# Page 1 Central Angles & Arc Measures

Size: px
Start display at page:

Transcription

1 Geometry/Trig Unit 8 ll bout ircles! Name: ate: Page 1 entral ngles & rc Measures Example 1: JK is a diameter of ircle. Name two examples for each: K Minor rc:, Major rc:, M Semicircle:, Name Pair of djacent rcs:, J L Example 2: G is the center of the circle. G ^ m = 75 m = m = 2. m = 3. m G = 4. m G = 5. m = 6. m G = 7. m G = 8. m = 9. m = 10. m = 11. m = 12. m = 13. m = 14. m = 15. mg = 16. m = 17. mg = 18. m = 19. mg = 20. mg =

2 Page 2 Problem Set 1 irections: Solve for each indicated variable or segment. is the center of each circle. 1. z refers to an 2. = 8 arc measure. z y x x = y = z = 3. = = = y x 130 m = 120 x z z y z refers to an arc measure. y and z refers to arc measures. x = y = z = x = y = z = 5. m = m 1 = m 2 = Textbook Practice: p. 341 E #1-13; p WE #1-6, 10, 11

3 Page 3 Example Tab Theorem 9-1 Sketch the diagram: Observations: ill in the Measurements: m PR onclusion (Theorem 9-1): If a line is tangent to a circle, then the line is to the radius drawn to the point of tangency. Example 1: Given ircle with a radius length of 5. is a point of tangency. = 5 3. Example 2: Given ircle with a radius length of 7. is a point of tangency. = 24. G ind: = m = m = Example 3: Given JK is a diameter and KL is a tangent. The radius of the circle is 8. J ind: = G = G = m = Is G the midpoint of? mg = UI UIZ EXMPLE Given ircle and is a point of tangency. = 8 = 17 K 45 L ind: JK = JL = KL = Example uia uiz: / 5

4 Page 4 Tab 1 orollary of Theorem 9-1 Sketch the diagram: Observations: ill in the Measurements: onclusion (orollary to Theorem 9-1): Segments that are tangent to a circle from a point are. Example 1: and are points of tangency. lassify by sides: m = 32 m = m = Example 2: and are points of tangency. x = ½x + 9 = = Example 3: Points J, K, L, and M are points of tangency. ind the perimeter of quadrilateral. J K J = 4, K = 7, L = 3, M = 5 K 4x + 2 UI UIZ 1 L Points K and J are points of Tangency. J KL = 7; KJ = 6; m LKJ = 70 M L Perimeter: uia uiz 1: / 4

5 Page 5 Problem Set 2 irections: ind the value of each indicated variable and measure. 1. is a tangent of ircle. 2. and are tangents to the circle. 8 3 = 2x + 2 = 4x + 8 = 7x + 2 = 5x + 1 G x = = = m = G = m = = x = = = 3. P,, R, and S are points of tangency. P 4. and are tangent segments. m = S 9 9 R ind the perimeter of uadrilateral. = m = Textbook Practice: p. 335 WE #1-5

6 Page 6 Tab 2 Theorem 9-4 Sketch the diagram: ill in Measurements: mg mh Observations: onclusion (Theorem 9-4): In the same circle or in congruent circles, congruent chords intercept arcs. Example 1: ind all angle and arc measurements. m = 40 m = m = m = 140 m = m = Example 2: ind all angle and arc measurements concerning circle. m = 86 m = m = lassify by sides: If m = 128, then m = UI UIZ 2 = 9 = 9 uia uiz 2: / 4 m = 131 m = 33

7 Page 7 Tab 3 Theorem 9-5 Sketch the diagram: ill in Measurements: mg mh Observations: onclusion (Theorem 9-5): The diameter that is perpendicular to a chord the chord and its intercepted arc. Example 1: ind all measurements. is the center of the circle. S RT = R 15 T M 17 S = M = MS = SP = P Example 2: ind all measurements. is the center of the circle. m = m = m = m = m = m = m = 220 HLLENGE: If = 10, find. UI UIZ 3 S ^ RP S is a diameter. RP = 18 mrs = 70 R T P uia uiz 3: / 6 S

8 Page 8 Tab 4 Theorem 9-6 Sketch the diagram: To measure the distance between a point and segment, you must measure the distance. ill in Measurements: E G mhg mk Observations: onclusion (Theorem 9-6): In the same circle or in congruent circles, chords are equally distant from the center. Example 1: ind all measurements. is the center of the circle. K JP = NM = J LM = LN = P M = K = N L M m NL = Given: KP ^ J; NM ^ L J = L = 3 KP = 8 E UI UIZ 4 E ^ G ^ G = 8 m = 106 = 3 E = 3 You will need to drawn in M, K, and N to complete this problem. uia uiz 4: / 3

9 Page 9 Problem Set 3 omplete each problem from the Written Exercises on page 347. raw and label a diagram for each problem

10 Page 10 Tab 5 Theorem 9-7 & orollaries 1 & 2 Sketch the diagram: Recall Inscribed ngle: _ m m m m Observations: _ onclusion (Theorem 9-7): The measure of an inscribed angle is equal to the measure of its intercepted arc. orollary 1: Inscribed ngles that intercept the same arc are. orollary 2: n angle inscribed inside of a semicircle is. Example 1: ind all measurements. G J m GJ = mhj = Example 2: ind all measurements. me = 102 m E= 109 mg = m E = H mgh = m E = mhg = E m = 129 m = Example 3: ind all measurements. is a diameter. Round all decimal answers to the nearest tenth. N UI UIZ 5 M P iagram 2 = 26, = 24, = m = m = iagram 1 mmp = 122; mmn = 40 is a diameter; = 6; = 10 uia uiz 5: / 7

11 Page 11 Tab 6 Theorem 9-7 orollary 3 Sketch the diagram (include the four angle measurements): Observations: onclusion (orollary 3): If a quadrilateral is inscribed in a circle, then its opposite angles are. Example 1: ind all measurements. Given: M m LMJ = 73 J m MJK = 88 mmj = 102 K L ind: m JKL = m KLM = mmjk = mjk = mmlk = mlmj = mlmk = Example 2: UI UIZ 6 R S T Given: uadrilateral is inscribed in ircle. = 8 and = 15. ind each measure: iameter Length = Radius Length = m RST = 102 m SRP = 65 P m = uia uiz 6: / 4

12 Page 12 Problem Set 4 irections: ind each indicated measure X is the center of the circle. G 75 X 120 mg = m = m G = N is a diameter J 100 K P 40 N M L m JMK = m JLK = 5. R 6. m NP = mnp = S T m SRT = m = m = Textbook Practice: p. 353 E #4, 5, 6, 9; p. 354 WE #1-4, 6

13 Page 13 Tab 7 Theorem 9-8 Sketch the diagram: Observations: onclusion (Theorem 9-8): mg m m mg The measure of an angle formed by a chord and a tangent is equal to the measure of the intercepted arc. Example 1: ind all indicated measurements. is a point of tangency. Example 2: ind all indicated measurements. is a point of tangency. m = 78 x 72 m = m = m = x = m = m = UI UIZ 7 N M K is a point of tangency. m MKL = 74 J K L uia uiz 7: / 3

14 Page 14 Tab 8 Theorem 9-10 RULE: ngle = ½(igger rc Smaller rc) ase 1 Two Secants ase 2 Two Tangents ase 3 Secant & Tangent m 1 = m 2 = m 3 = Example 1: is a point of tangency. Example 2: and are points of tangency. m = 20 m = 115 m = m = m = m = m = 116 m = m = UI UIZ 8 is a point of tangency. m = 120 m = 50 G H uia uiz 8: / 4

15 Page 15 Problem Set 5 omplete each problem from the lassroom Exercises on pages raw an label a diagram for each Textbook Practice: p. 353 E #7, 8; p. 354 WE #5, 7, 8, 9; p. 360 #15-21

16 Page 16 nswers to Examples Example Tab Theorem 9-1 Example 1: = 10 m = 60 m = 30 Example 2: = 25, G = 7, G = 18 m = 73.7 mg = 73.7 Is G the midpoint of? No Example 3: JK = 16, KL = 16, JL = 16 2 Tab 1 orollary to Theorem 9-1 Example 1: lassify by sides: Isosceles m = 74 m = 74 Example 2: x = 2, = 10, = 10 Example 3: Perimeter = 38 Tab 2 Theorem 9-4 Example 1: m = 70 m = 70 m = 140 m = 80 Example 2: m = 86 m = 86 lassify by sides: Isosceles m = 232 Tab 3 Theorem 9-5 Example 1: RT = 30 M = 8 S = 17 MS = 9 SP = 34 Example 2: m = 140 m = 70 m = 70 m = 70 m = 140 m = 20 HLLENGE: = 18.8 Tab 4 Theorem 9-6 Example 1: JP = 4 NM = 8 LM = 4 LN = 4 M = 5 K = 5 m NL = 36.9 Tab 5 Theorem 9-7 & orollaries 1 & 2 Example 1: m GJ = 46 mhj = 88 mg = 71 mgh = 251 mhg = 289 Example 2: m E= 51 m E = 51 m E = 51 m = 129 m = 64.5 Example 3: = 26, = 24, = 10 m = 67.4 m = 22.6 Tab 6 Section 9.5 orollary 3 Example 1: m JKL = 107 mmlk = 176 m KLM = 92 mlmj = 214 mmjk = 184 mlmk = 296 mjk = 82 Example 2: iameter Length = 17 Radius Length = 17 2 m = 28.1 Tab 7 Theorem 9-8 Example 1: m = 156 m = 204 m = 102 Example 2: x = 108 m = 108 m = 54 Tab 8 Theorem 9-10 Example 1: m = 75 m = 170 m = 285 m = 245 Example 2: m = 244 m = 64

### 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

### 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

### 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

### 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,

### ( ) 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

### 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

### 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

### 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

### 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:

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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.

### 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

### 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

### 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.

### 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

### ( ) 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

### Chapter 12 Practice Test

hapter 12 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. ssume that lines that appear to be tangent are tangent. is the center of the circle.

### Indicate whether the statement is true or false.

PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### 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, `

### 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

### 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

### 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

### 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

### 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

### Find the area of the triangle. You try: D C. Determine whether each of the following statements is true or false. Solve for the variables.

lameda USD Geometr enchmark Stud Guide ind the area of the triangle. 9 4 5 D or all right triangles, a + b c where c is the length of the hpotenuse. 5 4 a + b c 9 + b 5 + b 5 b 5 b 44 b 9 he area of a

### 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

### 0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30

### Name Grp Pd Date. Circles Test Review 1

ircles est eview 1 1. rc 2. rea 3. entral ngle 4. hord 5. ircumference 6. Diameter 7. Inscribed 8. Inscribed ngle 9. Intercepted rc 10. Pi 11. adius 12. ector 13. emicircle 14. angent 15. πr 2 16. 2πr

### 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

### 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 Circles 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. Chord b.

### 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

### 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:

### 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.

### Pre-Test. Use the following figure to answer Questions 1 through 6. B C. 1. What is the center of the circle? The center of the circle is point G.

Pre-Test Name Date Use the following figure to answer Questions 1 through 6. A B C F G E D 1. What is the center of the circle? The center of the circle is point G. 2. Name a radius of the circle. A radius

### 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

### Answer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.

9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in

### Geometry H Ch. 10 Test

Geometry H Ch. 10 est 1. In the diagram, point is a point of tangency,, and. What is the radius of? M N J a. 76 c. 72 b. 70 d. 64 2. In the diagram, is tangent to at, is tangent to at,, and. Find the value

### 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.

### Circles-Tangent Properties

15 ircles-tangent roperties onstruction of tangent at a point on the circle. onstruction of tangents when the angle between radii is given. Tangents from an external point - construction and proof Touching

### 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

### 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

### Name. 9. Find the diameter and radius of A, B, and C. State the best term for the given figure in the diagram.

Name LESSON 10.1 State the best term for the given figure in the diagram. 9. Find the diameter and radius of A, B, and C. 10. Describe the point of intersection of all three circles. 11. Describe all the

### 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

### 0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

### Reteaching , or 37.5% 360. Geometric Probability. Name Date Class

Name ate lass Reteaching Geometric Probability INV 6 You have calculated probabilities of events that occur when coins are tossed and number cubes are rolled. Now you will learn about geometric probability.

### 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

### 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

### Name two radii in Circle E.

A C E B D Name two radii in Circle E. Unit 4: Prerequisite Terms A C E B D ECandED Unit 4: Prerequisite Terms A C E B D Name all chords in Circle E. Unit 4: Prerequisite Terms A C E B D AD, CD, AB Unit

### Geometry: A Complete Course

Geometry: omplete ourse (with Trigonometry) Module - Student WorkText Written by: Thomas E. lark Larry E. ollins Geometry: omplete ourse (with Trigonometry) Module Student Worktext opyright 2014 by VideotextInteractive

### Math 9 Unit 8: Circle Geometry Pre-Exam Practice

Math 9 Unit 8: Circle Geometry Pre-Exam Practice Name: 1. A Ruppell s Griffon Vulture holds the record for the bird with the highest documented flight altitude. It was spotted at a height of about 11 km

### 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

### 10.6 Find Segment Lengths

10. Find Segment Lengths in ircles Goal p Find segment lengths in circles. Your Notes VOULRY Segments of a chord Secant segment Eternal segment THEOREM 10.14: SEGMENTS OF HORS THEOREM If two chords intersect

### ( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.

. A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590

### Park Forest Math Team. Meet #4. Geometry. Self-study Packet

Park Forest Math Team Meet #4 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:

### 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

### b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem

Chapter 7 1. State which theorem you can use to show that the quadrilateral is a parallelogram. a) Parallelogram Opposite Angles Converse b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals

### 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

### 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

### 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.

### 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

### Topic 4 Congruent Triangles PAP

opic 4 ongruent riangles PP Name: Period: eacher: 1 P a g e 2 nd Six Weeks 2015-2016 MONY USY WNSY HUSY FIY Oct 5 6 7 8 9 3.4/3.5 Slopes, writing and graphing equations of a line HW: 3.4/3.5 Slopes, writing

### Geometry: A Complete Course

Geometry: omplete ourse (with Trigonometry) Module Progress Tests Written by: Larry E. ollins Geometry: omplete ourse (with Trigonometry) Module - Progress Tests opyright 2014 by VideotextInteractive Send

### 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

### 0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle

### To construct the roof of a house, an architect must determine the measures of the support beams of the roof.

Metric Relations Practice Name : 1 To construct the roof of a house, an architect must determine the measures of the support beams of the roof. m = 6 m m = 8 m m = 10 m What is the length of segment F?

### Circles. 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle ACB.

ircles Name: Date: 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle AB. 4. In the accompanying diagram, P is tangent to circle at and PAB is a secant.

### 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

### Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary

### Geometry 1.0 Errata October 15, 2012

Geometry Errors on Current Printing Geometry.0 Errata October 5, 202 Lesson 23 #2: Answer key should say if two angles are complementary to the same angle they are congruent. The solution should say this

### 0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD

### Name. Chapter 12: Circles

Name Chapter 12: Circles Chapter 12 Calendar Sun Mon Tue Wed Thu Fri Sat May 13 12.1 (Friday) 14 Chapter 10/11 Assessment 15 12.2 12.1 11W Due 16 12.3 12.2 HW Due 17 12.1-123 Review 12.3 HW Due 18 12.1-123

### Name: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?

GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and

### 0114ge. Geometry Regents Exam 0114

0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?

### GCSE METHODS IN MATHEMATICS

Q Qualifications GCSE METHODS IN MTHEMTICS Linked Pair Pilot Specification (9365) ssessment Guidance Our specification is published on our website (www.aqa.org.uk). We will let centres know in writing

### MT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 6 (E)

04 00 Seat No. MT - MTHEMTIS (7) GEOMETRY - PRELIM II - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : ll questions are compulsory. Use of calculator is not allowed. Q.. Solve NY FIVE of the following

### Circles. Exercise 9.1

9 uestion. Exercise 9. How many tangents can a circle have? Solution For every point of a circle, we can draw a tangent. Therefore, infinite tangents can be drawn. uestion. Fill in the blanks. (i) tangent

### Geometry Honors Final Exam Review June 2018

Geometry Honors Final Exam Review June 2018 1. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television

### MAHESH TUTORIALS. GEOMETRY Chapter : 1, 2, 6. Time : 1 hr. 15 min. Q.1. Solve the following : 3

S.S.C. Test - III Batch : SB Marks : 0 Date : MHESH TUTORILS GEOMETRY Chapter : 1,, 6 Time : 1 hr. 15 min..1. Solve the following : (i) The dimensions of a cuboid are 5 cm, 4 cm and cm. Find its volume.

### 10-3 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.

### 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

### 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 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

### C Given that angle BDC = 78 0 and DCA = Find angles BAC and DBA.

UNERSTNING IRLE THEREMS-PRT NE. ommon terms: (a) R- ny portion of a circumference of a circle. (b) HR- line that crosses a circle from one point to another. If this chord passes through the centre then

### Math 9 Chapter 8 Practice Test

Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the

### 10.1 Tangents to Circles. Geometry Mrs. Spitz Spring 2005

10.1 Tangents to Circles Geometry Mrs. Spitz Spring 2005 Objectives/Assignment Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment: Chapter 10 Definitions