Finding Angle Measures. Solve. 2.4 in. Label the diagram. Draw AE parallel to BC. Simplify. Use a calculator to find the square root. 14 in.
|
|
- Joan Fields
- 7 years ago
- Views:
Transcription
1 lan bjectives 1 To use the relationship between a radius and a tangent To use the relationship between two tangents from one point amples 1 inding ngle Measures Real-World onnection inding a Tangent Using Theorems 1- ircles Inscribed in olygons Math ackground 1-1 What You ll Learn To use the relationship between a radius and a tangent To use the relationship between two tangents from one point... nd Why To find the distance between the centers of two dirt bike gears, as in ample Tangent Lines heck kills You ll eed G for Help kills Handbook page 7 and Lesson -1 ind each product. 1. (p + ) p ± 6p ± 9 w ± 0w ± 100. (w + 10) m m ±. (m - ) lgebra ind the value of. Leave your answer in simplest radical form... " " ew Vocabulary tangent to a circle point of tangency inscribed in circumscribed about tangent to a circle is related to the geometric interpretation of a derivative, the fundamental concept of differential calculus. derivative measures the rate of change of a function at any point and corresponds to the slope of the tangent to the graph of the function at that point. More Math ackground: p Using the Radius-Tangent Relationship Vocabulary Tip The word tangent may refer to a line, ray, or segment. In hapter, you studied the tangent ratio in right triangles. The tangents you will study here relate to circles. tangent to a circle is a line in the plane of the circle that intersects the circle in eactly one point. The point where a circle and a tangent intersect is the point of tangency. is a tangent ray and is a tangent segment. Lesson lanning and Resources Theorem 1-1 relates a tangent and a radius in a given circle. You will write an indirect proof for Theorem 1-1 in ercise 9. ee p. 660 for a list of the resources that support this lesson. oweroint ell Ringer ractice heck kills You ll eed or intervention, direct students to: kills Handbook, p. 7 The ythagorean Theorem Lesson -1: ample tra kills, Word roblems, roof ractice, h. Key oncepts Theorem 1-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. * ) ' You can use Theorem 1-1 to solve problems involving tangents to circles. 66 hapter 1 ircles 66 pecial eeds L1 Have students draw two intersecting lines and fit a quarter between the lines so that it is tangent to both lines. tudents measure the distances from the point of intersection to the points of tangency. learning style: tactile elow Level L tudents may be confused by using tangent in a new way. Try to use the phrases tangent of an angle and tangent to a circle to help reinforce the difference. learning style: verbal
2 1 ML inding ngle Measures. Teach 1 Test-Taking Tip Remember that you can find the sum of the angles of a polygon with n sides using the formula (n )10. uick heck Multiple hoice ML and M are tangent to. ind the value of ince ML and M are tangent to, &L and & are right angles. LM is a quadrilateral whose angle measures have a sum of 60. m&l + m&m + m& + m& = = 60 ubstitute. The correct answer is = 60 implify. = 6 olve. 1 is tangent to. ind the value of. L 117 M Guided Instruction onnection to Language rts The term tangent is derived from the Latin verb tangere, which means to touch. Math Tip or a ray or segment to be tangent to a circle, the line containing the ray or segment must be tangent to the circle. ote that a radius is never tangent to a circle. Real-World onnection This motorcycle and many other two-wheeled vehicles have chain-drive systems like the one shown in ample. uick heck ML Real-World onnection irt ikes dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one at the right. ind the distance between the centers of the gears. 6. in.. in. Label the diagram. raw parallel to. is a rectangle. # is a right triangle with = 6. in. and = = 6.9 in. = + ythagorean Theorem = ubstitute. = 79.6 < in. implify. Use a calculator to find the square root. The distance between the centers is about 7. in. belt fits tightly around two circular pulleys, as shown at the right. ind the distance between the centers of the pulleys. about. in. dvanced Learners L fter ample, have students write an equation for the radius of a circle inscribed in an equilateral triangle with sides of length s. 1 in. 6. in.. in. in. 9. in. Theorem 1- (net page) is the converse of Theorem 1-1. You can use it to prove that a line or segment is tangent to a circle. You can also use it to construct a tangent to a circle (see ercise ). You will prove this theorem in ercise. learning style: verbal in. Lesson 1-1 Tangent Lines 66 nglish Language Learners LL ome students may confuse the terms circumscribe and inscribe. It helps students to remember that a figure that is circumscribed goes around another figure and a figure that is inscribed is in another figure. learning style: verbal ML Make sure that students remember the properties of rectangles well enough to prove that is a rectangle. sk: How do you know that & and & are right angles? n, l and l are right angles, and same-side interior angles are supplementary. How do you know that =? pposite sides of a rectangle are congruent. oweroint dditional amples 1 is tangent to at point. ind the value of. 6 belt fits tightly around two circular pulleys, as shown below. ind the distance between the centers of the pulleys. Y cm Z 1 cm 1 cm has radius. oint is outside such that = 1, and point is on such that = 1. Is tangent to at? plain. o; u ±. W 7 cm 1. cm 66
3 Guided Instruction Math Tip oint out that this lesson provides another way to define an inscribed circle: circle is inscribed in a polygon if it is tangent to each side of the polygon. Key oncepts Theorem 1- If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. * ) is tangent to. oweroint dditional amples and T are tangent to at points and T, respectively. Give a convincing argument that the diagonals of quadrilateral T are perpendicular. uick heck ML inding a Tangent Is ML tangent to at L? plain. L + LM 0 M Is kml a right triangle? ubstitute. 6 = 6 implify. y the onverse of the ythagorean Theorem, #ML is a right triangle with right &L. Therefore ML ' L, and ML is tangent to at L by Theorem 1-. If L =, LM = 7, and M =, is ML tangent to at L? plain. o; ± 7 u. 7 L M T is a kite or a rhombus, so its diagonals are perpendicular. is inscribed in quadrilateral YZW. ind the perimeter of YZW. 11 ft 6 ft U T Y ft R W Z 6 ft T 7 ft 1 Using Multiple Tangents Key oncepts Theorem 1- If a circle is circumscribed about a triangle (hapter ), the triangle is inscribed in the circle. imilarly, when a circle is inscribed in a triangle, as in the diagram, the triangle is circumscribed about the circle. ach side of the triangle is tangent to the circle. The tangent segments from each verte are congruent. You will prove this theorem in ercise 0. The two segments tangent to a circle from a point outside the circle are congruent. > Resources aily otetaking Guide 1-1 L aily otetaking Guide 1-1 dapted Instruction L1 losure ind the radius of the circle inscribed in the right triangle below. in. in. uick heck 66 hapter 1 ircles ML Using Theorem 1- The diagram represents a chain drive system on a bicycle. Give a convincing argument that = G. tend and G to intersect in point H. y Theorem 1-, H = H, or H + = HG + G. H y Theorem 1- again, H = HG, so by the ubtraction roperty of quality, = G. ritical Thinking Give a convincing argument that = G above if you know that and G never intersect. If and G never intersect, then G is a rectangle. G G in. 1 in. 66
4 uick heck ample 1 (page 66) amples, (pages 66, 66) ample (page 66) ML ircles Inscribed in olygons is inscribed in #. ind the perimeter of #. = = 10 cm The two segments tangent to a = = 1 cm circle from a point outside the = = cm circle are congruent. p = + + efinition of perimeter p = egment ddition ostulate = ubstitute. = 66 The perimeter is 66 cm. is inscribed in #R. #R has a perimeter of cm. ind Y. 1 cm lgebra ssume that lines that appear to be tangent are tangent. is the center of each circle. ind the value of belt fits snugly around the two circular pulleys shown.. ind the distance between the centers of the R pulleys. Round to the nearest hundredth. 1.0 in.. Give a convincing argument why the belt M lengths R and are equal. ee margin. in. in. or the pulley system shown, use the lengths given below. ind the missing length to the nearest tenth. 1 in. ercises 7 6. M = 10 cm, = cm, 7. M = in., = in., = 1 cm, M = 7 cm 1. = 0 in., M = 7 in cm 1 cm cm 1 cm Y Z 17 cm R RI or more eercises, see tra kill, Word roblem, and roof ractice. ractice and roblem olving G ractice by ample for Help Vocabulary Tip R and are common tangents.. o; ± 16 u Yes;. ± Yes; 6 ± 10. etermine whether a tangent line is shown in each diagram. plain ee left ractice ssignment Guide G nrichment Guided roblem olving Reteaching dapted ractice earson ducation, Inc. ll rights reserved. 1 ractice 1-, 6-10, 1-1, 17-19, -7, 9, 11, 1, 16, 0-,, 0 hallenge 1- Test rep - Mied Review 9-6 Homework uick heck To check students understanding of key skills and concepts, go over ercises,, 1, 1, 9. ame lass ate ractice 1-1 Use the figures to complete ercises or figure IJKL, draw its reflection image in each line. a. -ais b. y-ais. In the diagram, is the image of. a. ame the images of and. b. List the pairs of corresponding sides.. In the diagram, M is the image of M. a. ame the images of M and. b. List the pairs of corresponding sides.. is the image of. a. ame the images of and. b. List the pairs of corresponding sides.. or figure WYZ, draw its reflection image in each line. a. -ais b. y-ais tate whether each transformation appears to be an isometry. plain Given points T(, ), (, ), and (0, ), draw kt and its reflection image in each line. 9. -ais 10. y-ais 11. =- 1. y = 6 6 y I J L Reflections W 6 6 Z Y y L L1 M L L L M K Lesson 1-1 Tangent Lines 66. tend R and until they meet at a point, H. y Thm. 11-, RH H, or H ± R ± H. y 11- again, H H. Thus, R. 66
5 onnection to stronomy ercise 16 s the diagram suggests, a solar eclipse occurs when the moon blocks sunlight from reaching arth. total eclipse occurs when the moon completely blocks the sun s rays, as in the region between the moon and arth bounded by the common internal tangents to the sun and the moon. ercise tudents may benefit from a review of the properties of triangles. Tactile Learners ercise Have students manipulate a nickel, a dime, and a quarter to show how three circles can be mutually tangent. onnection to oordinate Geometry ercise 7 efore drawing a tangent segment, students must find its length,, using the ythagorean Theorem. Then they can place a compass point at (0, ), swing an arc of length until it intersects the circle, and join either point of intersection and (0, ). ercises 1 You may want students to work with partners or in small groups. uggest that they begin each proof by writing a plan. 1. a. 16a. eternal b. eternal c. internal Real-World ample (page 66) pply Your kills onnection This diamond ring effect in a solar eclipse may be seen by a person on arth at the end of a common eternal tangent of the sun and moon. (ee diagram at right.) G nline Homework Help Visit: Hchool.com Web ode: aue-101 ach polygon circumscribes a circle. ind the perimeter of the polygon in. cm 16 cm 6 cm 9 cm lgebra ssume that lines that appear to be tangent are tangent. is the center of each circle. ind the value of to the nearest tenth. in in cm 1 9 in. 7 cm 7 cm.6 cm.7 in..6 in. 1.9 in.. in. 16. olar clipse ommon tangents to two circles may be internal or eternal. If you draw a segment joining the centers of the circles, a common internal tangent will intersect the segment. common eternal tangent will not. or this cross-sectional diagram of the sun, moon, and arth during a solar eclipse, use the terms above to describe the types un arth of tangents of each color. a-c. ee a. red b. blue c. green above. not to scale Moon d. Which tangents show the etent blue lines; green lines on arth s surface of total eclipse? f partial eclipse? e. Reasoning In general, does every pair of circles have common tangents of both types? plain. o; eplanations may vary. ample: Two circles that have a common center have no common tangents. arth The circle at the right represents arth. The radius of arth h d is about 600 km. ind the distance d that a person can see on a r clear day from each of the following heights h above arth. r Round your answer to the nearest tenth of a kilometer m. km m 0.0 km km 11.1 km 0. and K at the right are diameters of. 7. and are tangents to. What is m&? K 1. History Leonardo da Vinci wrote, When each of G two squares touch the same circle at four points, one is double the other. a-b. ee margin. a. ketch a figure that illustrates this statement. b. Writing plain why the statement is true.. Multiple hoice regular heagon is circumscribed about the ring surrounding the clock face. The diameter of the ring is 10 in. What is the perimeter of the heagon? 0.0 in..6 in.. in. 1.7 in. 666 b. nswers may vary. ample: If you draw diagonals for both squares, >are formed in the entire figure with in the small square. 666 hapter 1 ircles. 0. a and are tangent to ( at and (Given) T. # and # R (If a line is tan. to a circle, it is # to the radius.). k and k are right >. (ef.
6 .ll four are ; the two tangents to each coin from are, so by the Trans. rop., all are R or ; 1 ml is ml1. Real-World onnection areers HV technicians often specialize in either installation or maintenance and repair of heating, ventilation, and air conditioning systems. lesson quiz, Hchool.com, Web ode: aua-101 of rt. k). (Radii of a circle are.). (Refl. rop. of ) 6. k k (HL Thm.) 7. (T). ritical Thinking nickel, a dime, and a quarter are touching as shown. Tangents are drawn from point to both sides of each coin. What can you conclude about the four tangent segments? plain.. onstructions raw a circle. Label the center T. Locate a point on the circle and label it R. onstruct a tangent to T at R. ee margin. is tangent to at, and ml ind m&. 6. Let m&1 =. ind m& in terms of. What is the relationship between &1 and &? 1 7. oordinate Geometry Graph the equation + y = 9. Then draw a segment from (0, ) tangent to the circle. ind the length of the segment. ee back of book.. Maintenance Mr. Gonzales is replacing a cylindrical airconditioning duct. He estimates the radius of the duct by folding a ruler to form two 6-in. tangents to the duct. The tangents form an angle. Mr. Gonzales measures the angle bisector from the verte to the duct. It is about in. long. What is the radius of the duct? about. in. 9. omplete the following indirect proof of Theorem 1-1. Given: Line n is tangent to at. rove: line n ' tep 1 ssume that line n is not perpendicular to. n L in. K tep If line n is not perpendicular to, some other segment L must be a. 9 to line n. y the Ruler ostulate, there is a point K on L such that K = L, so L = b. 9. #L > #KL by c. 9, so = K because d. 9. ince and K are the same distance from, both K and are on. This contradicts the given fact that line n is e. 9 to at. a. '; b. LK; c. ; d. T; e. tangent; f. false tep The assumption that line n is not perpendicular to is f. 9, so line n '. roof 0. rove Theorem 1-. Given: and are tangent to at and, respectively. rove: > ee margin. 1. Given: is tangent to at.. Given: and with common > tangents and rove: > ee margin. ee rove: #G, #G margin is tangent to ( at. (Given). (Given). # (If a line is tan. to a circle, it is # to the radius.). l Lesson 1-1 Tangent Lines 667 G r 6 in. and l are rt. ' (ef. of #). l l (rt. ' are ) 6. (Refl. rop. of ) 7. k k (). (T). ssess & Reteach oweroint Lesson uiz and are tangent to. Use the figure for ercises 1. 0 cm 1. ind the value of. 7.. ind the perimeter of quadrilateral. cm. ind. 9 cm *HJ ) is tangent to and to. Use the figure for ercises and. H cm 9. 0 cm 1 cm J cm. ind to the nearest tenth. 0. cm. What type of special quadrilateral is HJ? plain how you know. Trapezoid; the tangent line forms right angles at vertices H and J, so H n J. ecause H u J, HJ is not a parallelogram but a trapezoid. lternative ssessment Have students use compass and straightedge to construct a circle and then construct a line through a point on the circle perpendicular to a radius of the circle. Have students repeat the construction using a different radius and then find the intersection of the two lines they constructed. fter constructing each line and finding the intersection, students should state a conclusion based on a theorem in this lesson. 667
7 Test rep Resources or additional practice with a variety of test item formats: tandardized Test rep, p. 711 Test-Taking trategies, p. 706 Test-Taking trategies with Transparencies hallenge roof. Write an indirect proof of Theorem 1-. Given: ' at. rove: is tangent to. ee back of book.. Two circles that have one point in common are tangent circles. Given any triangle, eplain how to draw three circles that are centered at each verte of the triangle and are tangent to each other. t each verte, let the radius of a circle be the distance from the verte to either point of tangency of the incircle. Test rep. 1. ( and ( with common tangents and (Given). G G and G G (Two tan. segments from a pt. to a circle are.) G G. G 1, G 1 (iv. rop. of ) G G. G G (Trans. rop. of ). lg lg (Vert. ' are.) 6. kg M kg ( M Thm.) Multiple hoice 9. [] 9. R equivalent solution [1] correct eq. solved incorrectly hort Response Mied Review oint is the center of each circle. ssume the lines that appear tangent are tangent. What is the value of the variable? G H J J G.. 1 H.. 17 J. 9. ind the value of. how your work. ee above left. G for Help Lesson 11- Lesson - Lesson 7-66 hapter 1 ircles Two cubes have heights 6 in. and in. ind each ratio. 0. similarity ratio 1. ratio of surface areas. ratio of volumes : 9:16 7:6 lgebra ind the value of. Round answers to the nearest tenth The polygons are similar. (a) tate the similarity ratio and (b) find the values of the variables. a. 10:17 a. : 1 6. m b. m 1.; n a b. n 6 c b. a 1.6; b 1.7; c 66
Areas of Circles and Sectors. GO for Help
-7 What You ll Learn To find the areas of circles, sectors, and segments of circles... nd Why To compare the area of different-size pizzas, as in Example reas of ircles and Sectors heck Skills You ll Need
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 informationNAME DATE PERIOD. Study Guide and Intervention
opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. 5-1 M IO tudy Guide and Intervention isectors, Medians, and ltitudes erpendicular isectors and ngle isectors perpendicular bisector
More informationCK-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 informationFor each Circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1. x = 2. x =
Name: ate: Period: Homework - Tangents For each ircle, find the value of. ssume that segments that appear to be tangent are tangent. 1. =. = ( 5) 1 30 0 0 3. =. = (Leave as simplified radical!) 3 8 In
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 informationHow 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 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 information8.2 Angle Bisectors of Triangles
Name lass Date 8.2 ngle isectors of Triangles Essential uestion: How can you use angle bisectors to find the point that is equidistant from all the sides of a triangle? Explore Investigating Distance from
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 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 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 M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
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 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 informationMeasure and classify angles. Identify and use congruent angles and the bisector of an angle. big is a degree? One of the first references to the
ngle Measure Vocabulary degree ray opposite rays angle sides vertex interior exterior right angle acute angle obtuse angle angle bisector tudy ip eading Math Opposite rays are also known as a straight
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 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 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 Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
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) 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 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 informationChapter 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 informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
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 information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
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 informationDefinitions, 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 informationAlgebra 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 informationThe 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 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 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 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 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 informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationLesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.
More informationEND 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 informationConjectures. 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 informationGEOMETRY 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 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 Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationThe 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 informationName: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain
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 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 informationSection 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 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 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 informationDuplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
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 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 informationThe 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 information6.2 PLANNING. Chord Properties. Investigation 1 Defining Angles in a Circle
LESSN 6.2 You will do foolish things, but do them with enthusiasm. SINIE GRIELL LETTE Step 1 central Step 1 angle has its verte at the center of the circle. Step 2 n Step 2 inscribed angle has its verte
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationThe 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 information11 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 informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationAdvanced 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 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 informationPERIMETER 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 informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
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 informationGeometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More informationProperties of Circles
10 10.1 roperties of ircles Use roperties of Tangents 10.2 ind rc Measures 10.3 pply roperties of hords 10.4 Use Inscribed ngles and olygons 10.5 pply Other ngle elationships in ircles 10.6 ind egment
More informationGEOMETRY 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 informationGeorgia 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 information12.4 Problems. Excerpt from "Introduction to Geometry" 2014 AoPS Inc. Copyrighted Material CHAPTER 12. CIRCLES AND ANGLES
HTER 1. IRLES N NGLES Excerpt from "Introduction to Geometry" 014 os Inc. onider the circle with diameter O. all thi circle. Why mut hit O in at leat two di erent point? (b) Why i it impoible for to hit
More informationCurriculum 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 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 information56 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 informationCAMI Education linked to CAPS: Mathematics
- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
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 informationThe 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 informationGEOMETRIC 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 informationGeometry 8-1 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 8-1 ngles of Polygons 1. Interior angles - The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
More informationCONGRUENT TRIANGLES 6.1.1 6.1.4
ONGUN INGL 6.1.1 6.1.4 wo triangles are congruent if there is a sequence of rigid transformations that carry one onto the other. wo triangles are also congruent if they are similar figures with a ratio
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationThe 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 informationGeometry 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 informationGeometry 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 informationGrade 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 informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More information1-1. Nets and Drawings for Visualizing Geometry. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
1-1 Nets and Drawings for Visualizing Geometry Vocabulary Review Identify each figure as two-dimensional or three-dimensional. 1. 2. 3. three-dimensional two-dimensional three-dimensional Vocabulary uilder
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 informationChapter 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 informationWeek 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test
Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationKristen 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 informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
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 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 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 informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More information