April 28, 2017 Geometry 11.1 Circumference and Arc Length
|
|
|
- Cynthia Brooks
- 5 years ago
- Views:
Transcription
1 11.1 Warmup April 28, 2017 Geometry 11.1 Circumference and Arc Length 1
2 Geometry 11.1 Circumference and Arc Length
3 11.1 Essential Question How can you find the length of a circular arc? April 28, 2017 Geometry 11.1 Circumference and Arc Length 3
4 Goals Find the circumference of a circle. Find the length of an arc. Solve problems using circumference and arc length. arc April 28, 2017 Geometry 11.1 Circumference and Arc Length 4
5 Circumference The circumference is the distance around a circle. April 28, 2017 Geometry 11.1 Circumference and Arc Length 5
6 Pi π d The ratio of the circumference to the diameter is called pi π. Use the Greek letter for pi: C C d April 28, 2017 Geometry 11.1 Circumference and Arc Length 6
7 More About Pi The fraction 22/7 is close. 355/113 is closer. The Hebrews thought it was 3. Current computer calculations have pi to over 5 trillion places. April 28, 2017 Geometry 11.1 Circumference and Arc Length 7
8 Pi to a few decimal places: April 28, 2017 Geometry 11.1 Circumference and Arc Length 8
9 Pi is Irrational does not repeat. does not terminate. There is NO algebraic technique than can be used to find its value. Computing requires the use of calculus. April 28, 2017 Geometry 11.1 Circumference and Arc Length 9
10 Circumference You can find the circumference if you know the diameter (d) or the radius (r) of the circle. C C 2 d r April 28, 2017 Geometry 11.1 Circumference and Arc Length 10
11 Example 1 Find the circumference of a circle with a radius of 8. C 2 (8) This is the circumference in terms of pi. When computing C in decimal, use 3.14 or the π button on your calculator. April 28, 2017 Geometry 11.1 Circumference and Arc Length 11
12 Arc Length The ratio of the length of an arc to the circumference of a circle is equal to the ratio of the measure of the arc⁰ to 360. A B Arc Length of AB mab 2r 360 Recall: the measure of the arc is equal to the central angle that intercepts it. April 28, 2017 Geometry 11.1 Circumference and Arc Length 12
13 Example 2 Find the length of AB. A Write the proportion: L B 80 5 Length of Arc Circumference of circle L 80 2 (5) 360 Central Angle April 28, 2017 Geometry 11.1 Circumference and Arc Length 13
14 Solve the proportion L 80 2 (5) 360 L L 20 L 6.98 B A 80 5 L April 28, 2017 Geometry 11.1 Circumference and Arc Length 14
15 Your Turn Find the length of AB B x A 25 8 x 25 2 (8) 360 x x 400 x x April 28, 2017 Geometry 11.1 Circumference and Arc Length 15
16 Example 3 A 25 x B 10 The length of AB is 25 and the radius is 10. Find the mab. 25 x 2 (10) x x 20 x April 28, 2017 Geometry 11.1 Circumference and Arc Length 16
17 Semicircle Half of a circle. Its measure is 180. Its length is one-half the circumference. April 28, 2017 Geometry 11.1 Circumference and Arc Length 17
18 Example 4 An indoor track at a gym has the design below. What is the length of the entire track? 40 ft 100 ft April 28, 2017 Geometry 11.1 Circumference and Arc Length 18
19 Example 4 Solution The ends make one circle. The diameter is 40 ft. C = (40) 40 ft 100 ft April 28, 2017 Geometry 11.1 Circumference and Arc Length 19
20 Example 4 Solution Add 200 for the straight segments. Perimeter = ft Or, ft. 40 ft 100 ft April 28, 2017 Geometry 11.1 Circumference and Arc Length 20
21 Practice 1 The circumference of a circle is 200 ft. Find its radius. C 2 r r r r April 28, 2017 Geometry 11.1 Circumference and Arc Length 21
22 Practice 2 The radius of a circle is 16 in and central angle ACB measures 42. Find the length of arc AB. x 42 2 (16) (16)(42) x 360 x April 28, 2017 Geometry 11.1 Circumference and Arc Length 22
23 Practice 3 An arc of a circle has a length of 12 cm. Its central angle is 15. What is the radius of the circle? r (15) r 12(360) 30 r 4320 r r April 28, 2017 Geometry 11.1 Circumference and Arc Length 23
24 Practice 4 A circle has a diameter of 20 cm. An arc on the circle is 10 cm in length. Find the measure of the central angle. 10 x 2 (10) x 3600 x x April 28, 2017 Geometry 11.1 Circumference and Arc Length 24
25 Summary The length of an arc on a circle is proportional to the measure of the arc and to the central angle. A semicircle has 180 and it s length is half the circumference. April 28, 2017 Geometry 11.1 Circumference and Arc Length 25
26 Homework April 28, 2017 Geometry 11.1 Circumference and Arc Length 26
Curvaceous Circles BUT IT DOES WORK! Yep we can still relate the formula for the area of a circle to the formula for the area of a rectangle
Curvaceous Circles So our running theme on our worksheets has been that all the formulas for calculating the area of various shapes comes back to relating that shape to a rectangle. But how can that possibly
CIRCLE PROPERTIES M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier
Mathematics Revision Guides Circle Properties Page 1 of 5 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier CIRCLE PROPERTIES Version:.1 Date: 8-10-01 Mathematics Revision Guides
CK-12 Geometry: Circumference and Arc Length
CK-12 Geometry: Circumference and Arc Length Learning Objectives Find the circumference of a circle. Define the length of an arc and find arc length. Review Queue a. Find a central angle in that intercepts
ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS.
ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS. A B X Z Y A MINOR arc is LESS than 1/2 way around the circle. A MAJOR arc is MORE than 1/2 way around
( ) Find the value of x mhg. H x G. Find m AXB and m Y A D X 56. Baroody Page 1 of 18
1. ( ) Find the value of x mhg 30 F 80 H x G E 2. Find m X and m Y 120 X 56 Y aroody age 1 of 18 3. Find mq X 70 30 Y Q 4. Find the radius of a circle in which a 48 cm. chord is 8 cm closer to the center
Name Period Date. GEO2.2: Area of Circles Derive the area formula for circles. Solve application problems that involve areas of circles.
Name Period Date GEOMETRY AND MEASUREMENT Student Pages for Packet 2: Circles GEO2.1 Circumference Use multiple representations to explore the relationship between the diameter and the circumference of
Question 1: Is zero a rational number? Can you write it in the form p, where p and q are integers and q 0?
Class IX - NCERT Maths Exercise (.) Question : Is zero a rational number? Can you write it in the form p, where p and q are integers and q 0? q Solution : Consider the definition of a rational number.
Lesson 9. Exit Ticket Sample Solutions ( )= ( ) The arc length of is (. ) or.. Homework Problem Set Sample Solutions S.79
Exit Ticket Sample Solutions 1. Find the arc length of. ( )= ()() ( )=. ( ) = The arc length of is (. ) or.. Homework Problem Set Sample Solutions S.79 1. and are points on the circle of radius, and the
Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle.
Circles Circles and Basic Terminology I. Circle - the set of all points in a plane that are a given distance from a given point (called the center) in the plane. Circles are named by their center. II.
Math Multiple Choice Identify the choice that best completes the statement or answers the question.
Math 7-4.2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the circumference of this circle. Leave π in your answer. 12 m A) m B) m C) m D) 12 m 2.
( ) = 28. 2r = d 2 = = r d = r. 2 = r or 1. Free Pre-Algebra Lesson 33! page 1. Lesson 33 Formulas for Circles
Free Pre-Algebra Lesson 33! page 1 Lesson 33 Formulas for Circles What is a Circle? Everyone knows what a circle looks like. A sprinkler line rotates around a center pivot, forming circles of irrigated
Key competencies (student abilities)
Year 9 Mathematics Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful Cambridge IGCSE Mathematics candidates gain lifelong
UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction
Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of
Circles. Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: Angles & Arcs Class Work
Circles Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: 1. Name the radii 2. Name the chord(s) 3. Name the diameter(s) 4. If AC= 7, what does TC=? 5. If
UNIT 6. BELL WORK: Draw 3 different sized circles, 1 must be at LEAST 15cm across! Cut out each circle. The Circle
UNIT 6 BELL WORK: Draw 3 different sized circles, 1 must be at LEAST 15cm across! Cut out each circle The Circle 1 Questions How are perimeter and area related? How are the areas of polygons and circles
How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots
. Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,
Unit 3: Number, Algebra, Geometry 2
Unit 3: Number, Algebra, Geometry 2 Number Use standard form, expressed in standard notation and on a calculator display Calculate with standard form Convert between ordinary and standard form representations
A π day celebration! Everyone s favorite geometric constant!
A π day celebration! Everyone s favorite geometric constant! Math Circle March 10, 2019 The circumference of a circle is another word for its perimeter. A circle s circumference is proportional to its
Yes zero is a rational number as it can be represented in the
1 REAL NUMBERS EXERCISE 1.1 Q: 1 Is zero a rational number? Can you write it in the form 0?, where p and q are integers and q Yes zero is a rational number as it can be represented in the form, where p
Class IX Chapter 1 Number Sustems Maths
Class IX Chapter 1 Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form 0? and q, where p and q are integers Yes. Zero is a rational number as it can be represented
Circumference and Arc Length
Circumference and Arc Length Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit
Number Sets 1,0,1,2,3,... } 3. Rational Numbers ( Q) 1. Natural Numbers ( N) A number is a rational number if. it can be written as where a and
Number Sets 1. Natural Numbers ( N) N { 0,1,,,... } This set is often referred to as the counting numbers that include zero.. Integers ( Z) Z {...,,, 1,0,1,,,... }. Rational Numbers ( Q) A number is a
Trigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.1 Radian and Degree Measure Copyright Cengage Learning. All rights reserved. What You Should Learn Describe angles. Use radian
Arkansas Tech University MATH 2914: Calculus I Dr. Marcel B. Finan. Solution to Section 4.5
Arkansas Tech University MATH 914: Calculus I Dr Marcel B Finan Solution to Section 45 1 (a) y y 1 3 1 4 3 0 60 4 19 76 5 18 90 6 17 10 7 16 11 8 15 10 9 14 16 10 13 130 11 1 13 1 11 13 13 10 130 14 9
AREAS RELATED TO CIRCLES Introduction
AREAS RELATED TO CIRCLES 3 AREAS RELATED TO CIRCLES 1 1.1 Introduction You are already familiar with some methods of finding perimeters and areas of simple plane figures such as rectangles, squares, parallelograms,
Good Morning! Make sure ur rdy2go when the bell rings!
Good Morning! Make sure ur rdy2go when the bell rings! 1 2 3 4 5 How would you define circle congruence? 6 Defn: Circle congruence Circle with radii. 7 Defn: Circle congruence Circle with radii. Defn:
An angle on the coordinate plane is in standard form when the vertex is on the origin and one ray lies on the positive x-axis.
Name: Topic: Main Ideas/Questions Notes/Eamples Date: Class: Angles in Standard Form y θ An angle on the coordinate plane is in standard form when the verte is on the origin and one ray lies on the positive
I can translate between a number line graph, an inequality, and interval notation.
Unit 1: Absolute Value 2 I can translate between a number line graph, an inequality, and interval notation. 2 2 I can translate between absolute value expressions and English statements about numbers on
The GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
Assignment Assigned Date Due Date Grade 6.7 Worksheet
Geometry Unit 6: Packet 2 CIRCLES This is a packet containing the homework and some classwork for the second half of unit 6. You will turn in completed assignments by their designated due date. If you
106 Circles and Arcs :]p Mafhematics Florida Standards
![106 Circles and Arcs :]p Mafhematics Florida Standards](/thumbs/83/88357734.jpg "106 Circles and Arcs :]p Mafhematics Florida Standards")
106 Circles and Arcs :]p Mafhematics Florida Standards MAFS.912.G-C0.1.1 Know precise definitions of... circle... MAFS.912.G-C.1.1 Prove that all circles are similar. Also MAFS.912.G-C.1.2, MAFS.912.G-C.2.5
Angles and Transformations - Ms Buerckner
Angles and Transformations - Ms Buerckner Question 1 The marked angle is: a revolution a reflex angle Question 2 This rectangle has: four right angles four obtuse angles four acute angles Question 3 Each
10.5 Areas of Circles and Sectors
10.5. Areas of Circles and Sectors www.ck12.org 10.5 Areas of Circles and Sectors Learning Objectives Find the area of circles, sectors, and segments. Review Queue Find the area of the shaded region in
Geometry Honors Homework
Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle
( ) Chapter 10 Review Question Answers. Find the value of x mhg. m B = 1 2 ( 80 - x) H x G. E 30 = 80 - x. x = 50. Find m AXB and m Y A D X 56
hapter 10 Review Question nswers 1. ( ) Find the value of mhg 30 m = 1 2 ( 30) = 15 F 80 m = 1 2 ( 80 - ) H G E 30 = 80 - = 50 2. Find m X and m Y m X = 1 120 + 56 2 ( ) = 88 120 X 56 Y m Y = 1 120-56
Corresponding parts of congruent triangles are congruent. (CPCTC)
Corresponding parts of congruent triangles are congruent. (CPCTC) Corresponding parts of congruent triangles are congruent. (CPCTC) Definition: Congruent triangles: Triangles that have all corresponding
Math-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms
Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms Describe the idea of area. Area attempts to answer the question how big is it? The area
Circles. Parts of a Circle: Vocabulary. Arc : Part of a circle defined by a chord or two radii. It is a part of the whole circumference.
Page 1 Circles Parts of a Circle: Vocabulary Arc : Part of a circle defined by a chord or two radii. It is a part of the whole circumference. Area of a disc : The measure of the surface of a disc. Think
Chapter 5: Measurement of Circles
Chapter 5: Measurement of Circles Getting Started, p. 151 1. a) Perimeter, since the word around is used. b) Area, since since the word wrap is used. c) Perimeter, since the word wrap is used. 2. a) 5
Item 8. Constructing the Square Area of Two Proving No Irrationals. 6 Total Pages
Item 8 Constructing the Square Area of Two Proving No Irrationals 6 Total Pages 1 2 We want to start with Pi. How Geometry Proves No Irrations They call Pi the ratio of the circumference of a circle to
Example 1 Give the degree measure of the angle shown on the circle.
Section 5. Angles 307 Section 5. Angles Because many applications involving circles also involve q rotation of the circle, it is natural to introduce a measure for the rotation, or angle, between two rays
1.1 Angles and Degree Measure
J. Jenkins - Math 060 Notes. Angles and Degree Measure An angle is often thought of as being formed b rotating one ra awa from a fied ra indicated b an arrow. The fied ra is the initial side and the rotated
Stepping stones for Number systems. 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit)
Quality for Equality Stepping stones for Number systems 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit) 2) Counting numbers: 1,2,3,... Natural numbers Represent
Arcs and Inscribed Angles of Circles
Arcs and Inscribed Angles of Circles Inscribed angles have: Vertex on the circle Sides are chords (Chords AB and BC) Angle ABC is inscribed in the circle AC is the intercepted arc because it is created
Chapter 13: Trigonometry Unit 1
Chapter 13: Trigonometry Unit 1 Lesson 1: Radian Measure Lesson 2: Coterminal Angles Lesson 3: Reference Angles Lesson 4: The Unit Circle Lesson 5: Trig Exact Values Lesson 6: Trig Exact Values, Radian
CLASS-IX MATHEMATICS. For. Pre-Foundation Course CAREER POINT
CLASS-IX MATHEMATICS For Pre-Foundation Course CAREER POINT CONTENTS S. No. CHAPTERS PAGE NO. 0. Number System... 0 3 0. Polynomials... 39 53 03. Co-ordinate Geometry... 54 04. Introduction to Euclid's
Verulam School Mathematics. Year 9 Revision Material (with answers) Page 1
Verulam School Mathematics Year 9 Revision Material (with answers) Page 1 Q1. (a) Simplify a 2 a 4 Answer... (b) Simplify b 9 b 3 Answer... (c) Simplify c 5 c c 5 Answer... (Total 3 marks) Q2. (a) Expand
x n+1 = ( x n + ) converges, then it converges to α. [2]
![x n+1 = ( x n + ) converges, then it converges to α. [2]](/thumbs/92/110299841.jpg "x n+1 = ( x n + ) converges, then it converges to α. [2]")
1 A Level - Mathematics P 3 ITERATION ( With references and answers) [ Numerical Solution of Equation] Q1. The equation x 3 - x 2 6 = 0 has one real root, denoted by α. i) Find by calculation the pair
I can calculate percent of change. I can calculate percent increases (sales tax, tip/gratuity, commission, fees, markup, etc ).
RATIO & PROPORTIONAL RELATIONSHIPS 7.RP.: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions,
Circles and Arcs. Objectives To find the measures of central angles and arcs To find the circumference and arc length
10-6 ircles and rcs ommon ore tate tandards G-..1 Know precise definitions of... circle... G-..1 rove that all circles are similar. lso G-..2, G-..5 M 1, M 3, M 4, M 6, M 8 bjectives o find the measures
AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
AP Calculus Summer Homework 2015-2016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points
King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
Mu Alpha Theta State 2007 Euclidean Circles
Mu Alpha Theta State 2007 Euclidean Circles 1. Joe had a bet with Mr. Federer saying that if Federer can solve the following problem in one minute, Joe would be his slave for a whole month. The problem
4.1 Angles and Angle Measure.notebook. Chapter 4: Trigonometry and the Unit Circle
Chapter 4: Trigonometry and the Unit Circle 1 Chapter 4 4.1 Angles and Angle Measure Pages 166 179 How many radii are there around any circle??? 2 There are radii around the circumference of any circle.
11. Concentric Circles: Circles that lie in the same plane and have the same center.
Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The
Grade 8. Concepts and Procedures. The Number System. Expressions and Equations
Grade 8 Concepts and Procedures The Number System Target A: Know that there are numbers that are not rational and approximate them by rational numbers. identify pi as not rational, classify numbers as
4 The Cartesian Coordinate System- Pictures of Equations
4 The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the
Algebra 2 End of Course Review
1 Natural numbers are not just whole numbers. Integers are all whole numbers both positive and negative. Rational or fractional numbers are all fractional types and are considered ratios because they divide
Circles Test Circumference/Area Calculator Active. Clearly label the following in the circle to the right.
Circles Test Circumference/Area Calculator Active Clearly label the following in the circle to the right. 1. Point B as the center 2. Diameter AC 3. Radius BD 4. Chord EF 5. Arc FG Find the following.
Solution: The graph is certainly not a line, since the variables are squared. Let s plot points and see what we get.
1 CH 81 THE CIRCLE INTRODUCTION W e re now ready for a new type of graph. In this chapter we analyze nature s perfect shape, the circle. Whereas the equation of a line has no variables that are squared,
What is the longest chord?.
Section: 7-6 Topic: ircles and rcs Standard: 7 & 21 ircle Naming a ircle Name: lass: Geometry 1 Period: Date: In a plane, a circle is equidistant from a given point called the. circle is named by its.
EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE
1 EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE INSTRUCTIONAL ACTIVITY Lesson 1 LEARNING GOAL Students will develop an understanding of diameter, radius, circumference, and pi and the relationships among
Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Math League SCASD Meet #4 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Circles 3. Number Theory: Modular Arithmetic,
Circle Notes. Circumference and Area of Circles
Love of Learning Educational Services Bringing Curiosity, Relevance, and Enjoyment to the Math Classroom Circle Notes Circumference and Area of Circles Guided note taking pages for calculating circumference
Mid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER:
Refer to. 1. Name the circle. The center of the circle is A. Therefore, the circle is 2. Name a diameter. ; since is a chord that passes through the center, it is a diameter. 3. Name a chord that is not
11.3 areas of circles and sectors 2016 ink.notebook. April 12, Page 134 Page Areas of Circles and Sectors. Standards.
11.3 areas of circles and sectors 2016 ink.notebook Page 134 Page 133 11.3 Areas of Circles and Sectors Round to the nearest Lesson Objectives Standards Lesson Notes 11.3 Areas of Circles and Sectors Lesson
Programme 6 Area of Circles and Composite Shapes Worksheet 1: Programme Questions
Worksheet 1: Programme Questions 1. The large pizza is a 12 inch one. What is the diameter of the smaller size pizza? 2. What formula gives the area of a circle? 3. Whose pizza was better value, Katie
CN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.
CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will
radii: AP, PR, PB diameter: AB chords: AB, CD, AF secant: AG or AG tangent: semicircles: ACB, ARB minor arcs: AC, AR, RD, BC,
h 6 Note Sheets L Shortened Key Note Sheets hapter 6: iscovering and roving ircle roperties eview: ircles Vocabulary If you are having problems recalling the vocabulary, look back at your notes for Lesson
1. Draw and label a diagram to illustrate the property of a tangent to a circle.
Master 8.17 Extra Practice 1 Lesson 8.1 Properties of Tangents to a Circle 1. Draw and label a diagram to illustrate the property of a tangent to a circle. 2. Point O is the centre of the circle. Points
Pi: The Ultimate Ratio
Pi: The Ultimate Ratio Exploring the Ratio of Circle Circumference to Diameter 1 WARM UP Scale up or down to determine an equivalent ratio. 1. 18 miles 3 hours 5? 1 hour 2. $750 4 days 3. 4. 12 in. 1 ft
Regents Exam Questions by Topic Page 1 ANGLES: Arc Length NAME:
Regents Exam Questions by Topic Page 1 1. 010725b As shown in the accompanying diagram, a dial in the shape of a semicircle has a radius of 4 centimeters. Find the measure of, in radians, when the pointer
Core Mathematics C2 Advanced Subsidiary
Paper Reference(s) 6664 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Wednesday 19 January 2005 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae (Green) Items
Mth 076: Applied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE
Mth 076: pplied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE INTRODUTION TO GEOMETRY Pick up Geometric Formula Sheet (This sheet may be used while testing) ssignment Eleven: Problems Involving
CBSE Class IX Syllabus. Mathematics Class 9 Syllabus
Mathematics Class 9 Syllabus Course Structure First Term Units Unit Marks I Number System 17 II Algebra 25 III Geometry 37 IV Co-ordinate Geometry 6 V Mensuration 5 Total 90 Second Term Units Unit Marks
2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
Wheels Radius / Distance Traveled
Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating
Algebra 2 Summer Assignment
Geometr Algebra Summer Assignment Name ID: 1 Date Period This assignment is for students who have completed Geometr and are taking Algebra in the 018-019 school ear. 1) Did ou read the instructions? )
Replacement for a Carpenter s Square
Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed
Honors Geometry Circle Investigation - Instructions
Honors Geometry ircle Investigation - Instructions 1. On the first circle a. onnect points and O with a line segment. b. onnect points O and also. c. Measure O. d. Estimate the degree measure of by using
Number Systems. Exercise 1.1. Question 1. Is zero a rational number? Can you write it in the form p q,
s Exercise. Question. Is zero a rational number? Can you write it in the form p q, where p and q are integers and q 0? Solution Yes, write 0 (where 0 and are integers and q which is not equal to zero).
WARM UP. Sunday, November 16, 2014
WARM UP Sunday, November 16, 2014 1 2 3 4 5 6 7 8 9 10 Objectives Use properties of circles to derive the formula for sector area. Determine arc length and arc measure for given central and inscribed angle
Grade 6 Curriculum Map Key: Math in Focus Course 1 (MIF)
TIME FRAME September (10 days) UNIT/CONCEPTS Course 1A Content Chapter 1: Positive Numbers and the Number Line CORE GOALS & SKILLS Big Idea: Whole numbers, fractions, and decimals are numbers that can
Angles and Applications
CHAPTER 1 Angles and Applications 1.1 Introduction Trigonometry is the branch of mathematics concerned with the measurement of the parts, sides, and angles of a triangle. Plane trigonometry, which is the
UNIT I : NUMBER SYSTEMS
CLASS X First Term Marks : 80 UNITS MARKS I. NUMBER SYSTEMS 10 II. ALGEBRA 20 III. GEOMETRY 15 IV TRIGONOMETRY 20 V STATISTICS 15 TOTAL 80 UNIT I : NUMBER SYSTEMS 1. REAL NUMBERS (15) Periods Euclid's
Chapter 3. Radian Measure and Circular Functions. Copyright 2005 Pearson Education, Inc.
Chapter 3 Radian Measure and Circular Functions Copyright 2005 Pearson Education, Inc. 3.1 Radian Measure Copyright 2005 Pearson Education, Inc. Measuring Angles Thus far we have measured angles in degrees
UNIT 13 Areas: CSEC Revision Test
Area of square 64 cm (4 marks) MEP Jamaica: STRAND E : 1. The shaded square has sides of length 1 cm. It is enlarged a number of times as shown. Complete the table. Length of side of square 1 cm cm 3 cm
150 Lecture Notes - Section 6.1 Angle Measure
c Marcia Drost, February, 008 Definition of Terms 50 Lecture Notes - Section 6. Angle Measure ray a line angle vertex two rays with a common endpoint the common endpoint initial side terminal side Standard
Core Mathematics 2 Coordinate Geometry
Core Mathematics 2 Coordinate Geometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Coordinate Geometry 1 Coordinate geometry in the (x, y) plane Coordinate geometry of the circle
Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle
College Algebra. Chapter 1 Review Created by: Lauren Atkinson. Math Coordinator, Mary Stangler Center for Academic Success
College Algebra Chapter 1 Review Created by: Lauren Atkinson Math Coordinator, Mary Stangler Center for Academic Success Note: This review is composed of questions from the chapter review at the end of
Write an equation and solve for x, then find the missing angle measures. Pictures are not drawn to scale. 1. Equation: Solution: Equation: Solution:
6.1d Class Activity: Triangles and Circles In chapter 5, you worked with angle measures in triangles. Now, you are going to practice writing equations to solve for a missing angle measure. Recall from
The City School. Syllabus Breakup for Academic Year Class 9. Mathematics. First Term Syllabus Breakup Topic Objectives Resources
The City School Syllabus Breakup for Academic Year 2014-15 Class 9 All mentioned topics included in Final Term Exam Mathematics First Term Syllabus Breakup Topic Objectives Resources Recap of Previous
Paper Reference. Core Mathematics C2 Advanced Subsidiary. Wednesday 19 January 2005 Morning Time: 1 hour 30 minutes. Mathematical Formulae (Green)
Centre No. Candidate No. Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Wednesday 19 January 2005 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical
Fundamentals of Mathematics (MATH 1510)
Fundamentals of Mathematics () Instructor: Email: shenlili@yorku.ca Department of Mathematics and Statistics York University March 14-18, 2016 Outline 1 2 s An angle AOB consists of two rays R 1 and R
"Full Coverage": Non-Right Angled Triangles
"Full Coverage": Non-Right Angled Triangles This worksheet is designed to cover one question of each type seen in past papers, for each GCSE Higher Tier topic. This worksheet was automatically generated
If x = 180 then the arc subtended by x is a semicircle which we know has length πr. Now we argue that:
Arclength Consider a circle of radius r and an angle of x degrees as shown in the figure below. The segment of the circle opposite the angle x is called the arc subtended by x. We need a formula for its
Ms. Woodman s Mathematics Name: Period:
Ms. Woodman s Mathematics Name: Period: Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle
Physics 6303 Lecture 22 November 7, There are numerous methods of calculating these residues, and I list them below. lim
Physics 6303 Lecture 22 November 7, 208 LAST TIME:, 2 2 2, There are numerous methods of calculating these residues, I list them below.. We may calculate the Laurent series pick out the coefficient. 2.