Circle The set of all points equidistant from a given
More informationCatty 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
More information2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
More informationFind the area and perimeter of any enlargement of the original rug above. Your work must include the following:
7-1.Your friend Alonzo owns a rug manufacturing company, which is famous for its unique designs. Each rug design has an original size as well as enlargements that are exactly the same shape. Find the area
More informationUse a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 )
Use a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 ) A telescope is supported by a tower that casts a shadow 40 meters long. The distance from the top of the tower to the
More informationgame pieces game board spinner game cards lined paper solutions paper (folded in half to conceal the answers)
RACE TO THE FINISH! Materials needed: game pieces game board spinner game cards lined paper solutions paper (folded in half to conceal the answers) Directions: Each player starts with his or her game piece
More informationInvestigation 1 Going Off on a Tangent
Investigation 1 Going Off on a Tangent a compass, a straightedge In this investigation you will discover the relationship between a tangent line and the radius drawn to the point of tangency. Construct
More informationThe CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Fryer Contest. Thursday, April 18, 2013
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 2013 Fryer Contest Thursday, April 18, 2013 (in North America and South America) Friday, April 19, 2013 (outside of North America
More informationJune 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
More informationBasic Trigonometry You Should Know (Not only for this class but also for calculus)
Angle measurement: degrees and radians. Basic Trigonometry You Should Know (Not only for this class but also for calculus) There are 360 degrees in a full circle. If the circle has radius 1, then the circumference
More information5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY
Area of Polygons and Circles SUGGESTED LEARNING STRATEGIES: Think/Pair/Share ACTIVITY 5.3 Pictured below is an aerial view of a playground. An aerial view is the view from above something. Decide what
More informationGeometry. Teacher s Guide
Geometry Teacher s Guide WALCH PUBLISHING Table of Contents To the Teacher.......................................................... vi Classroom Management..................................................
More informationUniversity of Houston High School Mathematics Contest Geometry Exam Spring 2016
University of Houston High School Mathematics ontest Geometry Exam Spring 016 nswer the following. Note that diagrams may not be drawn to scale. 1. In the figure below, E, =, = 4 and E = 0. Find the length
More informationCovering and Surrounding Assessment. 1. (1 point) Find the area and perimeter of this rectangle. Explain how you found your answers.
Name: Date: Score: /20 Covering and Surrounding Assessment Short Answer: Answer each question, making sure to show your work or provide an explanation or sketch to support your answer in the box. Make
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationMATH STUDENT BOOK. 6th Grade Unit 8
MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF
More information7 th Grade Math Third Quarter Unit 4: Percent and Proportional Relationships (3 weeks) Topic A: Proportional Reasoning with Percents
HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT 7 th Grade Math Third Quarter Unit 4: Percent and Proportional Relationships (3 weeks) Topic A: Proportional Reasoning with Percents In Unit 4, students
More informationChapter 1 and Section 2.1
Chapter 1 and Section 2.1 Diana Pell Section 1.1: Angles, Degrees, and Special Triangles Angles Degree Measure Angles that measure 90 are called right angles. Angles that measure between 0 and 90 are called
More information3 Kevin s work for deriving the equation of a circle is shown below.
June 2016 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?
More informationGeometry: Measuring Two-Dimensional Figures
C H A P T E R Geometry: Measuring Two-Dimensional Figures What does landscape design have to do with math? In designing a circular path, pool, or fountain, landscape architects calculate the area of the
More informationACT Coordinate Geometry Review
ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this
More informationFSA 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
More informationChapter 9. Perimeter, Area, and Volume. 03/2017 LSowatsky
Chapter 9 Perimeter, Area, and Volume 03/2017 LSowatsky 1 9-1A: Area of Parallelograms I can find the areas and missing dimensions of parallelograms. LSowatsky 2 Mini-lab Materials: Graph paper Pencil
More informationFor full credit, show all work. Label all answers. For all problems involving a formula you must show the formula and each step. LABEL!
Accelerated Review 0: Polygons and Circles Name: For full credit, show all work. Label all answers. For all problems involving a formula you must show the formula and each step. LABEL! Find the area and
More information0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0)
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
More informationMath 1205 Trigonometry Review
Math 105 Trigonometry Review We begin with the unit circle. The definition of a unit circle is: x + y =1 where the center is (0, 0) and the radius is 1. An angle of 1 radian is an angle at the center of
More informationAREA See the Math Notes box in Lesson for more information about area.
AREA..1.. After measuring various angles, students look at measurement in more familiar situations, those of length and area on a flat surface. Students develop methods and formulas for calculating the
More informationLIST OF ACTIVITIES CLASS 9 TH
LIST OF ACTIVITIES CLASS 9 TH S.N. ACTIVITIES 1) 2) To create a wheel of THEODOROUS that demonstrates spiral in real number world. To verify algebraic identity (a + b + c) 2 = a 2 + b 2 + c 2 + 2 ab +
More informationMath + 4 (Red) SEMESTER 1. { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations
Math + 4 (Red) This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive
More informationSOL Review April Class work-nallari Math 8 Measurement & Geometry SOL -CAT Questions 13 SOL 8.6a, 8.7a-b, 8.8a-b,8.9,8.10a-b&8.
SOL Review April 18-22 Class work-nallari Math 8 Measurement & Geometry SOL -CAT Questions 13 SOL 8.6a, 8.7a-b, 8.8a-b,8.9,8.10a-b&8.11 Nallari Math 8 1 SOL8.6a 1.Lines l, m, and n intersect at the same
More informationStandards of Learning Guided Practice Suggestions. For use with the Mathematics Tools Practice in TestNav TM 8
Standards of Learning Guided Practice Suggestions For use with the Mathematics Tools Practice in TestNav TM 8 Table of Contents Change Log... 2 Introduction to TestNav TM 8: MC/TEI Document... 3 Guided
More informationAnalytic 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
More information1. Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. Begin with line segment XY.
1. onstruct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. egin with line segment. 2. lace the compass at point. djust the compass radius so that it is more
More informationBig Ideas Math: A Common Core Curriculum Geometry 2015 Correlated to Common Core State Standards for High School Geometry
Common Core State s for High School Geometry Conceptual Category: Geometry Domain: The Number System G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
More informationMATHEMATICS GEOMETRY HONORS. OPTIONS FOR NEXT COURSE Algebra II, Algebra II/Trigonometry, or Algebra, Functions, and Data Analysis
Parent / Student Course Information MATHEMATICS GEOMETRY HONORS Counselors are available to assist parents and students with course selections and career planning. Parents may arrange to meet with the
More informationPre Calc. Conics.
1 Pre Calc Conics 2015 03 24 www.njctl.org 2 Table of Contents click on the topic to go to that section Review of Midpoint and Distance Formulas Intro to Conic Sections Parabolas Circles Ellipses Hyperbolas
More informationThe problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in
The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Retiring and Hiring A
More informationPrint n Play Collection. Of the 12 Geometrical Puzzles
Print n Play Collection Of the 12 Geometrical Puzzles Puzzles Hexagon-Circle-Hexagon by Charles W. Trigg Regular hexagons are inscribed in and circumscribed outside a circle - as shown in the illustration.
More informationMeet #5 March Intermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2008 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2008 Category 1 Mystery 1. In the diagram to the right, each nonoverlapping section of the large rectangle is
More informationis formed where the diameters intersect? Label the center.
E 26 Get Into Shape Hints or notes: A circle will be folded into a variety of geometric shapes. This activity provides the opportunity to assess the concepts, vocabulary and knowledge of relationships
More informationGeometric Puzzle Medley
Geometric Puzzle Medley (16 August 2018) Jim Stevenson This is a collection of simple but elegant puzzles, mostly from a British high school math teacher Catriona Shearer @Cshearer41 (https://twitter.com/cshearer41),
More informationUNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles
UNIT PLAN Subject: Geometry Grade Level: 10-12 Unit #: 7 Unit Name: Circles Big Idea/Theme: The understanding of properties of circles, the lines that intersect them, and the use of their special segments
More informationSample. Do Not Copy. Chapter 5: Geometry. Introduction. Study Skills. 5.1 Angles. 5.2 Perimeter. 5.3 Area. 5.4 Circles. 5.5 Volume and Surface Area
Chapter 5: Geometry Study Skills 5.1 Angles 5.2 Perimeter 5.3 Area 5.4 Circles 5.5 Volume and Surface Area 5.6 Triangles 5.7 Square Roots and the Pythagorean Theorem Chapter 5 Projects Math@Work Foundations
More informationWorkout 5 Solutions. Peter S. Simon. Quiz, December 8, 2004
Workout 5 Solutions Peter S. Simon Quiz, December 8, 2004 Problem 1 Marika shoots a basketball until she makes 20 shots or until she has made 60% of her shots, whichever happens first. After she has made
More informationPerimeter, Circumference, Area and Ratio Long-Term Memory Review Grade 6 Review 1
Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width (l w) C) Add only one length and one width D) Multiply all of the lengths.
More informationAngles and Angle Measure
Angles and Angle Measure An angle θ is in standard position if the vertex of the angle is at the origin and the initial arm lies along the positive x-axis. The terminal arm can lie anywhere along the arc
More information