Using Chords. Essential Question What are two ways to determine when a chord is a diameter of a circle?
|
|
|
- Madeleine Glenn
- 5 years ago
- Views:
Transcription
1 10.3 Using hords ssential uestion What are two ways to determine when a chord is a diameter of a circle? rawing iameters OOKI O UU o be proficient in math, you need to look closely to discern a pattern or structure. Work with a partner. Use dynamic geometry software to construct a circle of radius 5 with center at the origin. raw a diameter that has the given point as an endpoint. xplain how you know that the chord you drew is a diameter. a. (4, 3) b. (0, 5) c. ( 3, 4) d. ( 5, 0) Work with a partner. Use dynamic geometry software to construct a chord of a circle. onstruct a chord on the perpendicular bisector of. What do you notice? hange the original chord and the circle several times. re your results always the same? Use your results to write a conjecture. Writing a onjecture about hords hord erpendicular to a iameter Work with a partner. Use dynamic geometry software to construct a diameter of a circle. hen construct a chord perpendicular to at point. ind the lengths and. What do you notice? hange the chord perpendicular to and the circle several times. o you always get the same results? Write a conjecture about a chord that is perpendicular to a diameter of a circle. ommunicate Your nswer 4. What are two ways to determine when a chord is a diameter of a circle? ection 10.3 Using hords 589
2 10.3 esson What You Will earn ore Vocabulary revious chord arc diameter I If, then the point, and any line, segment, or ray that contains, bisects. Use chords of circles to find lengths and arc measures. Using hords of ircles ecall that a chord is a segment with endpoints on a circle. ecause its endpoints lie on the circle, any chord divides the circle into two arcs. diameter divides a circle into two semicircles. ny other chord divides a circle into a minor arc and a major arc. heorems ongruent orresponding hords heorem In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. roof x. 19, p. 594 semicircle diameter semicircle major arc chord minor arc if and only if. bisects. erpendicular hord isector heorem If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. roof x. 22, p. 594 If is a diameter and, then and. erpendicular hord isector onverse If one chord of a circle is a perpendicular bisector of another chord, then the first chord is a diameter. roof x. 23, p. 594 If is a perpendicular bisector of, then is a diameter of the circle. Using ongruent hords to ind an rc Measure In the diagram,, JK, J and m JK = 80. ind m. 80 K OUIO ecause and JK are congruent chords in congruent circles, the corresponding minor arcs and JK are congruent by the ongruent orresponding hords heorem. o, m = m JK = hapter 10 ircles
3 Using a iameter a. ind K. b. ind m K. 11x OUIO a. iameter J is perpendicular to K. o, by the erpendicular hord isector heorem, J bisects K, and = K. J (70 + x) K 7 o, K = 2(K) = 2(7) = 14. b. iameter J is perpendicular to K. o, by the erpendicular hord isector heorem, J bisects K, and m J = m JK. m J = m JK erpendicular hord isector heorem 11x = (70 + x) ubstitute. 10x = 70 ubtract x from each side. x = 7 ivide each side by 10. o, m J = m JK = (70 + x) = (70 + 7) = 77, and m K = 2(m J ) = 2(77 ) = 154. Using erpendicular isectors hree bushes are arranged in a garden, as shown. Where should you place a sprinkler so that it is the same distance from each bush? OUIO tep 1 tep 2 tep 3 M sprinkler abel the bushes,, and, as shown. raw segments and. raw the perpendicular bisectors of and. y the erpendicular hord isector onverse, these lie on diameters of the circle containing,, and. ind the point where the perpendicular bisectors intersect. his is the center of the circle, which is equidistant from points,, and. Monitoring rogress In xercises 1 and 2, use the diagram of. 1. If m = 110, find m. 2. If m = 150, find m. In xercises 3 and 4, find the indicated length or arc measure m elp in nglish and panish at igideasmath.com 5 9x (80 x) 9 9 ection 10.3 Using hords 591
4 heorem quidistant hords heorem In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. roof x. 25, p. 594 if and only if =. Using ongruent hords to ind a ircle s adius W U 2x 5x 9 Y V X In the diagram, = = 16, U = 2x, and V = 5x 9. ind the radius of. OUIO ecause is a segment whose endpoints are the center and a point on the circle, it is a radius of. ecause U, U is a right triangle. pply properties of chords to find the lengths of the legs of U. W U 2x radius 5x 9 Y V X tep 1 ind U. ecause and are congruent chords, and are equidistant from by the quidistant hords heorem. o, U = V. U = V quidistant hords heorem 2x = 5x 9 ubstitute. x = 3 olve for x. o, U = 2x = 2(3) = 6. tep 2 ind U. ecause diameter WX, WX bisects by the erpendicular hord isector heorem. o, U = 1 (16) = 8. 2 J 3x K 7x 12 M tep 3 ind. ecause the lengths of the legs are U = 6 and U = 8, U is a right triangle with the ythagorean triple 6, 8, 10. o, = 10. o, the radius of is 10 units. Monitoring rogress elp in nglish and panish at igideasmath.com 5. In the diagram, JK = M = 24, = 3x, and = 7x 12. ind the radius of. 592 hapter 10 ircles
5 10.3 xercises ynamic olutions available at igideasmath.com Vocabulary and ore oncept heck 1. WII escribe what it means to bisect a chord. 2. WII wo chords of a circle are perpendicular and congruent. oes one of them have to be a diameter? xplain your reasoning. Monitoring rogress and Modeling with Mathematics In xercises 3 6, find the measure of the red arc or chord in. (ee xample 1.) Z W Y X U 34 V 6. 7 (5x + 2) (7x 12) In xercises 7 10, find the value of x. (ee xample 2.) M J 8 x 5x x U x O YI escribe and correct the error in reasoning. ecause bisects,. M 12. OM OVI In the cross section of the submarine shown, the control panels are parallel and the same length. escribe a method you can use to find the center of the cross section. Justify your method. (ee xample 3.) In xercises 13 and 14, determine whether is a diameter of the circle. xplain your reasoning In xercises 15 and 16, find the radius of. (ee xample 4.) x + 4 4x + 3 7x 6 16 ection 10.3 Using hords x OM OVI n archaeologist finds part of a circular plate. What was the 7 in. diameter of the plate to the nearest tenth of an 7 in. inch? Justify your answer. 6 in. 6 in.
6 18. OW O YOU I? What can you conclude from each diagram? ame a theorem that justifies your answer. a. c. J b. d OVI OM Use the diagram to prove each part of the biconditional in the ongruent orresponding hords heorem. a. iven and are congruent chords. rove b. iven rove 20. MMI OIO In, all the arcs shown have integer measures. how that x must be even. x M 22. OVI OM Use congruent triangles to prove the erpendicular hord isector heorem. iven is a diameter of. rove, 23. OVI OM Write a proof of the erpendicular hord isector onverse. iven is a perpendicular bisector of. rove is a diameter of the circle. (int: lot the center and draw and.) 24. OU OVOKI onsider two chords that intersect at point. o you think that =? Justify your answer. 25. OVI OM Use the diagram with the quidistant hords heorem on page 592 to prove both parts of the biconditional of this theorem. 26. MKI UM car is designed so that the rear wheel is only partially visible below the body of the car. he bottom edge of the panel is parallel to the ground. Your friend claims that the point where the tire touches the ground bisects. Is your friend correct? xplain your reasoning. 21. OI In, the lengths of the parallel chords are 20, 16, and 12. ind m. xplain your reasoning. Maintaining Mathematical roficiency ind the missing interior angle measure. (ection 7.1) eviewing what you learned in previous grades and lessons 27. uadrilateral JKM has angle measures m J = 32, m K = 25, and m = 44. ind m M. 28. entagon has angle measures m = 85, m = 134, m = 97, and m = 102. ind m. 594 hapter 10 ircles
Work with a partner. Use dynamic geometry software to draw any ABC. a. Bisect B and plot point D at the intersection of the angle bisector and AC.
.6 Proportionality heorems ssential uestion hat proportionality relationships eist in a triangle intersected by an angle bisector or by a line parallel to one of the sides? iscovering a Proportionality
b. Find the measures of the two angles formed by the chord and the tangent line.
0.5 NI NOW N I.5... ngle Relationships in ircles ssential Question When a chord intersects a tangent line or another chord, what relationships exist aong the angles and arcs fored? ngles ored by a hord
Seismograph (p. 582) Car (p. 554) Dartboard (p. 547) Bicycle Chain (p. 539)
10 ircles 10.1 ines and egments hat Intersect ircles 10. inding rc easures 10.3 Using hords 10.4 Inscribed ngles and olygons 10.5 ngle elationships in ircles 10.6 egment elationships in ircles 10.7 ircles
Chords and Arcs. Objectives To use congruent chords, arcs, and central angles To use perpendicular bisectors to chords
- hords and rcs ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. M, M bjectives To use congruent chords, arcs, and central angles To use perpendicular
Using Properties of Segments that Intersect Circles
ig Idea 1 H UY I I Using roperties of egments that Intersect ircles or Your otebook You learned several relationships between tangents, secants, and chords. ome of these relationships can help you determine
Essential Question How can you use a flowchart to prove a mathematical statement?
.6 Proving Geometric Relationships OMMON OR Learning Standard HSG-O..9 MOLING WITH MTHMTIS To be proficient in math, you need to map relationships using such tools as diagrams, two-way tables, graphs,
THEOREM 10.3 B C In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
10.3 Your Notes pply Properties of hords oal p Use relationships of arcs and chords in a circle. HOM 10.3 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their
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
Riding a Ferris Wheel
Lesson.1 Skills Practice Name ate iding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. center of the circle 6. central angle T H I 2. chord 7. inscribed
Geometry: A Complete Course
eometry: omplete ourse with rigonometry) odule - tudent Worket Written by: homas. lark Larry. ollins 4/2010 or ercises 20 22, use the diagram below. 20. ssume is a rectangle. a) f is 6, find. b) f is,
Introduction Circle Some terms related with a circle
141 ircle Introduction In our day-to-day life, we come across many objects which are round in shape, such as dials of many clocks, wheels of a vehicle, bangles, key rings, coins of denomination ` 1, `
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
10.3 Start Thinking Warm Up Cumulative Review Warm Up
10.3 tart hinking etermine if the statement is always true, sometimes true, or never true. plain your reasoning. 1. chord is a diameter. 2. diameter is a chord. 3. chord and a radius have the same measure.
10-1 Study Guide and Intervention
opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. NM I 10-1 tudy Guide and Intervention ircles and ircumference arts of ircles circle consists of all points in a plane that are
Circle-Chord properties
14 ircle-hord properties onstruction of a chord of given length. Equal chords are equidistant from the centre. ngles in a segment. ongrue nt circles and concentric circles. onstruction of congruent and
1.2 Perpendicular Lines
Name lass ate 1.2 erpendicular Lines Essential Question: What are the key ideas about perpendicular bisectors of a segment? 1 Explore onstructing erpendicular isectors and erpendicular Lines You can construct
Theorem 1.2 (Converse of Pythagoras theorem). If the lengths of the sides of ABC satisfy a 2 + b 2 = c 2, then the triangle has a right angle at C.
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a + b = c. roof. b a a 3 b b 4 b a b 4 1 a a 3
Study Guide and Assessment
tudy uide and ssessment nderstanding and sing the ocabulary fter completing this chapter, you should be able to define each term, property, or phrase and give an example or two of each. altitude (p. 4)
What You ll Learn. Why It s Important. We see circles in nature and in design. What do you already know about circles?
We see circles in nature and in design. What do you already know about circles? What You ll Learn ircle properties that relate: a tangent to a circle and the radius of the circle a chord in a circle, its
Chapter 19 Exercise 19.1
hapter 9 xercise 9... (i) n axiom is a statement that is accepted but cannot be proven, e.g. x + 0 = x. (ii) statement that can be proven logically: for example, ythagoras Theorem. (iii) The logical steps
Chapter 1. Some Basic Theorems. 1.1 The Pythagorean Theorem
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a 2 + b 2 = c 2. roof. b a a 3 2 b 2 b 4 b a b
Ready To Go On? Skills Intervention 11-1 Lines That Intersect Circles
Name ate lass STION 11 Ready To Go On? Skills Intervention 11-1 Lines That Intersect ircles ind these vocabulary words in Lesson 11-1 and the Multilingual Glossary. Vocabulary interior of a circle exterior
Geo - CH11 Practice Test
Geo - H11 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b. l d. 2. satellite rotates 50 miles
12.1 Triangle Proportionality Theorem
ame lass Date 12.1 Triangle roportionality Theorem ssential Question: When a line parallel to one side of a triangle intersects the other two sides, how does it divide those sides? Resource ocker xplore
10.4 Explore Inscribed Angles
Investigating g eometry IIY se before esson 0.4 0.4 Eplore Inscribed ngles E I compass straightedge protractor Q E I O N How are inscribed angles related to central angles? he verte of a central angle
UNIT OBJECTIVES. unit 9 CIRCLES 259
UNIT 9 ircles Look around whatever room you are in and notice all the circular shapes. Perhaps you see a clock with a circular face, the rim of a cup or glass, or the top of a fishbowl. ircles have perfect
NAME DATE PERIOD. 4. If m ABC x and m BAC m BCA 2x 10, is B F an altitude? Explain. 7. Find x if EH 16 and FH 6x 5. G
5- NM IO ractice isectors, Medians, and ltitudes LG In, is the angle bisector of,,, and are medians, and is the centroid.. ind x if 4x and 0.. ind y if y and 8.. ind z if 5z 0 and 4. 4. If m x and m m
Chapter 6. Worked-Out Solutions. Chapter 6 Maintaining Mathematical Proficiency (p. 299)
hapter 6 hapter 6 Maintaining Mathematical Proficiency (p. 99) 1. Slope perpendicular to y = 1 x 5 is. y = x + b 1 = + b 1 = 9 + b 10 = b n equation of the line is y = x + 10.. Slope perpendicular to y
Review for Grade 9 Math Exam - Unit 8 - Circle Geometry
Name: Review for Grade 9 Math Exam - Unit 8 - ircle Geometry Date: Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is the centre of this circle and point
Solve problems involving tangents to a circle. Solve problems involving chords of a circle
8UNIT ircle Geometry What You ll Learn How to Solve problems involving tangents to a circle Solve problems involving chords of a circle Solve problems involving the measures of angles in a circle Why Is
Practice For use with pages
Name ate ON 0. ractice For use with pages 678 686 se ( to draw the described part of the circle.. raw a diameter and label it }.. raw a tangent ra and label it ###$. 3. raw a secant and label it } F. 4.
Lesson 12.1 Skills Practice
Lesson 12.1 Skills Practice Introduction to ircles ircle, Radius, and iameter Vocabulary efine each term in your own words. 1. circle circle is a collection of points on the same plane equidistant from
Objectives To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord
1-3 Inscribed ngles ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. lso G-..3, G-..4 M 1, M 3, M 4, M 6 bjectives To find the measure of an
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
Work with a partner. Use dynamic geometry software. Draw any scalene ABC. a. Find the side lengths and angle measures of the triangle.
OMMON ORE Learning Standard HSG-O..0 6.5 Indirect Proof and Inequalities in One riangle Essential Question How are the sides related to the angles of a triangle? How are any two sides of a triangle related
15.3 Tangents and Circumscribed Angles
Name lass ate 15.3 Tangents and ircumscribed ngles Essential uestion: What are the key theorems about tangents to a circle? esource Locker Explore Investigating the Tangent-adius Theorem tangent is a line
15.5 Angle Relationships in Circles
ame lass ate 15.5 ngle Relationships in ircles ssential uestion: What are the relationships between angles formed by lines that intersect a circle? xplore xploring ngle Measures in ircles The sundial is
Lesson 1.7 circles.notebook. September 19, Geometry Agenda:
Geometry genda: Warm-up 1.6(need to print of and make a word document) ircle Notes 1.7 Take Quiz if you were not in class on Friday Remember we are on 1.7 p.72 not lesson 1.8 1 Warm up 1.6 For Exercises
Proportions in Triangles
- roportions in Triangles ontent tandard G.RT. rove theorems about triangles...a line parallel to one side of a triangle divides the other two proportionally... Objective To use the ide-plitter Theorem
11.2 Areas of Circles and Sectors
11.2 Areas of Circles and Sectors ssential Question How can ou find the area of a sector of a circle? Finding the Area of a Sector of a Circle Work with a partner. A sector of a circle is the region bounded
Essential Question How can you measure and construct a line segment? Work with a partner. a. Draw a line segment that has a length of 6 inches.
M 1. TEXS ESSENTIL KNOWLEDE ND SKILLS...5. Preparing for.5. USIN PROLEM-SOLVIN STRTEIES To be proficient in math, you need to explain to yourself the meaning of a problem and look for entry points to its
Lesson 9.1 Skills Practice
Lesson 9.1 Skills Practice Name Date Earth Measure Introduction to Geometry and Geometric Constructions Vocabulary Write the term that best completes the statement. 1. means to have the same size, shape,
Assignment. Riding a Ferris Wheel Introduction to Circles. 1. For each term, name all of the components of circle Y that are examples of the term.
ssignment ssignment for Lesson.1 Name Date Riding a Ferris Wheel Introduction to ircles 1. For each term, name all of the components of circle Y that are examples of the term. G R Y O T M a. hord GM, R,
Work with a partner. a. Draw a line segment that has a length of 6 inches.
M 1. Measuring and onstructing Segments Essential Question ow can you measure and construct a line segment? Measuring Line Segments Using Nonstandard Units MKIN SENSE O PROLEMS To be proficient in math,
Student Exploration: Chords and Arcs
Name: ate: Student xploration: hords and rcs Vocabulary: arc, central angle, chord Prior nowledge Questions (o these BFOR using the Gizmo.) In circle to the right, and are central angles because their
Apply Other Angle Relationships in Circles
0.5 pply Other ngle elationships in ircles efore You found the measures of angles formed on a circle. Now You will find the measures of angles inside or outside a circle. Why So you can determine the part
2 Explain 1 Proving the Intersecting Chords Angle Measure Theorem
xplain 1 Proving the Intersecting hords ngle easure Theorem In the xplore section, you discovered the effects that line segments, such as chords and secants, have on angle measures and their intercepted
If the measure ofaacb is less than 180, then A, B, and all the points on C that lie in the
age 1 of 7 11.3 rcs and entral ngles oal Use properties of arcs of circles. Key Words minor arc major arc semicircle congruent circles congruent arcs arc length ny two points and on a circle determine
Click on a topic to go to that section. Euclid defined a circle and its center in this way: Euclid defined figures in this way:
lide 1 / 59 lide / 59 New Jersey enter for eaching and Learning Progressive Mathematics Initiative his material is made freely available at www.njctl.org and is intended for the non-commercial use of students
SM2H Unit 6 Circle Notes
Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:
4.3 Isosceles and Equilateral
4.3 Isosceles and quilateral Triangles Goal Use properties of isosceles and equilateral triangles. Key Words legs of an isosceles triangle base of an isosceles triangle base angles Geo-ctivity Properties
12.1 Triangle Proportionality Theorem
Name lass Date 12.1 Triangle Proportionality Theorem ssential Question: When a line parallel to one side of a triangle intersects the other two sides, how does it divide those sides? Resource Locker xplore
5.3 Use Angle Bisectors of
5.3 Use ngle isectors of Triangles Goal p Use angle bisectors to find distance relationships. Your Notes VOURY Incenter THEOREM 5.5: NGE ISETOR THEOREM In geometry, distance means the shortest length between
MF9SB_CH09_p pp8.qxd 4/15/09 6:51 AM Page NEL
408 NEL hapter 9 ircle Geometry GLS ou will be able to identify and apply the relationships between inscribed angles and central angles use properties of chords to solve problems identify properties of
Properties of Circles
10 10.1 roperties of ircles Use roperties of Tangents 10.2 ind rc Measures 10.3 pply roperties of hords 10.4 Use Inscribed ngles and olygons 10.5 pply Other ngle elationships in ircles 10.6 ind egment
Geometry Unit 1 Practice
Lesson 1-1 1. Persevere in solving problems. Identify each figure. hen give all possible names for the figure. a. S Geometry Unit 1 Practice e. P S G Q. What is a correct name for this plane? W R Z X b..
8.2 Investigate Parallelograms
Investigating g Geometry TIVITY 8.2 Investigate arallelograms T E I graphing calculator or computer Use before esson 8.2 classzone.com Keystrokes Q U E T I O N What are some of the properties of a parallelogram?
Riding a Ferris Wheel. Students should be able to answer these questions after Lesson 10.1:
.1 Riding a Ferris Wheel Introduction to ircles Students should be able to answer these questions after Lesson.1: What are the parts of a circle? How are the parts of a circle drawn? Read Question 1 and
Skills Practice Skills Practice for Lesson 11.1
Skills Practice Skills Practice for Lesson.1 Name ate Riding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. circle X T 2. center of the circle H I
14.3 Tangents and Circumscribed Angles
Name lass Date 14.3 Tangents and ircumscribed ngles Essential uestion: What are the key theorems about tangents to a circle? Explore G.5. Investigate patterns to make conjectures about geometric relationships,
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.
Inequalities Within a Triangle
7 3 Inequalities ithin a Triangle hat You ll earn You ll learn to identify the relationships between the sides and angles of a triangle. hy It s Important urveying Triangle relationships are important
Name Date Period. Notes - Tangents. 1. If a line is a tangent to a circle, then it is to the
Name ate Period Notes - Tangents efinition: tangent is a line in the plane of a circle that intersects the circle in eactly one point. There are 3 Theorems for Tangents. 1. If a line is a tangent to a
6.6 Investigate Proportionality
Investigating g Geometry TIVITY 6.6 Investigate roportionality M T I LS graphing calculator or computer Use before Lesson 6.6 classzone.com Keystrokes Q U S T I O N How can you use geometry drawing software
Answers. Chapter10 A Start Thinking. and 4 2. Sample answer: no; It does not pass through the center.
hapter10 10.1 Start Thinking 6. no; is not a right triangle because the side lengths do not satisf the Pthagorean Theorem (Thm. 9.1). 1. (3, ) 7. es; is a right triangle because the side lengths satisf
Chapter-wise questions
hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm
Introduction to Geometric Proof
5 Introduction to Geometric roof 37 4 Refer to the circle with center O a) Use a protractor to find m b) Use a protractor to find m D c) Compare results in parts (a) and (b) 44 Refer to the circle with
New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 150 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
7. a) What is the relationship between a central angle and an inscribed angle that stands on the same arc?
10.1 xploring ngles in a ircle ocus on fter this lesson, you will be able to describe a relationship between inscribed angles in a circle relate the inscribed angle and central angle subtended by the same
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
Geometry Arcs and Chords. Geometry Mr. Austin
10.2 Arcs and Chords Mr. Austin Objectives/Assignment Use properties of arcs of circles, as applied. Use properties of chords of circles. Assignment: pp. 607-608 #3-47 Reminder Quiz after 10.3 and 10.5
Similar Right Triangles
9.3 EX EENIL KNOWLEGE N KILL G.8. G.8. imilar igt riangles Essential Question How are altitudes and geometric means of rigt triangles related? Writing a onjecture Work wit a partner. a. Use dnamic geometr
GEOMETRY REVIEW FOR MIDTERM
Y VIW I he midterm eam for period is on /, 0:00 to :. he eam will consist of approimatel 0 multiple-choice and open-ended questions. Now is the time to start studing!!! PP eviews all previous assessments.
Math & 8.7 Circle Properties 8.6 #1 AND #2 TANGENTS AND CHORDS
Math 9 8.6 & 8.7 Circle Properties 8.6 #1 AND #2 TANGENTS AND CHORDS Property #1 Tangent Line A line that touches a circle only once is called a line. Tangent lines always meet the radius of a circle at
DO NOW #1. Please: Get a circle packet
irclengles.gsp pril 26, 2013 Please: Get a circle packet Reminders: R #10 due Friday Quiz Monday 4/29 Quiz Friday 5/3 Quiz Wednesday 5/8 Quiz Friday 5/10 Initial Test Monday 5/13 ctual Test Wednesday 5/15
Activity Sheet 1: Constructions
Name ctivity Sheet 1: Constructions Date 1. Constructing a line segment congruent to a given line segment: Given a line segment B, B a. Use a straightedge to draw a line, choose a point on the line, and
Unit 1: Introduction to Proof
Unit 1: Introduction to Proof Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted
( ) 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
Evaluate: Homework and Practice
valuate: Homework and Practice Identify the chord (s), inscribed angle (s), and central angle (s) in the figure. The center of the circles in xercises 1, 2, and 4 is. Online Homework Hints and Help xtra
Circles in Neutral Geometry
Everything we do in this set of notes is Neutral. Definitions: 10.1 - Circles in Neutral Geometry circle is the set of points in a plane which lie at a positive, fixed distance r from some fixed point.
Chapter 10. Properties of Circles
Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Objective: Use properties of a tangent to a circle. Essential Question: how can you verify that a segment is tangent to a circle? Terminology:
Study Guide. Exploring Circles. Example: Refer to S for Exercises 1 6.
9 1 Eploring ircles A circle is the set of all points in a plane that are a given distance from a given point in the plane called the center. Various parts of a circle are labeled in the figure at the
Essential Question How can you prove a mathematical statement?
.5 TEXS ESSENTIL KNOWLEDGE ND SKILLS Preparing for G.6. G.6. G.6.D G.6.E RESONING To be proficient in math, you need to know and be able to use algebraic properties. Proving Statements about Segments and
In the same way that you used proportional reasoning to find the length of an arc, you can use proportional reasoning to find the area of a sector.
Name Class Date 16.3 Sector rea Essential Question: How do you find the area of a sector of a circle? Explore Derive the Formula for the rea of a Sector sector of a circle is a region bounded by two radii
Example 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x
Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able
Tangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them.
Tangent Lines Unit 10 Lesson 1 EQ: How can you verify that a segment is tangent to a circle? Circle: Center: Radius: Chord: Diameter: Secant: Tangent: Tangent Lines Unit 10 Lesson 1 Example 1: Tell how
MT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 1 (E)
04 00 eat No. MT - MTHEMTI (7) GEOMETY - PELIM II - PPE - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : (i) ll questions are compulsory. Use of calculator is not allowed. Q.. olve NY FIVE of the following
KEY STANDARDS ADDRESSED: MM2G3. Students will understand the properties of circles.
KEY STANDARDS ADDRESSED:. Students will understand the properties of circles. a. Understand and use properties of chords, tangents, and secants an application of triangle similarity. b. Understand and
Incoming Magnet Precalculus / Functions Summer Review Assignment
Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were
B C. You try: What is the definition of an angle bisector?
US Geometry 1 What is the definition of a midpoint? The midpoint of a line segment is the point that divides the segment into two congruent segments. That is, M is the midpoint of if M is on and M M. 1
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
Geometry Arcs and Chords. Geometry Mr. Peebles Spring 2013
10.2 Arcs and Chords Geometry Mr. Peebles Spring 2013 Bell Ringer: Solve For r. B 16 ft. A r r 8 ft. C Bell Ringer B 16 ft. Answer A r r 8 ft. C c 2 = a 2 + b 2 Pythagorean Thm. (r + 8) 2 = r 2 + 16 2
Chapter 2. The laws of sines and cosines. 2.1 The law of sines. Theorem 2.1 (The law of sines). Let R denote the circumradius of a triangle ABC.
hapter 2 The laws of sines and cosines 2.1 The law of sines Theorem 2.1 (The law of sines). Let R denote the circumradius of a triangle. 2R = a sin α = b sin β = c sin γ. α O O α as Since the area of a
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
C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle
10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by
Unit 10 Geometry Circles. NAME Period
Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference
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.
Use Properties of Tangents
6.1 Georgia Performance Standard(s) MM2G3a, MM2G3d Your Notes Use Properties of Tangents Goal p Use properties of a tangent to a circle. VOULRY ircle enter Radius hord iameter Secant Tangent Example 1
So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x.
ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.
10.6 Investigate Segment Lengths
Investigating g Geometry TIVITY. Investigate Segment Lengths M T R I LS graphing calculator or computer Use before Lesson. classzone.com Keystrokes Q U S T I O N What is the relationship between the lengths