EXAMPLE. Step 1 Draw a ray with endpoint C. Quick Check

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "EXAMPLE. Step 1 Draw a ray with endpoint C. Quick Check"

Transcription

1 -7. lan -7 asic onstructions Objectives o use a compass and a straightedge to construct congruent segments and congruent angles o use a compass and a straightedge to bisect segments and angles Examples onstructing ongruent egments onstructing ongruent ngles 3 onstructing the erpendicular isector Finding ngle easures 5 onstructing the ngle isector What ou ll Learn o use a compass and a straightedge to construct congruent segments and congruent angles o use a compass and a sraightedge to bisect segments and angles... nd Why o construct the bisector of an angle to illustrate angles of incidence and reflection, as in Exercise 8 onstructing egments and ngles heck kills ou ll Need GO for Help In Exercises 6, sketch each figure. 6. ee back of book. *.. GH 3.. line m 5. acute & E = 0. oint is the midpoint of E. Find E Use a protractor to draw a 608 angle ee back of book. 9. Use a protractor to draw a 08 angle. New Vocabulary construction straightedge compass perpendicular lines angle bisector perpendicular bisector Lessons -5 and -6 ath ackground onstruction methods are justified by postulates such as Euclid s Fourth ostulate, that a circle can be drawn with any center and any positive radius, and by, for example, triangle congruency theorems. ompassand-straightedge constructions provide a hands-on introduction to these postulates and theorems. In a construction you use a straightedge and a compass to draw a geometric figure. straightedge is a ruler with no markings on it. compass is a geometric tool used to draw circles and parts of circles called arcs. Four basic constructions involve constructing congruent segments, congruent angles, and bisectors of segments and angles. ELE onstructing ongruent egments onstruct a segment congruent to a given segment. Given: onstruct: so that > ore ath ackground: p. tep raw a ray with endpoint. Lesson lanning and esources ee p. E for a list of the resources that support this lesson. oweroint ell inger ractice heck kills ou ll Need For intervention, direct students to: Finding egment Lengths Lesson -3: Example Extra kills, Word roblems, roof ractice, h. Finding ngle easures Lesson -: Examples and 5 Extra kills, Word roblems, roof ractice, h.. uick heck hapter ools of Geometry tep Open the compass to the length of. tep 3 With the same compass setting, put the compass point on point. raw an arc that intersects the ray. Label the point of intersection. > pecial Needs L For Example 3 on constructing a perpendicular bisector, ask: Why does the opening of the compass need to be greater than half the length of the segment? the arcs must intersect Use a straightedge to draw. hen construct so that =. learning style: verbal elow Level L emonstrate the construction steps in Examples,, 3, and 5 by using a large demonstration compass. hen ask student volunteers to demonstrate the constructions. learning style: visual

2 ELE onstructing ongruent ngles. each For: onstruction ctivity Use: Interactive extbook, -7 onstruct an angle congruent to a given angle. Given: & onstruct: & so that & > & tep raw a ray with endpoint. tep With the compass point on point, draw an arc that intersects the sides of &. Label the points of intersection and. tep 3 With the same compass setting, put the compass point on point. raw an arc and label its point of intersection with the ray as. Guided Instruction eaching ip If students have problems using a compass and straightedge, have them work in pairs to share the construction steps. ELE Error revention Have students make sure that their compasses are not so loose that they slip during use and make an incorrect arc. oint out that some compasses can be tightened. tep Open the compass to the length. Keeping the same compass setting, put the compass point on. raw an arc to locate point. tep 5 raw. oweroint dditional Examples onstruct W congruent to K. K uick heck & > & onstruct &F with m&f = m&. onstruct & so that & &G. W F onstructing isectors erpendicular lines are two lines that intersect to form right angles. he symbol ' means is perpendicular to. In the diagram at * * * the right, ' and '. * perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments. G eal-world onnection erpendicular hands signal ime out. s you will learn in hapter 5, there is just one line that is the perpendicular bisector of a segment in a given plane. Here is a way to construct the perpendicular bisector. Lesson -7 asic onstructions 5 dvanced Learners L Have students investigate ancient and modern attempts to trisect an angle. learning style: verbal English Language Learners ELL Help students understand the difference between drawing and constructing. Emphasize that when drawing, a ruler and protractor can be used. In constructions, only a compass and straightedge can be used. learning style: verbal 5

3 Guided Instruction eaching ip oint out that the symbol for perpendicular resembles perpendicular lines. sk: What other symbol resembles what it represents? ample: the symbol for parallel 3 ELE onnection to Language rts he word bisector contains the prefix bi-, which means two. oweroint dditional Examples 3 Open the compass less than in step of Example 3. Explain why the construction is not possible. ample: When the opening is less than, the arcs drawn in steps and do not intersect. o, the perpendicular bisector cannot be drawn. W bisects &W. m&w = x and m&w = x - 8. Find m&w. 3 5 onstruct, the bisector of &. esources aily Notetaking Guide -7 L3 aily Notetaking Guide -7 dapted Instruction L eal-world onnection areers rchitects use construction tools to work with their designs. uick heck uick heck 3 ELE onstructing the erpendicular isector onstruct the perpendicular bisector of a segment. Given: onstruct: so that ' at the midpoint of. tep ut the compass point on point and draw a long arc as shown. e sure the opening is greater than. tep With the same compass setting, put the compass point on point and draw another long arc. Label the points where the two arcs intersect as and. *. tep 3 raw he point of intersection of and is, the midpoint of. * * ' at the midpoint of, so is the perpendicular bisector of. 3 raw. onstruct its perpendicular bisector. n angle bisector is a ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex.within the ray, a segment with the same endpoint is also an angle bisector.ou may say that the ray or segment bisects the angle. ELE Finding ngle easures lgebra KN bisects &JKL so that m&jkn = 5x - 5 and m&nkl = 3x + 5. olve for x and find m&jkn. m&jkn = m&nkl efinition of angle bisector 5x - 5 = 3x + 5 ubstitute. 5x = 3x + 30 dd 5 to each side. x = 30 ubtract 3x from each side. x = 5 ivide each side by. m&jkn = 5x - 5 = 5(5-5 = 50 ubstitute 5 for x. m&jkn = 50 * * * Find m&nkl and m&jkl. 50; 00 J N K L losure 6 hapter ools of Geometry Write steps in your own words for bisecting an angle and bisecting a segment. Use drawings that show the arcs in each step. heck students work. 6 uick heck. 5. a. Z Exercises.. V W

4 uick heck Example (page Example (page 5 Example 3 (page 6 Example (page 6 5 onstruct the bisector of an angle. onstructing the ngle isector Given: & onstruct:, the bisector of & tep ut the compass point on vertex. raw an arc that intersects the sides of &. Label the points of intersection and. tep ut the compass point on point and draw an arc. With the same compass setting, draw an arc using point. e sure the arcs intersect. Label the point where the two arcs intersect as. tep 3 raw. is the bisector of &. 5 a. raw obtuse &Z. hen construct its bisector. ee margin, p. 6. b. Explain how you can use your protractor to check your construction. easure l and lz to see that they are O. x ELE EEIE For more exercises, see Extra kill, Word roblem, and roof ractice. ractice and roblem olving GO ractice by Example for Help In Exercises 8, draw a diagram similar to the given one. hen do the construction. heck your work with a ruler or a protractor. 8. ee margin, pp onstruct congruent to.. onstruct VW so that VW =. 3. onstruct E so that E = +.. onstruct J so that J = onstruct & so that & > &. 6. onstruct &F so that m&f = m&. 7. onstruct the perpendicular bisector of. 8. onstruct the perpendicular bisector of. 9. lgebra GH bisects &FGI. a. olve for x and find m&fgh. ; 30 b. Find m&hgi. 30 c. Find m&fgi. 60 G F (3x - 3 H (x - I Lesson -7 asic onstructions 7 3. ractice ssignment Guide -6, 5, -, 9-3, 3 7-, 6-, 5-8, 33 hallenge est rep 37-0 ixed eview -50 Homework uick heck o check students understanding of key skills and concepts, go over Exercises,, 8, 6, 8. echnology ip Have students investigate what software can model compass and straightedge constructions. ome programs use a mouse and pointer to model the action of compass, straightedge, and pencil. Exercises If necessary, discuss ways that students can copy the segment lengths. G Enrichment Guided roblem olving eteaching dapted ractice ractice earson Education, Inc. ll rights reserved. Name lass ate ractice -7 Find the area of each rectangle with the given base and height. erimeter, ircumference, and rea. base: 3 ft. base: 60 in. 3. base: m height: in. height:.5 yd height: 0 cm Find the circumference of each circle in terms of π Find the perimeter and area of each rectangle with the given base and height. 7. b = 7 cm, h = 6 cm 8. b = cm, h = cm 9. b = in., h = 0.5 in. 0. b = 7 ft, h = 3 ft. b = m, h = 9 m. b = 3 m, h = 7 m Find the perimeter and area of each figure. ll angles in the figures are right angles Find the area of each circle in terms of π Find the area and perimeter of rectangle with vertices (3, 7, (9, 7, (9, -, and (3, Find the perimeter of with vertices (-, 9, (7, -3, and (-, -3.. he circumference of a circle is 6p. Find the diameter and the radius p 8 L L 7 L3 L L F E. J 7

5 Visual Learners Exercises 0 Have students draw each angle and its bisector before beginning to solve the exercise. onnection to lgebra Exercise 5 his exercise is important to assign. iscuss why both Lani and enyse are correct. Exercise 3 ome students may think the answer choices are the same. Encourage them to read the answer choices carefully looking for how each choices differs. 3.. Example 5 (page 7 pply our kills x lgebra For Exercises 0, bisects &. olve for x and find m&. 0. m& = 5x, m& = 3x + 0 5; 50. m& = x -, m& = 5; 8. m& = x - 6, m& = x + 6 ; raw acute &. hen construct its bisector. ee margin.. raw right &UV. hen construct its bisector. ee margin. 5. Use your protractor and draw &W with m&w = 0. onstruct &Z > &W. hen construct the bisector of &Z. ee margin. ketch * the * figure described. Explain how to construct it. hen do the construction. 6. ' Z 6 7. ee margin. 7. bisecting right & 8. Optics beam of light and a mirror G can be used to study the behavior of light. Light that strikes the mirror is reflected so that the angle of reflection and the angle of incidence are congruent. In the diagram, is ngle of incidence ngle of reflection perpendicular to the mirror, and E & has a measure of 8. F a. Name the angle of reflection and find its measure. l; b. Find m&. 8 c. Find m&e and m&f. 9; 9 9. Use a straightedge and protractor. a b. ee back of book. a. raw a mirror and a light beam striking the mirror and reflecting from it. b. onstruct the bisector of the angle formed by the incoming and reflected light beams. Label the angles of incidence and reflection. 5. U Z 6. Find a segment on so that you can construct Z as its # bisector. Z V Z 0 W b. Infinitely many; there s only midpt. but there exist infinitely many lines through the midpoint. segment has exactly one # bisecting line because there can be only one line # to a segment at its midpt. c. here are an infinite number of lines in space that are # to a segment at its midpt. he lines are coplanar. GO nline Homework Help Visit: Hchool.com Web ode: aue Open-Ended noopy can draw squares with his compass. ou can only draw circles. ou can, however, construct a square. Explain how to do this. Use sketches if needed. hen do the construction. ee back of book.. nswer these questions about a segment in a plane. Explain each answer. a. How many midpoints does the segment have? ee back of book. b. How many bisectors does it have? How many lines in the plane are its perpendicular bisectors? b c. ee left. c. How many lines in space are its perpendicular bisectors? For Exercises, copy & and &.. ee back of book.. onstruct & so that m& = m& + m&. 3. onstruct & so that m& = m& - m&.. onstruct & so that m& = m&. 8 hapter ools of Geometry 8 7. Find a segment on so that you can construct as its # bisector. hen bisect /. U

6 5. hey are both correct. If you mult. each side of Lani s eq. by, the result is enyse s eq hallenge est rep ultiple hoice 5. easoning When bisects &, & > &. Lani claims there is always a related equation, m& = m&. enyse claims the related equation is m& = m&. Which equation is correct? Explain. 6. Writing escribe how to construct the midpoint of a segment. ee back of book. 7. onstruct a 58 angle. ee left. 8. a. raw a large triangle with three acute angles. onstruct the bisectors of the three angles. What appears to be true about the three angle bisectors? b. epeat the constructions with a triangle that has one obtuse angle. c. ake a onjecture What appears to be true about the three angle bisectors of any triangle? a c. ee back of book. Use a ruler to draw segments of cm, cm and 5 cm. hen construct each triangle, if possible. If not possible, explain ee back of book. 9. with -cm, -cm, and 5-cm sides 30. with -cm, 5-cm, and 5-cm sides 3. with -cm, -cm, and 5-cm sides 3. with -cm, -cm, and -cm sides 3 3. Impossible; the short segments are not long enough to form a n. 33. a. raw a segment,. onstruct a triangle with sides congruent to. b. easure the angles of the triangle. a c. ee margin. c. Writing escribe how to construct a 608 angle; a 308 angle. 3. ultiple hoice Which steps best describe how to construct this pattern? Use a straightedge to draw the segment and then a compass to draw five half circles. Use a straightedge to draw the segment and then a compass to draw six half circles. Use a compass to draw five half circles and then a straightedge to join their ends. Use a compass to draw six half circles and then a straightedge to join their ends. 35. a. Use your compass to draw a circle. a c. ee back of book. Locate three points,, and on the circle. b. onstruct the perpendicular bisectors of and. c. ritical hinking Label the intersection of the two perpendicular bisectors as point O. ake a conjecture about point O. 36. tudy the figures. omplete the definition of a line perpendicular to a plane: line is perpendicular to a plane if it is 9 to every line in the plane that 9. #; the line intersects 37. What must you do to construct the midpoint of a segment?. easure half its length.. easure twice its length.. onstruct an angle bisector.. onstruct a perpendicular bisector. r Line r plane. Line t is not plane. t. ssess & eteach oweroint Lesson uiz Use the figure above. For problems, check students work.. onstruct so that N.. onstruct the perpendicular bisector of. 3. onstruct & so that & &N.. onstruct the bisector of &. N bisects &N. 5. Find x Find m&n. 88 lternative ssessment Have each student construct a right triangle using the methods learned in this lesson. tudents should write a set of steps that other students could use to complete the construction. est rep x + 0 N 3x 7 esources For additional practice with a variety of test item formats: tandardized est rep, p. 75 est-aking trategies, p.70 est-aking trategies with ransparencies lesson quiz, Hchool.com, Web ode: aua-007 Lesson -7 asic onstructions a. b. hey are all 60. c. nswers may vary. ample: ark a pt.,. wing a long arc from. From a pt. on the arc, swing another arc the same size that intersects the arc at a second pt.,. raw l. o construct a 30 l, bisect the 60 l. 9

7 38. Which of these is the first step in constructing a congruent segment? F F. raw a ray. G. raw a line. H. Label two points. J. easure the segment. hort esponse 39. Explain how to do each construction using a compass and a straightedge. a b. a. raw an acute angle, &. onstruct an angle congruent to &. ee margin. b. onstruct an angle whose measure is twice that of &. Extended esponse 0. Explain how to do each construction using a compass and a straightedge. a. ivide a segment into two congruent segments. a c. ee margin. b. ivide a segment into four congruent segments. c. onstruct a segment that is.5 times as long as a given segment. ixed eview 39. [] a. raw. With the compass pt. on swing an arc that intersects and. Label the intersections and, respectively. With the compass point on, swing a O arc intersecting. Label the intersection K. Open the compass to. With compass pt. on K, swing an arc to intersect the arc that already passes through K. Label the intersection. raw. b. With the compass open to K, put the compass point on and swing an arc intersecting. With the compass on and open to K, swing an arc to intersect the first arc. Label the intersection. raw. 50 [] one part correct 0. [] a. onstruct its # bisector. b. onstruct the # bisector. hen construct the # bisector of two new segments. GO for Help Lesson -6. Use a protractor to draw a 7 angle. ee left.. &EF is a straight angle. m&eg = 80. Find m&gef m&uv = 00 and m&vuw = 80. Find possible values of m&uw.. 0 and 80 Lesson -5 Use the number line at the right. Find the length of each segment Lesson - 50 hapter ools of Geometry c. raw. o constructions as in parts a and b. Open the compass to the length of the shortest segment in part b. With the * 8. raw. Use your drawing from Exercise 8. nswer and explain. 9. re and opposite rays? 50. re and the same segment? No; they do not have the same endpt. es; they both represent a segment with endpts. and. Geometry at Work abinetmaker abinetmakers not only make cabinets but all types of wooden furniture. he artistry of cabinetmaking can be seen in the beauty and uniqueness of the finest doors, shelves, and tables. he craft is in knowing which types of wood and tools to use, and how to use them. he carpenter s square is one of the most useful of the cabinetmaker s tools. It can be applied to a variety of measuring tasks. he figure shows how to use a carpenter s square to bisect &O. Hchool.com For: Information about cabinetmaking Web ode: aub-03 pt. of the compass on, swing an arc in the opp. direction from intersecting at..5 (. O First, mark equal lengths O and O on the sides GEO_3eE005ta3 of the angle. hen position the square so that = to locate point. Finally, draw O. O bisects &O. [3] explanations are not thorough [] two explanations correct [] part (a correct

The height of a trapezoid is the. EXAMPLE Real-World Connection

The height of a trapezoid is the. EXAMPLE Real-World Connection 0-. lan Objectives To find the area of a trapezoid To find the area of a rhombus or a kite Examples eal-world onnection Finding rea Using a Triangle Finding the rea of a Kite 4 Finding the rea of a hombus

More information

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.

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. 1-1 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

More information

New Vocabulary inscribed angle. At the right, the vertex of &C is on O, and the sides of &C are chords of the circle. &C is an

New Vocabulary inscribed angle. At the right, the vertex of &C is on O, and the sides of &C are chords of the circle. &C is an -. lan - Inscribed ngles bjectives o find the measure of an inscribed angle o find the measure of an angle formed by a tangent and a chord amples Using the Inscribed ngle heorem Using orollaries to Find

More information

Measure 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

Measure 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 information

To use properties of perpendicular bisectors and angle bisectors

To use properties of perpendicular bisectors and angle bisectors 5-2 erpendicular and ngle isectors ommon ore tate tandards G-O..9 rove theorems about lines and angles... points on a perpendicular bisector of a line segment are exactly those equidistant from the segment

More information

Warm Up #23: Review of Circles 1.) A central angle of a circle is an angle with its vertex at the of the circle. Example:

Warm 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 information

Duplicating Segments and Angles

Duplicating Segments and Angles ONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson you will Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using

More information

Areas of Circles and Sectors. GO for Help

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 information

Chapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1.

Chapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name: lass: ate: I: hapter 1 Exam Multiple hoice Identify the choice that best completes the statement or answers the question. 1. bisects, m = (7x 1), and m = (4x + 8). Find m. a. m = c. m = 40 b. m =

More information

5.6 Angle Bisectors and

5.6 Angle Bisectors and age 1 of 8 5.6 ngle isectors and erpendicular isectors oal Use angle bisectors and perpendicular bisectors. ey Words distance from a point to a line equidistant angle bisector p. 61 perpendicular bisector

More information

Geometry Chapter 1 Review

Geometry Chapter 1 Review Name: lass: ate: I: Geometry hapter 1 Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name two lines in the figure. a. and T c. W and R b. WR and

More information

Duplicating Segments and Angles

Duplicating 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 information

6.1. Perpendicular and Angle Bisectors

6.1. Perpendicular and Angle Bisectors 6.1 T TI KOW KI.2..5..6. TI TOO To be proficient in math, you need to visualize the results of varying assumptions, explore consequences, and compare predictions with data. erpendicular and ngle isectors

More information

from a vertex to the midpoint of the opposite side. median 1 Draw a Median In TSTR, draw a median from S to its opposite side.

from a vertex to the midpoint of the opposite side. median 1 Draw a Median In TSTR, draw a median from S to its opposite side. age of 4.6 edians of a riangle Goal Identify s in triangles. ey Words of a triangle centroid cardboard triangle will balance on the end of a pencil if the pencil is placed at a particular point on the

More information

Lesson 3.1 Duplicating Segments and Angles

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

Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles]

Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles] h 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and ngles [and Triangles] Warm up: Directions: Draw the following as accurately as possible. Pay attention to any problems you may be having.

More information

NAME DATE PERIOD. Study Guide and Intervention

NAME 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 information

1.2 Informal Geometry

1.2 Informal Geometry 1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior

More information

The Polygon Angle-Sum Theorems 55 A equiangular polygon

The Polygon Angle-Sum Theorems 55 A equiangular polygon -5 What You ll Learn To classify polygons To find the sums of the measures of the interior and exterior angles of polygons... nd Why To find the measure of an angle of a triangle used in packaging, as

More information

A geometric construction is a drawing of geometric shapes using a compass and a straightedge.

A geometric construction is a drawing of geometric shapes using a compass and a straightedge. Geometric Construction Notes A geometric construction is a drawing of geometric shapes using a compass and a straightedge. When performing a geometric construction, only a compass (with a pencil) and a

More information

CK-12 Geometry: Midpoints and Bisectors

CK-12 Geometry: Midpoints and Bisectors CK-12 Geometry: Midpoints and Bisectors Learning Objectives Identify the midpoint of line segments. Identify the bisector of a line segment. Understand and the Angle Bisector Postulate. Review Queue Answer

More information

1.7 Find Perimeter, Circumference,

1.7 Find Perimeter, Circumference, .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square Rectangle side length s length l and width w P 5 P 5 s 5

More information

Geometry Final Assessment 11-12, 1st semester

Geometry Final Assessment 11-12, 1st semester Geometry Final ssessment 11-12, 1st semester Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name three collinear points. a. P, G, and N c. R, P, and G

More information

Relevant Vocabulary. The MIDPOINT of a segment is a point that divides a segment into 2 = or parts.

Relevant Vocabulary. The MIDPOINT of a segment is a point that divides a segment into 2 = or parts. im 9: How do we construct a perpendicular bisector? Do Now: 1. omplete: n angle bisector is a ray (line/segment) that divides an into two or parts. 48 Geometry 10R 2. onstruct and label D, the bi sector

More information

8.2 Angle Bisectors of Triangles

8.2 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 information

CONGRUENCE BASED ON TRIANGLES

CONGRUENCE BASED ON TRIANGLES HTR 174 5 HTR TL O ONTNTS 5-1 Line Segments ssociated with Triangles 5-2 Using ongruent Triangles to rove Line Segments ongruent and ngles ongruent 5-3 Isosceles and quilateral Triangles 5-4 Using Two

More information

New Vocabulary concurrent. Folding a Perpendicular. Bisector

New Vocabulary concurrent. Folding a Perpendicular. Bisector 5-. Plan Objectives o identif properties of perpendicular bisectors and angle bisectors o identif properties of medians and altitudes of a triangle amples inding the ircumcenter Real-orld onnection inding

More information

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

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

Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24

Geometry 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 information

An angle consists of two rays that have the same endpoint. sides. vertex. The endpoint is the vertex of the angle.

An angle consists of two rays that have the same endpoint. sides. vertex. The endpoint is the vertex of the angle. age 1 of 7 1.6 ngles and heir easures oal easure and classify angles. dd angle measures. ey Words angle sides and vertex of an angle measure of an angle degree congruent angles acute, right, obtuse, and

More information

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

Name: 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 information

Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.

Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have

More information

Measuring Angles. To find and compare the measures of angles

Measuring Angles. To find and compare the measures of angles hsmgmse_4_t829. -4 easuring ngles ommon ore State Standards G-.. now precise definitions of angle, circle, perpendicular line, parallel line, and line segment... P, P 3, P 6 bjective To find and compare

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information

1. 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. 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 information

GEOMETRY. Constructions OBJECTIVE #: G.CO.12

GEOMETRY. 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 information

A (straight) line has length but no width or thickness. A line is understood to extend indefinitely to both sides. beginning or end.

A (straight) line has length but no width or thickness. A line is understood to extend indefinitely to both sides. beginning or end. Points, Lines, and Planes Point is a position in space. point has no length or width or thickness. point in geometry is represented by a dot. To name a point, we usually use a (capital) letter. (straight)

More information

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p.

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p. Vocabulary Flash ards acute angle adjacent angles hapter 1 (p. 39) hapter 1 (p. 48) angle angle bisector hapter 1 (p.38) hapter 1 (p. 42) axiom between hapter 1 (p. 12) hapter 1 (p. 14) collinear points

More information

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry The Protractor Postulate and the SAS Axiom Chapter 3.4-3.7 The Axioms of Plane Geometry The Protractor Postulate and Angle Measure The Protractor Postulate (p51) defines the measure of an angle (denoted

More information

Int. Geometry Unit 2 Quiz Review (Lessons 1-4) 1

Int. Geometry Unit 2 Quiz Review (Lessons 1-4) 1 Int. Geometry Unit Quiz Review (Lessons -4) Match the examples on the left with each property, definition, postulate, and theorem on the left PROPRTIS:. ddition Property of = a. GH = GH. Subtraction Property

More information

Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Drafting, Sports, Geography

Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Drafting, Sports, Geography 3-6 Conditional Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Applications Drafting, Sports, Geography Do you think each statement is true or false?

More information

Transversals. 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by vertical angles, corresponding angles,

Transversals. 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by vertical angles, corresponding angles, Transversals In the following explanation and drawing, an example of the angles created by two parallel lines and two transversals are shown and explained: 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by

More information

1-1. Nets and Drawings for Visualizing Geometry. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

1-1. 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 information

GEOMETRY FINAL EXAM REVIEW

GEOMETRY 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 information

NCERT. In examples 1 and 2, write the correct answer from the given four options.

NCERT. 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 information

The Basics: Geometric Structure

The Basics: Geometric Structure Trinity University Digital Commons @ Trinity Understanding by Design: Complete Collection Understanding by Design Summer 6-2015 The Basics: Geometric Structure Danielle Kendrick Trinity University Follow

More information

Constructing Perpendicular Bisectors

Constructing Perpendicular Bisectors Page 1 of 5 L E S S O N 3.2 To be successful, the first thing to do is to fall in love with your work. SISTER MARY LAURETTA Constructing Perpendicular Bisectors Each segment has exactly one midpoint. A

More information

PARALLEL LINES CHAPTER

PARALLEL LINES CHAPTER HPTR 9 HPTR TL OF ONTNTS 9-1 Proving Lines Parallel 9-2 Properties of Parallel Lines 9-3 Parallel Lines in the oordinate Plane 9-4 The Sum of the Measures of the ngles of a Triangle 9-5 Proving Triangles

More information

This is a tentative schedule, date may change. Please be sure to write down homework assignments daily.

This is a tentative schedule, date may change. Please be sure to write down homework assignments daily. Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (1-1) Points, Lines, & Planes Topic: (1-2) Segment Measure Quiz

More information

1) Perpendicular bisector 2) Angle bisector of a line segment

1) Perpendicular bisector 2) Angle bisector of a line segment 1) Perpendicular bisector 2) ngle bisector of a line segment 3) line parallel to a given line through a point not on the line by copying a corresponding angle. 1 line perpendicular to a given line through

More information

The Next Step. Mathematics Applications for Adults. Book Geometry

The Next Step. Mathematics Applications for Adults. Book Geometry The Next Step Mathematics Applications for Adults Book 14018 - Geometry OUTLINE Mathematics - Book 14018 Geometry Lines and Angles identify parallel lines and perpendicular lines in a given selection of

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

circle the set of all points that are given distance from a given point in a given plane

circle 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 information

Final Review Geometry A Fall Semester

Final 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 information

7.4 Showing Triangles are

7.4 Showing Triangles are age 1 of 7 7. howing riangles are imilar: and oal how that two triangles are similar using the and imilarity heorems. ey ords similar polygons p. he triangles in the avajo rug look similar. o show that

More information

The measure of an arc is the measure of the central angle that intercepts it Therefore, the intercepted arc measures

The 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 2013-2014 Ms. Lomac SLO: I can use definitions & theorems about points, lines, and planes to

More information

Calculate Angles on Straight Lines, at Points, in s & involving Parallel Lines iss1

Calculate Angles on Straight Lines, at Points, in s & involving Parallel Lines iss1 alculate ngles on Straight Lines, at Points, in s & involving Parallel Lines iss1 ngles on a Straight Line dd to 180 x 44 x = 180 44 = 136 ngles at a Point dd to 360 ngles in a Triangle dd to 180 15 z

More information

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the

More information

A polygon with five sides is a pentagon. A polygon with six sides is a hexagon.

A polygon with five sides is a pentagon. A polygon with six sides is a hexagon. Triangles: polygon is a closed figure on a plane bounded by (straight) line segments as its sides. Where the two sides of a polygon intersect is called a vertex of the polygon. polygon with three sides

More information

Geometry Unit 1. Basics of Geometry

Geometry Unit 1. Basics of Geometry Geometry Unit 1 Basics of Geometry Using inductive reasoning - Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture- an unproven statement that is based

More information

pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs.

pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs. age 1 of 5 6.5 rapezoids Goal Use properties of trapezoids. trapezoid is a quadrilateral with eactly one pair of parallel sides. he parallel sides are the bases. he nonparallel sides are the legs. leg

More information

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points

More information

Geometry Vocabulary. Created by Dani Krejci referencing:

Geometry Vocabulary. Created by Dani Krejci referencing: Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path

More information

Chapter One. Points, Lines, Planes, and Angles

Chapter One. Points, Lines, Planes, and Angles Chapter One Points, Lines, Planes, and Angles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately

More information

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

Final Review Problems Geometry AC Name

Final Review Problems Geometry AC Name Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x-6. Find the measure of the angles. State the theorem(s) that support your equation.

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: The point of intersection of the three medians of a triangle. Centroid Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

More information

Informal Geometry and Measurement

Informal Geometry and Measurement HP LIN N NGL LIONHIP In xercises 56 and 57, P is a true statement, while Q and are false statements. lassify each of the following statements as true or false. 56. a) (P and Q) or b) (P or Q) and 57. a)

More information

Honors Geometry Final Exam Study Guide

Honors Geometry Final Exam Study Guide 2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

More information

The Half-Circle Protractor

The Half-Circle Protractor The Half-ircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a half-circle protractor to measure and draw

More information

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

More information

6.2 PLANNING. Chord Properties. Investigation 1 Defining Angles in a Circle

6.2 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 information

Radius, diameter, circumference, π (Pi), central angles, Pythagorean relationship. about CIRCLES

Radius, diameter, circumference, π (Pi), central angles, Pythagorean relationship. about CIRCLES Grade 9 Math Unit 8 : CIRCLE GEOMETRY NOTES 1 Chapter 8 in textbook (p. 384 420) 5/50 or 10% on 2011 CRT: 5 Multiple Choice WHAT YOU SHOULD ALREADY KNOW: Radius, diameter, circumference, π (Pi), central

More information

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

More information

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,

More information

Chapter 4 Circles, Tangent-Chord Theorem, Intersecting Chord Theorem and Tangent-secant Theorem

Chapter 4 Circles, Tangent-Chord Theorem, Intersecting Chord Theorem and Tangent-secant Theorem Tampines Junior ollege H3 Mathematics (9810) Plane Geometry hapter 4 ircles, Tangent-hord Theorem, Intersecting hord Theorem and Tangent-secant Theorem utline asic definitions and facts on circles The

More information

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:

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.

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

Name Period 11/2 11/13

Name Period 11/2 11/13 Name Period 11/2 11/13 Vocabulary erms: ongruent orresponding Parts ongruency statement Included angle Included side GOMY UNI 6 ONGUN INGL HL Non-included side Hypotenuse Leg 11/5 and 11/12 eview 11/6,,

More information

BC AB = AB. The first proportion is derived from similarity of the triangles BDA and ADC. These triangles are similar because

BC AB = AB. The first proportion is derived from similarity of the triangles BDA and ADC. These triangles are similar because 150 hapter 3. SIMILRITY 397. onstruct a triangle, given the ratio of its altitude to the base, the angle at the vertex, and the median drawn to one of its lateral sides 398. Into a given disk segment,

More information

Geometry Review Flash Cards

Geometry Review Flash Cards point is like a star in the night sky. However, unlike stars, geometric points have no size. Think of them as being so small that they take up zero amount of space. point may be represented by a dot on

More information

STUDY OF THE LINE: THE PERPENDICULAR BISECTOR

STUDY OF THE LINE: THE PERPENDICULAR BISECTOR STUDY OF THE LINE: THE PERPENDICULR ISECTOR Study of the Line, Second Series: The Perpendicular isector (4: 20) Material Geometry Classified Nomenclature 4 (20) Paper Pencil Compass Ruler Presentation

More information

Draw Angle Bisectors

Draw Angle Bisectors raw Angle Bisectors ocus on After this lesson, you will be able to... φ draw lines that divide angles in half Carpenters work with wood. One job a carpenter does is install wood mouldings. To place mouldings

More information

12 CONSTRUCTIONS AND LOCI

12 CONSTRUCTIONS AND LOCI 12 ONSTRUTIONS N LOI rchitects make scale drawings of projects they are working on for both planning and presentation purposes. Originally these were done on paper using ink, and copies had to be made

More information

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures. Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.

More information

Kaleidoscopes, Hubcaps, and Mirrors Problem 1.1 Notes

Kaleidoscopes, Hubcaps, and Mirrors Problem 1.1 Notes Problem 1.1 Notes When part of an object or design is repeated to create a balanced pattern, we say that the object or design has symmetry. You can find examples of symmetry all around you. rtists use

More information

8.4 Midsegments of Triangles

8.4 Midsegments of Triangles OMMON OR Locker LSSON ommon ore Math Standards The student is expected to: OMMON OR G-O..10 Prove theorems about triangles. lso G-O..1, G-GP..4, G-GP..5 Mathematical Practices OMMON OR 8.4 Midsegments

More information

Geometry Made Easy Handbook Common Core Standards Edition

Geometry Made Easy Handbook Common Core Standards Edition Geometry Made Easy Handbook ommon ore Standards Edition y: Mary nn asey. S. Mathematics, M. S. Education 2015 Topical Review ook ompany, Inc. ll rights reserved. P. O. ox 328 Onsted, MI. 49265-0328 This

More information

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B.

2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B. Section 1.5 Triangles Notes Goal of the lesson: Explore the properties of triangles using Geometer s Sketchpad Define and classify triangles and their related parts Practice writing more definitions Learn

More information

Tangents to Circles. Circle The set of all points in a plane that are equidistant from a given point, called the center of the circle

Tangents 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 information

GEOMETRIC FIGURES, AREAS, AND VOLUMES

GEOMETRIC FIGURES, AREAS, AND VOLUMES HPTER GEOMETRI FIGURES, RES, N VOLUMES carpenter is building a deck on the back of a house. s he works, he follows a plan that he made in the form of a drawing or blueprint. His blueprint is a model of

More information

Perimeter, Circumference, and Area

Perimeter, Circumference, and Area -9 Perimeter, Circumference, and Area -9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why

More information

Chapters 6 and 7 Notes: Circles, Locus and Concurrence

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

Goal Find angle measures in triangles. Key Words corollary. Student Help. Triangle Sum Theorem THEOREM 4.1. Words The sum of the measures of EXAMPLE

Goal Find angle measures in triangles. Key Words corollary. Student Help. Triangle Sum Theorem THEOREM 4.1. Words The sum of the measures of EXAMPLE Page of 6 4. ngle Measures of Triangles Goal Find angle measures in triangles. The diagram below shows that when you tear off the corners of any triangle, you can place the angles together to form a straight

More information

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources

More information

Lesson 6: Drawing Geometric Shapes

Lesson 6: Drawing Geometric Shapes Student Outcomes Students use a compass, protractor, and ruler to draw geometric shapes based on given conditions. Lesson Notes The following sequence of lessons is based on standard 7.G.A.2: Draw (freehand,

More information

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

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

Chapter 1. Foundations of Geometry: Points, Lines, and Planes

Chapter 1. Foundations of Geometry: Points, Lines, and Planes Chapter 1 Foundations of Geometry: Points, Lines, and Planes Objectives(Goals) Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in

More information

Lines and Angles. Example 1 Recognizing Lines and Line Segments. Label each of the following as a line or a line segment. A E.

Lines and Angles. Example 1 Recognizing Lines and Line Segments. Label each of the following as a line or a line segment. A E. 7.4 Lines and ngles 7.4 JTIVS 1. istinguish between lines and line segments 2. etermine when lines are perpendicular or parallel 3. etermine whether an angle is right, acute, or obtuse 4. Use a protractor

More information