# So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x.

Size: px
Start display at page:

Download "So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x."

Transcription

1 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. m(arc RS) = m(arc ST) and by substitution, x = chords are congruent. Since m(arc AB) = m(arc CD) = 127, arc AB arc CD and. In, JK = 10 and. Find each measure. Round to the nearest hundredth. 2. Since HG = 4 and FG = 4, and are congruent chords and the corresponding arcs HG and FG are congruent. m(arc HG) = m(arc FG) = x Arc HG, arc GF, and arc FH are adjacent arcs that form the circle, so the sum of their measures is Radius is perpendicular to chord. So, by Theorem 10.3, bisects arc JKL. Therefore, m(arc JL) = m(arc LK). By substitution, m(arc JL) = or PQ Draw radius and create right triangle PJQ. PM = 6 and since all radii of a circle are congruent, PJ = 6. Since the radius is perpendicular to, bisects by Theorem So, JQ = (10) or 5. Use the Pythagorean Theorem to find PQ. So, PQ is about 3.32 units long. esolutions Manual - Powered by Cognero Page 1

2 6. In, GH = 9, KL = 4x + 1. Find x. 9. In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Since JS = JR, KL = GH. ALGEBRA Find the value of x. chords are congruent. So, The sum of the measures of the central angles of a circle with no interior points in common is 360. So, 2x = 254 x = chords are congruent. Therefore, 5x = 105 x = chords are congruent. Therefore, 2x 1 = 143 x = chords are congruent. Therefore, chords are congruent. Here, 3x + 5 = 26 x = 7 Therefore, esolutions Manual - Powered by Cognero Page 2

3 chords are congruent. Here, Therefore, 5x 1 = 4x + 3 x = 4 chords are congruent. Here, 5x = 3x + 54 x = 4 Therefore, 15. CCSS MODELING Angie is in a jewelry making class at her local arts center. She wants to make a pair of triangular earrings from a metal circle. She knows that is. If she wants to cut two equal parts off so that, what is x? chords are congruent. So, The sum of the measures of the central angles of a circle with no interior points in common is 360. So, 2x = 245 x = In, the radius is 14 and CD = 22. Find each measure. Round to the nearest hundredth, if necessary. 14. chords are congruent. Here, 16. CE Radius is perpendicular to chord. So, by Theorem 10.3, bisects. Therefore, CE = ED. By substitution, CE = (22) or 11 units. So, 3x = 7x 44 4x = 44 x = 11 Therefore, esolutions Manual - Powered by Cognero Page 3

5 21. ROADS The curved road is part of, which has a radius of 88 feet. What is AB? Round to the nearest tenth. 23. ALGEBRA In, LM = 16 and PN = 4x. What The radius of the circle is 88 ft. So, CD = CB = 88. Also, CE = CD ED = = 73. Use the Pythagorean Theorem to find EB, the length of a leg of the right triangle CEB. is x? In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Since SQ = SR, LM = PN. 4x = 16 x = 4 If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So, bisects Therefore, 22. ALGEBRA In,,DF = 3x 7, and FE = x + 9. What is x? In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Since 3x 7 = x + 9 2x = 16 x = 8, DF = EF. esolutions Manual - Powered by Cognero Page 5

6 PROOF Write a two-column proof. 24. Given: Prove: bisects and PROOF Write the specified type of proof. 25. paragraph proof of Theorem 10.2, part 2 Given: Prove: Given: Prove: bisects and Proof: Because all radii are congruent,. You are given that, so by SSS. Thus, by CPCTC. Since the central angles have the same measure, their intercepted arcs have the same measure and are therefore congruent. Thus,. Proof: Statements (Reasons) 1. (Given) 2. Draw radii and. (2 points determine a line.) 3. (All radii of a are.) 4. (Reflex. Prop. of ) 5. and are right. (Def. of ) 6. (All right are.) 7. (SAS) 8. (CPCTC) 9. bisects.(def. of bisect) 10. (CPCTC) 11. (In the same circle, two arcs are congruent if their corresponding central angles are congruent.) 12. bisects. (Def. of bisect) 26. two-column proof of Theorem 11.3 Given: Prove: Proof: Statements (Reasons) 1. (Given) 2. (All radii of a are.) 3. (Reflexive Prop.) 4. and are rt. (Definition of lines) 5. (HL) 6., (CPCTC) 7. (If central are, intercepted arcs are.) esolutions Manual - Powered by Cognero Page 6

7 27. DESIGN Roberto is designing a logo for a friend s coffee shop according to the design, where each chord is equal in length. What is the measure of each arc and the length of each chord? CCSS ARGUMENTS Write a two-column proof of the indicated part of Theorem In a circle, if two chords are equidistant from the center, then they are congruent. Given: Prove: Proof: The four chords are equal in length. So, the logo is a square inscribed in a circle. Each diagonal of the square is a diameter of the square and it is 3 ft long. The length of each side of a square of diagonal d units long is given by Therefore, the length of each chord is chords are congruent. Here, all the four chords are equal in length and hence the corresponding arcs are equal in measure. Therefore, each arc 28. PROOF Write a two-column proof of Theorem Given: is the bisector of. Prove: Proof: is a diameter of Statements (Reasons) 1. (All radii of a are.) 2. (Given) 3. and are right. (Definition of lines) 4. (HL) 5. (CPCTC) 6. XG = YH (Definition of segments) 7. 2(XG) = 2(YH) (Multiplication Property of Equality) 8. bisects ; bisects. ( and are contained in radii. A radius to a chord bisects the chord.) 9. FG = 2(XG), JH = 2(YH) (Definition of segment bisector) 10. FG = JH (Substitution) 11. (Definition of segments) Statements (Reasons) 1. is the bisector of (Given) 2. A is equidistant from B and C. (All radii of a are.) 3. A lies on the bisector of. (Conv. of the Bisector Thm.) 4. is a diameter of. (Def. of diameter) esolutions Manual - Powered by Cognero Page 7

8 30. In a circle, if two chords are congruent, then they are equidistant from the center. Given: and are radii. Find the value of x. 31. Prove: Proof: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. So, We have. Then, Statements (Reasons) 1. and and are radii. (Given) 2. bisects ; bisects. ( and are contained in radii. A radius to a chord bisects the chord.) 32. 9x = 2x x = 14 x = 2 3., (Definition of bisector) 4. FG = JH (Definition of segments) 5. (Multiplication Property of Equality) 6. XG = YH (Substitution) 7. (Definition of segments) 8. (All radii of a circle are.) 9. GXL and HYL are right (Def. of lines) 10. (HL) 11. (CPCTC) and are congruent chords, so the corresponding arcs GH and KJ are congruent. Use the labeled values of the arcs on the figure to find x. Therefore, the value of x is 55. esolutions Manual - Powered by Cognero Page 8

9 CHALLENGE The common chord between and is perpendicular to the segment connecting the centers of the circles. If AB = 10, what is the length of? Explain your reasoning. To find x we need to show that chords are congruent. and Use the values of the segments shown on the figure to find x. Therefore, the value of x is ADVERTISING A bookstore clerk wants to set up a display of new books. If there are three entrances into the store as shown in the figure, where should the display be to get maximum exposure? Here, P and Q are equidistant from the endpoints of so they both lie on the perpendicular bisector of, so is the perpendicular bisector of. Let S be the point of intersection of PS = QS = 5. Since is perpendicular to chord, is a right angle. So, is a right triangle. By the Pythagorean Theorem, triangle with. By substitution, Hence, or. Similarly, is a right. Since PQ = PS + SQ, PQ = or about or The display should be placed at the incenter of the triangle having the three entrances as vertices. Draw two segments connecting the centers of the three entrances. Next, construct the perpendicular bisector of each segment and mark the point of intersection. The display should be placed at this point. esolutions Manual - Powered by Cognero Page 9

10 36. REASONING In a circle, is a diameter and is a chord that intersects at point X. Is it sometimes, always, or never true that HX = GX? Explain. a. Use an indirect proof to show that passes through the center of the circle by assuming that the center of the circle is not on. b. Prove that O is the center of the circle. a. Given: is the perpendicular bisector of chord in. Prove: contains point X., HX = GX is not perpendicular to, HX GX If the diameter is perpendicular to the chord, then it bisects the chord. Therefore, the statement is sometimes true. 37. CHALLENGE Use a compass to draw a circle with chord. Refer to this construction for the following problem. Step 1 Construct. Step 2 Construct, the perpendicular bisector of, the perpendicular bisector of. Label the point of intersection O. Proof: Suppose X is not on.draw and radii and. Since is the perpendicular bisector of, E is the midpoint of and. Also,, since all radii of a are. by the Reflexive Property. So, by SSS. By CPCTC,. Since they also form a linear pair, By definition, and are right angles.so,. is the perpendicular bisector of. But is also the perpendicular bisector of. This contradicts the uniqueness of a perpendicular bisector of a segment. Thus, the assumption is false, and center X must be on. b. Given: In, X is on and bisects at O. Prove: Point O is point X. esolutions Manual - Powered by Cognero Page 10

12 41. ALGEBRA Write the ratio of the area of the circle to the area of the square in simplest form. F 43. SAT/ACT Point B is the center of a circle, tangent to the y-axis, and the coordinates of Point B are (3, 1). What is the area of the circle? G H J The radius of the circle is 3r and the length of each side of the square is 2(3r) or 6r. A units 2 B units 2 C units 2 D units 2 E units 2 Since the coordinates of B are (3, 1) and the y-axis is a tangent to the circle, the radius of the circle is 3 units. The area of the circle is units 2. Therefore, the correct choice is E. Therefore, the correct choice is F. 42. SHORT RESPONSE The pipe shown is divided into five equal sections. How long is the pipe in feet (ft) and inches (in.)? The length of each section is 15 inches. So, the total length of the pipe is 5(15) = 75 in. We have, 12 inches = 1 foot. Therefore, 75 in. = 6 ft 3in. or 6.25 ft. 44. Find x. The sum of the measures of the central angles of a circle with no interior points in common is 360. So, x = 360 x = 114 esolutions Manual - Powered by Cognero Page 12

13 45. The sum of the measures of the central angles of a circle with no interior points in common is 360. So, x = 360 x = 170 Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer , 15, 17 By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. 46. The sum of the measures of the central angles of a circle with no interior points in common is 360. So, x = 360 x = CRAFTS Ruby created a pattern to sew flowers onto a quilt by first drawing a regular pentagon that was 3.5 inches long on each side. Then she added a semicircle onto each side of the pentagon to create the appearance of five petals. How many inches of gold trim does she need to edge 10 flowers? Round to the nearest inch. The diameter of each semi circle is 3.5 inches. The circumference C of a circle of a circle of diameter d is given by Since the pattern contains semi circles, the circumference of each semi circle is The total number of semi circles in 10 flowers is 10 (5) = 50. So, the total circumference is Therefore, the set of numbers can be measures of a triangle. Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle , 21, 31 By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Substitute for d. Therefore, she will need about 275 inches of gold trim for the purpose. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. esolutions Manual - Powered by Cognero Page 13

14 50. 10, 16, 18 By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. 52. If, find. The opposite angles of a rhombus are congruent. So,. In a rhombus, each diagonal bisects a pair of opposite angles. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle. ALGEBRA Quadrilateral WXZY is a rhombus. Find each value or measure. 51. If m 3 = y 2 31, find y. The diagonals of a rhombus are perpendicular to each other. So, m 3 = 90. esolutions Manual - Powered by Cognero Page 14

### 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.

### 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

### 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

### Practice Test - Chapter 5

1. GARDENS Maggie wants to plant a circular flower bed within a triangular area set off by three pathways. Which point of concurrency related to triangles would she use for the center of the largest circle

### 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,

### 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

### So, the measure of arc TS is 144. So, the measure of arc QTS is 248. So, the measure of arc LP is Secants, Tangents, and Angle Measures

11-6 Secants, Tangents, Angle Measures Find each measure Assume that segments that appear to be tangent are tangent 4 1 5 So, the measure of arc QTS is 48 So, the measure of arc TS is 144 6 3 So, the measure

### 8-2 The Pythagorean Theorem and Its Converse. Find x. 27. SOLUTION: The triangle with the side lengths 9, 12, and x form a right triangle.

Find x. 27. The triangle with the side lengths 9, 12, and x form a right triangle. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

### 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

### Honors Geometry Mid-Term Exam Review

Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The

### 0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would

### 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)

### Name: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX

Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement

### 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

### 0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?

Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F

### UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'

### 0811ge. Geometry Regents Exam

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### 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

### Chapter 6 Summary 6.1. Using the Hypotenuse-Leg (HL) Congruence Theorem. Example

Chapter Summary Key Terms corresponding parts of congruent triangles are congruent (CPCTC) (.2) vertex angle of an isosceles triangle (.3) inverse (.4) contrapositive (.4) direct proof (.4) indirect proof

### Unit 1. GSE Analytic Geometry EOC Review Name: Units 1 3. Date: Pd:

GSE Analytic Geometry EOC Review Name: Units 1 Date: Pd: Unit 1 1 1. Figure A B C D F is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, 1). 2 Which statement is true?

### Geometry Final Exam 2014 Study Guide. Name Date Block

Geometry Final Exam 014 Study Guide Name Date Block The final exam for Geometry will take place on June 5. The following study guide will help you prepare for the exam. Everything we have covered is fair

### 0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

### Wahkiakum School District, Pre-EOC Geometry 2012

Pre-EOC Assesment Geometry #1 Wahkiakum School District GEOM Page 1 1. What is the converse of If there are clouds in the sky, then it is raining? 2-2 A If it is raining, then there are clouds in the sky.

### 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:

### Name: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.

Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The

### 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.

### 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

### 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

### Common Core Readiness Assessment 4

ommon ore Readiness ssessment 4 1. Use the diagram and the information given to complete the missing element of the two-column proof. 2. Use the diagram and the information given to complete the missing

### 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:

### 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.

1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged

### 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

### Geometry Honors: Midterm Exam Review January 2018

Name: Period: The midterm will cover Chapters 1-6. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize

### Honors Geometry Semester Review Packet

Honors Geometry Semester Review Packet 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear

### 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

### Cumulative Test. 101 Holt Geometry. Name Date Class

Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst

### 8-1 Geometric Mean. SOLUTION: We have the diagram as shown.

25. CCSS MODELING Makayla is using a book to sight the top of a waterfall. Her eye level is 5 feet from the ground and she is a horizontal distance of 28 feet from the waterfall. Find the height of the

### Midterm Review Packet. Geometry: Midterm Multiple Choice Practice

: Midterm Multiple Choice Practice 1. In the diagram below, a square is graphed in the coordinate plane. A reflection over which line does not carry the square onto itself? (1) (2) (3) (4) 2. A sequence

### 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

### 1 What is the solution of the system of equations graphed below? y = 2x + 1

1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x

### Vocabulary. Term Page Definition Clarifying Example altitude of a triangle. centroid of a triangle. circumcenter of a triangle. circumscribed circle

CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying eample. Term Page Definition Clarifying

### 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

### 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

### Study Guide and Review. 11. Find EG if G is the incenter of.

11. Find EG if G is the incenter of. By the Incenter Theorem, since G is equidistant from the sides of Pythagorean Theorem., EG = FG. Find FG using the Since length cannot be negative, use only the positive

### 5-5 The Triangle Inequality

Is it possible to form a triangle with the given side lengths? If not, explain why not. 1. 5 cm, 7 cm, 10 cm Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5 3. 6 m, 14 m, 10 m Yes; 6 + 14 > 10, 6 + 10 > 14,

### 0609ge. Geometry Regents Exam AB DE, A D, and B E.

0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible

Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The

### Chapter 6. Worked-Out Solutions AB 3.61 AC 5.10 BC = 5

27. onstruct a line ( DF ) with midpoint P parallel to and twice the length of QR. onstruct a line ( EF ) with midpoint R parallel to and twice the length of QP. onstruct a line ( DE ) with midpoint Q

### 0612ge. Geometry Regents Exam

0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent

### Use this space for computations. 1 In trapezoid RSTV below with bases RS and VT, diagonals RT and SV intersect at Q.

Part I Answer all 28 questions in this part. Each correct answer will receive 2 credits. For each statement or question, choose the word or expression that, of those given, best completes the statement

### Geometry Cumulative Review

Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D. 36 2. If EG = 42, find the value of y. A. 5 B. C. 6 D. 7

### 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

### JEFFERSON MATH PROJECT REGENTS AT RANDOM

JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-August 2009 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished

### 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

### Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

### Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.

1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of

### Geometry Midterm REVIEW

Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw

### NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the

### Geometry Honors Final Exam REVIEW

Class: Date: Geometry Honors Final Exam 2010-11 REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine whether the quadrilateral is a parallelogram.

### Ch 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Ch 10 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram shown, the measure of ADC is a. 55 b. 70 c. 90 d. 180 2. What is the measure

### 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?

### Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

### 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 (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

### Given that m A = 50 and m B = 100, what is m Z? A. 15 B. 25 C. 30 D. 50

UNIT : SIMILARITY, CONGRUENCE AND PROOFS ) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, ). ) Which transformation results in a figure that is similar

### Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

( Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is an isosceles triangle. is the longest side with length. = and =. Find. 4 x + 4 7

### 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,

### 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

### Proofs. by Bill Hanlon

Proofs by Bill Hanlon Future Reference To prove congruence, it is important that you remember not only your congruence theorems, but know your parallel line theorems, and theorems concerning triangles.

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

### + 10 then give the value

1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles P1 C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid For questions 3 4 use the diagram below. Y Z X U W V A

### 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 Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)

### Practice Test Student Answer Document

Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

### 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

### 4-6 Isosceles and Equilateral Triangles. Refer to the figure. 1. If name two congruent angles. ANSWER: BAC and BCA

Refer to the figure. 1. If name two congruent angles. BAC and BCA 2. If EAC ECA, name two congruent segments. 6. 16 7. PROOF Write a two-column proof. Given: is isosceles; bisects ABC. Prove: Find each

### Honors Geometry Qtr 2 Practice from Chapters 5-8

Block: Seat: Honors Geometry Qtr 2 Practice from Chapters 5-8 Short Answer 1. Use DEF, where J, K, and L are midpoints of the sides. If DE = 8x + 12 and KL = 10x 9, what is DE? 2. Use DEF, where J, K,

### 0116ge. Geometry Regents Exam RT and SU intersect at O.

Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram

### 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,

### 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

### Question 1 (3 points) Find the midpoint of the line segment connecting the pair of points (3, -10) and (3, 6).

Geometry Semester Final Exam Practice Select the best answer Question (3 points) Find the midpoint of the line segment connecting the pair of points (3, -0) and (3, 6). A) (3, -) C) (3, -) B) (3, 4.5)

### 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

### KCATM Geometry Group Test

KCATM Geometry Group Test Group name Choose the best answer from A, B, C, or D 1. A pole-vaulter uses a 15-foot-long pole. She grips the pole so that the segment below her left hand is twice the length

### 4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?

Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC,

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: Notice School Name: Print your name and the

### A plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)

Geometry - Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that

### So, the measure of arc TS is Secants, Tangents, and Angle Measures

Find each measure. Assume that segments that appear to be tangent are tangent. 1. 3. 110 73 2. 4. So, the measure of arc TS is 144. 144 31 esolutions Manual - Powered by Cognero Page 1 5. 7. STUNTS A ramp

### 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

### 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.

### ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1

ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1 N W A S Use the diagram to answer the following questions #1-3. 1. Give two other names for. Sample answer: PN O D P d F a. Give two other names for plane.

### Geometry - Review for Final Chapters 5 and 6

Class: Date: Geometry - Review for Final Chapters 5 and 6 1. Classify PQR by its sides. Then determine whether it is a right triangle. a. scalene ; right c. scalene ; not right b. isoceles ; not right

### Honors Geometry Review Exercises for the May Exam

Honors Geometry, Spring Exam Review page 1 Honors Geometry Review Exercises for the May Exam C 1. Given: CA CB < 1 < < 3 < 4 3 4 congruent Prove: CAM CBM Proof: 1 A M B 1. < 1 < 1. given. < 1 is supp to

### Geometry Note Cards EXAMPLE:

Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)

### Answers. Chapter 9 A92. Angles Theorem (Thm. 5.6) then XZY. Base Angles Theorem (Thm. 5.6) 5, 2. then WV WZ;

9 9. M, 0. M ( 9, 4) 7. If WZ XZ, then ZWX ZXW ; Base Angles Theorem (Thm..6). M 9,. M ( 4, ) 74. If XZ XY, then XZY Y; Base Angles Theorem (Thm..6). M, 4. M ( 9, ) 7. If V WZV, then WV WZ; Converse of

### A. 180 B. 108 C. 360 D. 540

Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior

### 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