# For each Circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1. x = 2. x =

Size: px
Start display at page:

Download "For each Circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1. x = 2. x ="

## Transcription

1 Name: ate: Period: Homework - Tangents For each ircle, find the value of. ssume that segments that appear to be tangent are tangent. 1. =. = ( 5) =. = (Leave as simplified radical!) 3 8 In the figure, and both are tangent to circle P and circle Q. lso, P = 8, Q = 5, and m P = 5. Find the measure of each of the following: 5. m = 13. Q = 6. m PG = 1. G = 7. m GP = 15. = P G F Q 8. G = 16. PG = 9. m Q = 17. GQ = 10. m FG = 18. PQ = 11. m FQ = 19. = 1. m F = 0. PX and PY are tangent to from an eternal point P. HJ = 18 and P = 1. (a) What is the distance from to X? (b) What is the distance from to Y? (c) Find PX. X (d) Find PY. J H Y P 1. The minor arc cut off by two tangents to a circle from an outside point is five-sevenths of the major arc. Find the angle formed by the tangents.

2 . and are radii and is a common eternal tangent. = 5, = 15, = 1 (a) Find. (b) Find. (c) Find FG. F G Find the indicated lengths. 3. ircle P is tangent to each side of. = 0. = 11, and = 1. Let Q = and find. Q P. Given: Tangent circles,, and. = 8, = 13, and = 11 Find: The radii of the three circles. 5. Find the perimeter of right triangle WXY if the radius of the circle is and WY = 0 Y W X Tangent relationships are indicated by the diagram. Find the length indicated. 6. JM = 7.1, JK = 7. OT=9, OK=15, = J K.5 O T M K 8. = 10, = 9. F = F =, = 6 find the perimeter of Δ F

3 nswers to Pg 665 # 1, - evens (omit # 6 and 16), 3, 5, 8; Pg 673 #,, 6, 1, 16-19, 6-7, 30. Pg in 8. No; Yes; = in cm km ll are congruent bout 5. in Pg 673. arcs T GH JN ML, segments T GH JN ML, angles TF HFG JKN MKL cm 7. He doesn t know that the chords are equidistant from the center in Review: 1. a) Find the measure of the arc. b) Find the arc length of arc.. Find the area of the shaded sector in the nd circle. 3. Find the area of the shaded segment in the 3 rd circle.. Find the degree measure of the arc of a sector with area 35 if the area of the circle is If =, what fraction of the circle is shaded? (Hint: Let the =. is the center of the big circle. is the diameter of a little circle and is the diameter of a medium circle. Find the areas in terms of.)

4 Inscribed ngles Notes n angle is inscribed if its verte is on the circle and its sides contain chords of the circle. is an inscribed angle. If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc. intercepts If m = 100 then m =. If m = 70, then m = If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent. 1 intercepts intercepts so 3 intercepts ; intercepts Since m = m, If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle. N The opposite angles of a quadrilateral inscribed in a circle are supplementary. R G The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. m = 1 m

5 1) Name an inscribed angle. ) Name an arc intercepted by P 3) If m P =, find m J ) Find 5) RS and TU are diameters of. L Find RT and m TRS. T N R K S 6) In, PQ RS and m 1 = 38 and m QR = 8. Find: m T = m = m 3 = m = m PT = P Q 1 U R 3 S T 7) In Z,, m = 9, m Z = 10. Find: m = m = m = m = m = m = m = 8) Quadrilateral QRST is inscribed in. If m T = 95 and m S = 100, find m Q and m R. Q R 9) In Q, is a diameter, m =68 and m =96. Find: m = m = m = Q m = Z T S

6 Practice: 1- ngle Measures only Find the measure of each numbered angle. Name: ate: Period: Given circle T, find the value of T 0 T 50 T 70 In K, m O = 98, m OY =8, m Y =60, and m =38. Find: 37. m 38. m m 0. m 3 K 1 O Y 3 1. m. m 5

7 Name ate Period Solve for. hords, Secants and Tangents = = = = = = = = = = = =

8 Geometry Find angles in circles Name ate Period. is a diameter of circle O. and are tangents of circle O m =76 and m =110. Find: H (a) m = (b) m = (i) m = (j) m F= (c) m O= (d) m O= (e) m O= (k) m = (l) m G= (m) m = O G (f) m = (g) m = (n) m O= (o) m O= F (h) m = (p) m H= 3. is a tangent. m F=85, m HJG=55, m GK=75, m =0, m =16, m =10 Find: G F (a) m F = (i) m HG= (b) m FG = (j) m GF= L (c) m GH = (d) m H = (e) m F= (f) m G= (g) m H= (k) m L= (l) m FI= (m) m KH= (n) m HG= (o) m GF= H K J I (h) m KH= nswers: : (a) 70 (b) 10 (c) 10 (d) 38 (e) 17 (f) 35 (g) 5 (h) 76 (i) 5 (j) 38 (k) 5 (l) 93 (m) 5 (n) 38 (o) 35 (p) 55 3: (a) 10 (b) 0 (c) 70 (d) 80 (e) 33 (f) 8 (g) 0 (h) 0 (i) 35 (j) 0 (k) 8 (l) 105 (m) 0 (n) 7 (o) 15

9 PreP/GT Geometry NOTS Name 1-5 quations of ircles ate Period Sketch the graph of the equation.. Write the equation of the circle graphed. - + y + = 36 ( ) ( ) 3. Write the equation of the line tangent to the circle in question # at the point: a. (-, ) b. (1, -3) c. (0, 0) d. (-1, -7) e. (-7, 1) f. (-8, 0). Finding the equation of the circle given 3 points on the circle. Write the equation of the circle that contains the points X( - 6, - 1), Y( -, 3), and Z(, - 5). ) Write the equations for the perpendicular bisectors for Δ XYZ. Tell what segments you used. ) Find the intersection of the two perpendicular bisectors. This will be the circumcenter (the center of the circumscribed circle). (Hint: solve as a system of equations.) ) etermine the radius of the circle. Write the formula and substitution step. ) Write the equation of the circle through X, Y, and Z.

10 Name ate Period Worksheet - ompleting the Square Standard Form of a quadratic equation: a b c PreP Geometry + + = 0 Find the value of c that makes each trinomial a perfect square. 1) + 1 +c ) c 3) + +c ) c 5) t + 0t+c 6) r 9r+ c 7) a + 1a+c 8) h 0h+ c 9) p p+c 10) t + t+ c 6 5 Find the eact solution for each equation by completing the square. 11) y y 5=0 1) + 13= 0 13) = 0 1) = 0 Let s try completing the square for equations of circles. Rewrite the equation in standard form. Solve for the center of the circle and the radius. Standard quation of a ircle ( - h ) + ( y - k ) = r 15) + y + + 6y 3=0 16) + y + 8 y+ 8 = 0 17) + y 10 1y 0 = 0 18) + y y+ 1= 0

11 ircles Review and Word Problems Name: ate: Period: Show all work! This is due the day of the test. Give eact answers if possible. If not, round to nearest tenth. 1. arl is planning to visit a circular park. The radius of the park is 8 miles. He is looking at a map of the park and sees that the park has five landmarks along its edge. The landmarks are connected by paths of equal length for biking. These paths form a regular pentagon inscribed in the circle. If arl bikes along these paths to visit each landmark, how many miles will he bike?. circle is inscribed in a triangle. The points of tangency form the vertices of a triangle inscribed in the circle. What are the angles of the inscribed triangle? 3. ora is wrapping a ribbon around a cylinder-shaped gift bo. The bo has a diameter of 15 inches and the ribbon is 60 inches long. ora is able to wrap the ribbon all the way around the bo once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.. wheel is rolling down an incline. Twelve evenly spaced diameters form spokes of the wheel. When spoke is vertical, which spoke will be perpendicular to the incline? 5. Vanessa looked through her telescope at a mountainous landscape. The figure shows what she saw. ased on the view, approimately what angle does the side of the mountain that runs from to make with the horizontal? 6. omplete the square to write the equation of the circle in standard form. Then give the location of the center and the radius. + y + 16y 13 = 0

12 7. Francisco is a painter. He places a circular canvas on his -frame easel and carefully centers it. The ape of the easel is 30 and the measure of arc is. What is the measure of arc? 8. geostationary satellite is about 35,800 kilometers above arth. How many arc degrees of the planet are visible to a camera in the satellite? 9. The circle below represents arth. The radius of arth is about 600 km. Find the distance d that a person can see on a clear day from each of the following heights h above arth. Round your answer to the nearest tenth of a kilometer. 10. rcheologists and scientists unearthed part of a circular wall. They made the measurements shown in the figure. ased on the information in the figure, what was the radius of the circle? a) 100 m b) 500 m c) 1 km 11. The figure shows the cross-section of an ale held in place by a triangular sleeve. brake etends from the ape of the triangle. When the brake is etended.5 inches into the sleeve, it comes into contact with the ale. a) What is the diameter of the ale? 1. The diameter of the base of a cylindrical milk tank is 59 in. The length of the tank is 70 in. You estimate that the depth of the milk in the tank is 0 in. Find the number of gallons of milk in the tank to the nearest gallon. (1 gal = 31 in. 3 ) (iagram is not to scale.) b) If the base of the triangular sleeve is 6. inches long, then what is the perimeter of the triangular sleeve? Hint: First find the length of the chord, then the area of the sector, and subtract the area of the triangle.

13 13. Some circular nglish gardens, like the one shown here, have paths in the shape of an inscribed regular star. a) Find the measure of an inscribed angle formed by the star in the garden shown here. 1. The radius of arth s equator is about 3960 miles. a) Write the equation of the equator with the center of arth as the origin. b) Find the length of a 1 arc on the equator to the nearest tenth of a mile. c) 1 arc along the equator is 60 nautical miles long. How many miles are in a nautical mile? Round to the nearest tenth. b) What is the measure of an inscribed angle in a garden with a five-pointed star? d) olumbus planned his trip to the ast by going west. He thought each 1 arc was 5 miles long. He estimated that the trip would take 1 days. Use your answer to part (b) to find a better estimate. 15. Graph a circle that contains a diameter with endpoints (, 3) and (, 5) and then write the standard equation of the circle. 16. In the circle with center, X =, = 7, XT is a secant, X and X are tangents, and H is the perpendicular bisector of. Find each measure. X = X = QX = TX = H H = Find the value of to the nearest hundredth. ssume that segments that appear tangent are tangent

14 1. Find each angle measure. SHOW LL WORK! (for eample, write 100+0, 70/, , etc.). Find each angle measure. SHOW LL WORK! T 3. In right triangle, is an altitude. The circles centered at P and Q are inscribed in triangles and, respectively. For = 15 and = 0, compute PQ. Q P nswers: miles.. 50, 60, spoke (-) + (y+8) = 81; center (, -8); radius a) 35.8 km, b) 80.0 km, c) km ft. 11. a) 3.9 in. b) 0.8 in gal. 13. a) 77.1, b) a) + y = 15,681,600. b) 69.1 mi. c) 1. mi. d) about 3 days. 15. ( 1) + (y 1) = X =, X = 5, QX = 18, TX = 3, H = m 1 = 70, m = 35, m 3 = 55, m = 30, m 5 = 55, m 6 = 50, m 7 = 75, m 8 = 5,, m 9 = 80, m 10 = 5.. m 1 = 5, m =, m 3 = 7, m = 0, m 5 =, m 6 = 0, m 7 = 66, m 8 = 56, m 9 = 65, m 10 = 9, m 11 = 35, m 1 = 65, m 13 = 31, m 1 =, m 15 =

### Circle Name: Radius: Diameter: Chord: Secant:

12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane

More information

### Chapter Review. 11-1 Lines that Intersect Circles. 11-2 Arcs and Chords. Identify each line or segment that intersects each circle.

HPTR 11-1 hapter Review 11-1 Lines that Intersect ircles Identify each line or segment that intersects each circle. 1. m 2. N L K J n W Y X Z V 3. The summit of Mt. McKinley in laska is about 20,321 feet

More information

### CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:

GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships

More information

### Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

More information

### Lesson 1: Introducing Circles

IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed

More information

### Geometry Unit 10 Notes Circles. Syllabus Objective: 10.1 - The student will differentiate among the terms relating to a circle.

Geometry Unit 0 Notes ircles Syllabus Objective: 0. - The student will differentiate among the terms relating to a circle. ircle the set of all points in a plane that are equidistant from a given point,

More information

### Chapters 6 and 7 Notes: Circles, Locus and Concurrence

Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of

More information

### Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.

CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture

More information

### Chapter 6 Notes: Circles

Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment

More information

### Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18

Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,

More information

### Intro to Circles Formulas Area: Circumference: Circle:

Intro to ircles Formulas rea: ircumference: ircle: Key oncepts ll radii are congruent If radii or diameter of 2 circles are congruent, then circles are congruent. Points with respect to ircle Interior

More information

### Name Date Class. Lines and Segments That Intersect Circles. AB and CD are chords. Tangent Circles. Theorem Hypothesis Conclusion

Section. Lines That Intersect Circles Lines and Segments That Intersect Circles A chord is a segment whose endpoints lie on a circle. A secant is a line that intersects a circle at two points. A tangent

More information

### How To Understand The Theory Of Ircles

Geometry hapter 9 ircle Vocabulary rc Length ngle & Segment Theorems with ircles Proofs hapter 9: ircles Date Due Section Topics ssignment 9.1 9.2 Written Eercises Definitions Worksheet (pg330 classroom

More information

### Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given

More information

### 2006 Geometry Form A Page 1

2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches

More information

### CK-12 Geometry: Parts of Circles and Tangent Lines

CK-12 Geometry: Parts of Circles and Tangent Lines Learning Objectives Define circle, center, radius, diameter, chord, tangent, and secant of a circle. Explore the properties of tangent lines and circles.

More information

### For the circle above, EOB is a central angle. So is DOE. arc. The (degree) measure of ù DE is the measure of DOE.

efinition: circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol to represent a circle. The a line segment from the center

More information

### Geometry Chapter 10 Study Guide Name

eometry hapter 10 Study uide Name Terms and Vocabulary: ill in the blank and illustrate. 1. circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center.

More information

### 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

More information

### Lesson 9.1 The Theorem of Pythagoras

Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius

More information

### Geo 9 1 Circles 9-1 Basic Terms associated with Circles and Spheres. Radius. Chord. Secant. Diameter. Tangent. Point of Tangency.

Geo 9 1 ircles 9-1 asic Terms associated with ircles and Spheres ircle Given Point = Given distance = Radius hord Secant iameter Tangent Point of Tangenc Sphere Label ccordingl: ongruent circles or spheres

More information

### Circle Theorems. This circle shown is described an OT. As always, when we introduce a new topic we have to define the things we wish to talk about.

Circle s circle is a set of points in a plane that are a given distance from a given point, called the center. The center is often used to name the circle. T This circle shown is described an OT. s always,

More information

### Conjectures. Chapter 2. Chapter 3

Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

### 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 Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

More information

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

More information

### Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

### Calculate the circumference of a circle with radius 5 cm. Calculate the area of a circle with diameter 20 cm.

RERTIES F CIRCLE Revision. The terms Diameter, Radius, Circumference, rea of a circle should be revised along with the revision of circumference and area. Some straightforward examples should be gone over

More information

### Unit 3: Circles and Volume

Unit 3: Circles and Volume This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,

More information

### Geometry Final Exam Review Worksheet

Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.

More information

### Contents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...

Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................

More information

### Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

### Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents

Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.

More information

### GEOMETRY OF THE CIRCLE

HTR GMTRY F TH IRL arly geometers in many parts of the world knew that, for all circles, the ratio of the circumference of a circle to its diameter was a constant. Today, we write d 5p, but early geometers

More information

### The Geometry of Piles of Salt Thinking Deeply About Simple Things

The Geometry of Piles of Salt Thinking Deeply About Simple Things PCMI SSTP Tuesday, July 15 th, 2008 By Troy Jones Willowcreek Middle School Important Terms (the word line may be replaced by the word

More information

### Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

### Applications for Triangles

Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given

More information

### Lesson 6.1 Tangent Properties

Lesson 6.1 angent roperties Name eriod ate 1. Ras r and s are tangents. w 2. is tangent to both circles and m 295. mqx r w 54 s 3. Q is tangent to two eternall tangent noncongruent circles, and N. X Q

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.

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: School Name: Print your name and the name

More information

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

More information

### Lesson 3.1 Duplicating Segments and Angles

Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each

More information

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

More information

### Area. Area Overview. Define: Area:

Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

More information

### Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

More information

### GEOMETRY B: CIRCLE TEST PRACTICE

Class: Date: GEOMETRY B: CIRCLE TEST PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measures of the indicated angles. Which statement

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

### 16 Circles and Cylinders

16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two

More information

### Exercise Worksheets. Copyright. 2002 Susan D. Phillips

Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.

More information

### MATH STUDENT BOOK. 8th Grade Unit 6

MATH STUDENT BOOK 8th Grade Unit 6 Unit 6 Measurement Math 806 Measurement Introduction 3 1. Angle Measures and Circles 5 Classify and Measure Angles 5 Perpendicular and Parallel Lines, Part 1 12 Perpendicular

More information

### 11 th Annual Harvard-MIT Mathematics Tournament

11 th nnual Harvard-MIT Mathematics Tournament Saturday February 008 Individual Round: Geometry Test 1. [] How many different values can take, where,, are distinct vertices of a cube? nswer: 5. In a unit

More information

### GEOMETRY (Common Core)

GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Thursday, January 28, 2016 9:15 a.m. to 12:15 p.m., only Student Name: School Name:

More information

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

### SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

More information

### Geometry Regents Review

Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

### 1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?

Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its

More information

### Unit 7 Circles. Vocabulary and Formulas for Circles:

ccelerated G Unit 7 ircles Name & ate Vocabulary and Formulas for ircles: irections: onsider 1) Find the circumference of the circle. to answer the following questions. Exact: pproximate: 2) Find the area

More information

### Grade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013

Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is

More information

### GEOMETRY CONCEPT MAP. Suggested Sequence:

CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

More information

### STRAND: ALGEBRA Unit 3 Solving Equations

CMM Subject Support Strand: ALGEBRA Unit Solving Equations: Tet STRAND: ALGEBRA Unit Solving Equations TEXT Contents Section. Algebraic Fractions. Algebraic Fractions and Quadratic Equations. Algebraic

More information

### Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

More information

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

### Definitions, Postulates and Theorems

Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

### 56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

More information

### The Geometry of a Circle Geometry (Grades 10 or 11)

The Geometry of a Circle Geometry (Grades 10 or 11) A 5 day Unit Plan using Geometers Sketchpad, graphing calculators, and various manipulatives (string, cardboard circles, Mira s, etc.). Dennis Kapatos

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

More information

### Kristen Kachurek. Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan. Technology and Manipulatives used:

Kristen Kachurek Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan Technology and Manipulatives used: TI-83 Plus calculator Area Form application (for TI-83 Plus calculator) Login application

More information

### Lesson 5-3: Concurrent Lines, Medians and Altitudes

Playing with bisectors Yesterday we learned some properties of perpendicular bisectors of the sides of triangles, and of triangle angle bisectors. Today we are going to use those skills to construct special

More information

### THE PARABOLA 13.2. section

698 (3 0) Chapter 3 Nonlinear Sstems and the Conic Sections 49. Fencing a rectangle. If 34 ft of fencing are used to enclose a rectangular area of 72 ft 2, then what are the dimensions of the area? 50.

More information

### 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 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

More information

### 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 EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

More information

### IMO Training 2008 Circles Yufei Zhao. Circles. Yufei Zhao.

ircles Yufei Zhao yufeiz@mit.edu 1 Warm up problems 1. Let and be two segments, and let lines and meet at X. Let the circumcircles of X and X meet again at O. Prove that triangles O and O are similar.

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

More information

### GEOMETRY COMMON CORE STANDARDS

1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

More information

### Not for distribution

SHPE, SPE ND MESURES Volume Volume of a cuboid Volume is the amount of space inside a -D shape. he common units for volume are: mm, cm or m. Volume = length x width x height height V = l x w x h V = lwh

More information

### MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

More information

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

More information

### 2014 2015 Geometry B Exam Review

Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists

More information

### GEOMETRIC MENSURATION

GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the

More information

### Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter

Heron s Formula Lesson Summary: Students will investigate the Heron s formula for finding the area of a triangle. The lab has students find the area using three different methods: Heron s, the basic formula,

More information

### Pythagorean Theorem: 9. x 2 2

Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

More information

### Unit 2 - Triangles. Equilateral Triangles

Equilateral Triangles Unit 2 - Triangles Equilateral Triangles Overview: Objective: In this activity participants discover properties of equilateral triangles using properties of symmetry. TExES Mathematics

More information

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd

More information

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

More information

### Advanced Euclidean Geometry

dvanced Euclidean Geometry What is the center of a triangle? ut what if the triangle is not equilateral?? Circumcenter Equally far from the vertices? P P Points are on the perpendicular bisector of a line

More information

### CIRCUMFERENCE AND AREA OF A CIRCLE

CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given

More information

### Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!

Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret

More information

### Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain

AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent

More information

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

More information

### END OF COURSE GEOMETRY CORE 1

SESSION: 24 PE: 1 5/5/04 13:29 OIN IS-glenn PT: @sunultra1/raid/s_tpc/rp_va_sprg04/o_04-ribsg11/iv_g11geom-1 VIRINI STNRS O ERNIN SSESSMENTS Spring 2004 Released Test EN O OURSE EOMETRY ORE 1 Property

More information

### 1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Stop signs are constructed in the shape of a polygon with 8 sides of equal length The polygon has 8 sides A polygon with 8 sides is an octagon All sides of the polygon are congruent and all angles are

More information

### *X100/12/02* X100/12/02. MATHEMATICS HIGHER Paper 1 (Non-calculator) NATIONAL QUALIFICATIONS 2014 TUESDAY, 6 MAY 1.00 PM 2.30 PM

X00//0 NTIONL QULIFITIONS 0 TUESY, 6 MY.00 PM.0 PM MTHEMTIS HIGHER Paper (Non-calculator) Read carefully alculators may NOT be used in this paper. Section Questions 0 (0 marks) Instructions for completion

More information

### Circumference CHAPTER. www.ck12.org 1

www.ck12.org 1 CHAPTER 1 Circumference Here you ll learn how to find the distance around, or the circumference of, a circle. What if you were given the radius or diameter of a circle? How could you find

More information

### Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

More information

### 3 e) x f) 2. Precalculus Worksheet P.1. 1. Complete the following questions from your textbook: p11: #5 10. 2. Why would you never write 5 < x > 7?

Precalculus Worksheet P.1 1. Complete the following questions from your tetbook: p11: #5 10. Why would you never write 5 < > 7? 3. Why would you never write 3 > > 8? 4. Describe the graphs below using

More information

### EUCLIDEAN GEOMETRY: (±50 marks)

ULIN GMTRY: (±50 marks) Grade theorems:. The line drawn from the centre of a circle perpendicular to a chord bisects the chord. 2. The perpendicular bisector of a chord passes through the centre of the

More information

### END OF COURSE GEOMETRY

SSSION: 27 P: 1 1/26/04 9:8 OIN IS-joer PT: @sunultra1/raid/s_tpc/rp_va_sprg03/o_03-olptg11/iv_g11geom-1 VIRINI STNRS O RNIN SSSSMNTS Spring 2003 Released Test N O OURS OMTRY Property of the Virginia epartment

More information