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


 Leonard Melton
 2 years ago
 Views:
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 fivesevenths 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, 1619, 67, 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 onehalf 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 15 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 cylindershaped 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 crosssection 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 fivepointed 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 =
Geometry SOL G.11 G.12 Circles Study Guide
Geometry SOL G.11 G.1 Circles Study Guide Name Date Block Circles Review and Study Guide Things to Know Use your notes, homework, checkpoint, and other materials as well as flashcards at quizlet.com (http://quizlet.com/4776937/chapter10circlesflashcardsflashcards/).
More informationCircle 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 informationc.) If RN = 2, find RP. N
Geometry 101 ircles and ircumference. Parts of ircles 1. circle is the locus of all points equidistant from a given point called the center of the circle.. circle is usually named by its point. 3. The
More informationChapter Review. 111 Lines that Intersect Circles. 112 Arcs and Chords. Identify each line or segment that intersects each circle.
HPTR 111 hapter Review 111 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 informationWarm Up #23: Review of Circles 1.) A central angle of a circle is an angle with its vertex at the of the circle. Example:
Geometr hapter 12 Notes  1  Warm Up #23: Review of ircles 1.) central angle of a circle is an angle with its verte at the of the circle. Eample: X 80 2.) n arc is a section of a circle. Eamples:, 3.)
More informationTest to see if ΔFEG is a right triangle.
1. Copy the figure shown, and draw the common tangents. If no common tangent exists, state no common tangent. Every tangent drawn to the small circle will intersect the larger circle in two points. Every
More informationDates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday. 3 (only see 6 th, 4
Name: Period GL UNIT 12: IRLS I can define, identify and illustrate the following terms: Interior of a circle hord xterior of a circle Secant of a circle Tangent to a circle Point of tangency entral angle
More informationCCGPS 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 M91.G..1 Prove that all circles are similar. M91.G.. Identify and describe relationships
More informationUnit 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 informationLesson 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 informationChapters 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 informationChapter 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 informationGeometry 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 informationTangents to Circles. Circle The set of all points in a plane that are equidistant from a given point, called the center of the circle
10.1 Tangents to ircles Goals p Identify segments and lines related to circles. p Use properties of a tangent to a circle. VOULRY ircle The set of all points in a plane that are equidistant from a given
More informationTangent 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 informationSection 91. Basic Terms: Tangents, Arcs and Chords Homework Pages 330331: 118
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 informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationName 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 informationIntro 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 informationcircle the set of all points that are given distance from a given point in a given plane
Geometry Week 19 Sec 9.1 to 9.3 Definitions: section 9.1 circle the set of all points that are given distance from a given point in a given plane E D Notation: F center the given point in the plane radius
More informationGeometry Chapter 9. Circle Vocabulary Arc Length Angle & Segment Theorems with Circles Proofs
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 informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More informationcircumscribed circle Vocabulary Flash Cards Chapter 10 (p. 539) Chapter 10 (p. 530) Chapter 10 (p. 538) Chapter 10 (p. 530)
Vocabulary Flash ards adjacent arcs center of a circle hapter 10 (p. 539) hapter 10 (p. 530) central angle of a circle chord of a circle hapter 10 (p. 538) hapter 10 (p. 530) circle circumscribed angle
More informationThe measure of an arc is the measure of the central angle that intercepts it Therefore, the intercepted arc measures
8.1 Name (print first and last) Per Date: 3/24 due 3/25 8.1 Circles: Arcs and Central Angles Geometry Regents 20132014 Ms. Lomac SLO: I can use definitions & theorems about points, lines, and planes to
More informationName: 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 informationFor 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 informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
More information2006 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 informationGeometry 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 informationCircle geometry theorems
Circle geometry theorems http://topdrawer.aamt.edu.au/geometricreasoning/bigideas/circlegeometry/angleandchordproperties Theorem Suggested abbreviation Diagram 1. When two circles intersect, the line
More information121. Tangent Lines. Vocabulary. Review. Vocabulary Builder HSM11_GEMC_1201_T Use Your Vocabulary
11 Tangent Lines Vocabulary Review 1. ross out the word that does NT apply to a circle. arc circumference diameter equilateral radius. ircle the word for a segment with one endpoint at the center of a
More informationPerimeter and area formulas for common geometric figures:
Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,
More informationCircle 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 informationLesson 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 informationUnit 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. (101) Circles and Circumference
More informationCK12 Geometry: Parts of Circles and Tangent Lines
CK12 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 informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationNCERT. In examples 1 and 2, write the correct answer from the given four options.
MTHEMTIS UNIT 2 GEOMETRY () Main oncepts and Results line segment corresponds to the shortest distance between two points. The line segment joining points and is denoted as or as. ray with initial point
More informationGeo 9 1 Circles 91 Basic Terms associated with Circles and Spheres. Radius. Chord. Secant. Diameter. Tangent. Point of Tangency.
Geo 9 1 ircles 91 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. SAMPLE RESPONSE SET
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. SAMPLE RESPONSE SET Table of Contents Question 29................... 2 Question 30...................
More information107 Special Segments in a Circle. Find x. Assume that segments that appear to be tangent are tangent. 1. SOLUTION: ANSWER: 2 SOLUTION: ANSWER:
Find x. Assume that segments that appear to be tangent are tangent. 1. 3. 2 5 2. 4. 6 13 esolutions Manual  Powered by Cognero Page 1 5. SCIENCE A piece of broken pottery found at an archaeological site
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
More informationA = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height
Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side
More informationA. 3y = 2x + 1. y = x + 3. y = x  3. D. 2y = 3x + 3
Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x  1 D. y = 3x + 1
More information107 Special Segments in a Circle. Find x. Assume that segments that appear to be tangent are tangent. 1. SOLUTION: 2. SOLUTION: 3.
Find x. Assume that segments that appear to be tangent are tangent. 1. 2. 3. esolutions Manual  Powered by Cognero Page 1 4. 5. SCIENCE A piece of broken pottery found at an archaeological site is shown.
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More information83 Perimeter and Circumference
Learn to find the perimeter of a polygon and the circumference of a circle. 83 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary The distance around a geometric figure
More informationThe 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 informationCIRCLE DEFINITIONS AND THEOREMS
DEFINITIONS Circle The set of points in a plane equidistant from a given point(the center of the circle). Radius A segment from the center of the circle to a point on the circle(the distance from the
More informationSenior Math Circles: Geometry I
Universit of Waterloo Facult of Mathematics entre for Education in Mathematics and omputing pening Problem (a) If 30 7 = + + z Senior Math ircles: Geometr I, where, and z are positive integers, then what
More informationPostulate 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) 111: 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 informationSeattle Public Schools KEY to Review Questions for the Washington State Geometry End of Course Exam
Seattle Public Schools KEY to Review Questions for the Washington State Geometry End of ourse Exam 1) Which term best defines the type of reasoning used below? bdul broke out in hives the last four times
More informationUnit 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 informationCalculate 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 informationContents. 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 informationGeometry 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 informationThe 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 information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationEND OF COURSE GEOMETRY
SESSION: 42 PE: 4/20/02 9:7 OIN ISpam PT: @sun/ydisk2/s_psycorp/rp_virginia/o_5752g/iv_ggeom VIRINI STNRS O ERNIN SSESSMENTS Spring 2002 Released Test EN O OURSE EOMETRY SESSION: 42 PE: 2 4/20/02 9:7
More informationSet 1: Circumference, Angles, Arcs, Chords, and Inscribed Angles
Goal: To provide opportunities for students to develop concepts and skills related to circumference, arc length, central angles, chords, and inscribed angles Common Core Standards Congruence Experiment
More informationAnalytic Geometry Section 26: Circles
Analytic Geometry Section 26: Circles Objective: To find equations of circles and to find the coordinates of any points where circles and lines meet. Page 81 Definition of a Circle A circle is the set
More informationBasics of Circles 9/20/15. Important theorems:
Basics of ircles 9/20/15 B H P E F G ID Important theorems: 1. A radius is perpendicular to a tangent at the point of tangency. PB B 2. The measure of a central angle is equal to the measure of its intercepted
More informationConjectures 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 informationTERRA Environmental Research Institute
TERR Environmental Research Institute MTHEMTIS FT PRTIE STRN 2 Measurement Perimeter and rea ircumference and rea of ircles Surface rea Volume Time, Weight/Mass, apacity, and Temperature SUNSHINE STTE
More information114 Areas of Regular Polygons and Composite Figures
1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,
More informationLesson 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 informationGEOMETRY 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 informationSolving Problems Involving Chords, Radii, Tangents, Secants and Arcs within the Same Circle Grade Ten
Ohio Standards Connection: Geometry and Spatial Sense Benchmark C Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines. Indicator 10
More informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180. C Vertical Angles Conjecture  If two angles are
More informationof one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 4592058 Mobile: (949) 5108153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:
More informationParallel 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 informationThe Inscribed Angle Alternate A Tangent Angle
Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays is
More informationName Geometry Exam Review #1: Constructions and Vocab
Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make
More informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
More informationChapter 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 informationThe 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 information10.5 and 10.6 Lesson Plan
Title: Secants, Tangents, and Angle Measures 10.5 and 10.6 Lesson Plan Course: Objectives: Reporting Categories: Related SOL: Vocabulary: Materials: Time Required: Geometry (Mainly 9 th and 10 th Grade)
More informationGeometry Work Samples Practice
1. If ABCD is a square and ABE is an equilateral triangle, then what is the measure of angle AFE? (H.1G.5) 2. Square ABCD has a circular arc of radius 2 with the center at A and another circular arc with
More informationThe 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 information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationLesson 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 informationThe 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 information128 Congruent and Similar Solids
Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio
More informationArea 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 information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More informationThe Parabola and the Circle
The Parabola and the Circle The following are several terms and definitions to aid in the understanding of parabolas. 1.) Parabola  A parabola is the set of all points (h, k) that are equidistant from
More informationA. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.
Geometry  Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle
More informationMATH 139 FINAL EXAM REVIEW PROBLEMS
MTH 139 FINL EXM REVIEW PROLEMS ring a protractor, compass and ruler. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice
More informationApplications 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(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationUnit 3 Circles and Spheres
Accelerated Mathematics I Frameworks Student Edition Unit 3 Circles and Spheres 2 nd Edition March, 2011 Table of Contents INTRODUCTION:... 3 Sunrise on the First Day of a New Year Learning Task... 8 Is
More information11 th Annual HarvardMIT Mathematics Tournament
11 th nnual HarvardMIT 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 informationArea 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 informationGeometry 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 informationArea. 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 information3D Geometry: Chapter Questions
3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the crosssection of 3Dimensional figures? 4.
More informationGEOMETRY (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 informationGEOMETRY 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 informationEach pair of opposite sides of a parallelogram is congruent to each other.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite
More informationGeometry 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