# 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

Save this PDF as:

Size: px
Start display at page:

Download "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"

## Transcription

1 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 angle. Its measure is 80. Unless otherwise specified, the term angle in this book means a nonstraight angle. 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 360 measure now known as a degree came from astronomer laudius tolemy. He based his observations of the solar system on a unit that resulted from dividing the circumference, or the distance around, a circle into 360 parts. his later became known as a degree. In this lesson, you will learn to measure angles in degrees. MEUE NGLE ray is part of a line. It has one endpoint and extends indefinitely in one direction. ays are named stating the endpoint first and then any other point on the ray. he figure at the right shows ray E, which can be symbolized as E. his ray could also be named as EG, but not as E because is not the endpoint of the ray. If you choose a point on a line, that point determines exactly two rays called opposite. Line m, shown below, is separated into two opposite rays, and rays. oint is the common endpoint of those rays. and are collinear rays. m E = 360 of a turn around a circle G n angle is formed by two noncollinear rays that have a common endpoint. he rays are called sides of the angle. he common endpoint is the vertex. ngle Words ymbols n angle is formed by two noncollinear rays that have a common endpoint. 4 Model vertex side 4 side n angle divides a plane into three distinct parts. oints,, and E lie on the angle. oints and lie in the interior of the angle. oints and G lie in the exterior of the angle. E G Lesson -4 ngle Measure 9

2 tudy ip Naming ngles ou can name an angle by a single letter only when there is one angle shown at that vertex. Example ngles and heir arts a. Name all angles that have W as a vertex.,, 3, W, WV b. Name the sides of. W and W are the sides of. W 3 V 5 4 c. Write another name for W. 4,, and W are other names for W. o measure an angle, you can use a protractor. ngle is a 65 degree (65 ) angle. We say that the degree measure of is 65, or simply m 65. he protractor has two scales running from 0 to 80 degrees in opposite directions ince is aligned with the 0 on the outer scale, use the outer scale to find that intersects the scale at 65 degrees. lign the 0 on either side of the scale with one side of the angle. ngles can be classified by their measures lace the center point of the protractor on the vertex. tudy ip lassifying ngles he corner of a piece of paper is a right angle. Use the corner to determine if an angle s measure is greater than 90 or less than 90. Name lassify ngles Measure m 90 m m 90 Model right angle his symbol means a 90 angle. acute angle obtuse angle Example Measure and lassify ngles Measure each angle named and classify it as right, acute, or obtuse. a. M Use a protractor to find that m M , so M is an acute angle. b. M M is marked with a right angle symbol, so measuring is not necessary; m M 90. c. M Use a protractor to find that m M 0. M is an obtuse angle. M 30 hapter oints, Lines, lanes, and ngles

3 ONGUEN NGLE Just as segments that have the same measure are congruent, angles that have the same measure are congruent. Words ngles that have the same Model measure are congruent angles. rcs on the figure also indicate which angles are congruent. N 5 ymbols NM M ongruent ngles M 5 ou can construct an angle congruent to a given angle without knowing the measure of the angle. opy an ngle raw an angle like on your paper. Use a straightedge to draw a ray on your paper. Label its endpoint. lace the tip of the compass at point and draw a large arc that intersects both sides of. Label the points of intersection and. 3 Using the same compass setting, put the compass at and draw a large arc that intersects the ray. Label the point of intersection. 4 lace the point of your compass on and adjust so that the pencil tip is on. 5 Without changing the setting, place the compass at and draw an arc to intersect the larger arc you drew in tep 3. Label the point of intersection U. 6 Use a straightedge to draw U. U U Lesson -4 ngle Measure 3

4 tudy ip hecking olutions heck that you have computed the value of x correctly by substituting the value into the expression for. If you don t get the same measure as, you have made an error. Example 3 Use lgebra to ind ngle Measures GENING trellis is often used to provide a frame for vining plants. ome of the angles formed by the slats of the trellis are congruent angles. In the figure,. If m 6x and m 8x 4, find the actual measurements of and. m m 6x 8x 4 6x 6 8x 6 x Given efinition of congruent angles ubstitution dd 4 to each side. ubtract 6x from each side. 8 x ivide each side by. (6x ) (8x 4) Use the value of x to find the measure of one angle. m 6x Given m 6(8) x 8 m 48 or 50 implify. ince m m, m 50. oth and measure 50. tudy ip dding ngle Measures Just as with segments, when a line divides an angle into smaller angles, the sum of the measures of the smaller angles equals the measure of the largest angle. o in the figure, m m m. isect an ngle Make a Model raw any on patty paper or tracing paper. old the paper through point so that and are aligned together. Open the paper and label a point on the crease in the interior of as point W. nalyze the Model. What seems to be true about W and W?. Measure, W, and W. 3. ou learned about a segment bisector in Lesson -3. Write a sentence to explain the term angle bisector. ray that divides an angle into two congruent angles is called an. If angle bisector is the angle bisector of, then point lies in the interior of and. W 3 hapter oints, Lines, lanes, and ngles ed Habegger/Grant Heilman hotography ou can construct the angle bisector of any angle without knowing the measure of the angle.

5 isect an ngle /3/003 3:8 M brian_batch GEO L raw an angle on With the compass at 3 your paper. Label the point, draw an arc vertex as. ut your in the interior of the compass at point angle. and draw a large arc that intersects both sides of. Label the points of intersection and. Keeping the same compass setting, place the compass at point and draw an 0-6 arc that intersects the arc drawn in tep. 4 Label the point of intersection. raw. is the bisector of. hus, m m and. oncept heck Guided ractice. etermine whether all right angles are congruent.. OEN ENE raw and label a figure to show that bisects and that bisects. Use a protractor to measure each angle. 3. Write a statement about the measures of congruent angles and. or Exercises 4 and 5, use the figure at the right. 4. Name the vertex of. 5. Name the sides of Write another name for. 4 3 Measure each angle and classify as right, acute, or obtuse. 7. W 8. W W pplication LGE In the figure, and are opposite rays, and bisects. 9. If m 6x 5 and m 7x, find m. 0. ind m if m a and m a 8.. OIGMI he art of origami involves folding paper at different angles to create designs and three-dimensional figures. One of the folds in origami involves folding a strip of paper so that the lower edge of the strip forms a right angle with itself. Identify each numbered angle as right, acute, or obtuse. 3 Lesson -4 ngle Measure 33

6 ractice and pply or Exercises ee Examples 3 Extra ractice ee page 755. Name the vertex of each angle Name the sides of each angle E G 7 H Write another name for each angle E Name a point in the interior of G. 5. Name an angle with vertex that appears to be acute. 6. Name a pair of angles that share exactly one point. 7. If bisects E and m E 60, find m 5 and m 6. Measure each angle and classify it as right, acute, or obtuse E 3. E E E LGE In the figure, and are opposite rays. U bisects W, and bisects W. 34. If m U 8p 0 and m UW 0p 0, find m U. 35. If m 5x 0 and m 8x 3, find m. 36. If m y and m W 6y 4, find y. 37. If m W 8 and m U 4r 5, find r. 38. If m W (b 7) and m U 9b, find m UW. 39. If W is a right angle and m U 3a 7, find a. W U 40. OG KING dog is tracking when it is following the scent trail left by a human being or other animal that has passed along a certain route. One of the training exercises for these dogs is a tracking trail. he one shown is called an acute tracking trail. Explain why it might be called this. wind direction tart food drop article 34 hapter oints, Lines, lanes, and ngles 4. LNGUGE he words obtuse and acute have other meanings in the English language. Look these words up and write how the everyday meaning relates to the mathematical meaning.

7 4. EN LOK attern blocks can be arranged to fit in a circular pattern without leaving spaces. emember that the measurement around a full circle is 360. etermine the angle measure of the numbered angles shown below HI ripple tank can be used to study the behavior of waves in two dimensions. s a wave strikes a barrier, it is reflected. he angle of incidence and the angle of reflection are congruent. In the diagram at the right, if m I 6, find the angle of reflection and m I. I angle of incidence N angle of reflection barrier hysics ripple tank is a large glass-bottomed tank of water. light is placed above the water, and a white sheet of paper is placed below the tank. ecause rays of light undergo bending as they pass through the troughs and crests of the water, there is a pattern of light and dark spots on the white sheet of paper. hese model the wave. 44. IIL HINKING How would you compare the size of and? Explain. IIL HINKING or Exercises 45 48, use the following information. Each figure below shows noncollinear rays with a common endpoint. rays 3 rays 4 rays 5 rays 6 rays tandardized est ractice 45. ount the number of angles in each figure. 46. escribe the pattern between the number of rays and the number of angles. 47. Make a conjecture of the number of angles that are formed by 7 noncollinear rays and by 0 noncollinear rays. 48. Write a formula for the number of angles formed by n noncollinear rays with a common endpoint. 49. WIING IN MH nswer the question that was posed at the beginning of the lesson. How big is a degree? Include the following in your answer: how to find degree measure with a protractor, and drawings of several angles and their degree measures. 50. If bisects, which of the following are true? m m m m m m all of these 5. LGE olve 5n 4 7(n ) n. 0 no solution all numbers Lesson -4 ngle Measure 35 (l)erich chrempp/hoto esearchers, (r)aron Haupt

8 Maintain our kills Mixed eview ind the distance between each pair of points. hen find the coordinates of the midpoint of the line segment between the points. (Lesson -3) 5. (, 3), (5, 7) 53. (, 0), (6, 4) 54. E( 3, ), (5, 8) ind the measurement of each segment. (Lesson -) 55. W 56. ft ft W 3.7 mm 5. mm 57. ind if lies between and, 6x 5, x 7, and. (Lesson -) efer to the figure at the right. (Lesson -) 58. How many planes are shown? 59. Name three collinear points. 60. Name a point coplanar with J, H, and. L K J G H Getting eady for the Next Lesson EEUIIE KILL olve each equation. (o review solving equations, see pages 737 and 738.) 6. 4x (6x 0) k y 90 7y t (80 t) (6m 8) (3m 0) (7n 9) (5n 45) 80 ractice uiz Lessons -3 and -4 ind the coordinates of the midpoint of each segment. hen find the distance between the endpoints. (Lesson -3). y. y 3. ( 4, 3) O x (3, ) (6, 4) O x (, 8) ( 0, 0) E(0, 0) In the figure, and are opposite rays. Given the following conditions, find the value of a and the measure of the indicated angle. (Lesson -4) 4. m 3a 4, m a 5, m ; m 5. m a 0, m 4a, m 9; m 36 hapter oints, Lines, lanes, and ngles

### 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

### 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

### 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

### 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

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

-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

### 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

### 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

### 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

### 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 =

### 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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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?

### 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

### Lines and Angles. Chapter 1 Points, Lines, Planes, and Angles. Chapter 2 Reasoning and Proof. Chapter 3 Parallel and Perpendicular Lines

Lines and ngles Lines and angles are all around us and can be used to model and describe real-world situations. In this unit, you will learn about lines, planes, and angles and how they can be used to

### 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

### 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

### 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

### 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)

### Math 366 Lecture Notes Section 11.1 Basic Notions (of Geometry)

Math 366 Lecture Notes Section. Basic Notions (of Geometry) The fundamental building blocks of geometry are points, lines, and planes. These terms are not formally defined, but are described intuitively.

### 13.1 Lines, Rays, and Angles

? Name Geometry and Measurement 4.6. 13.1 Lines, Rays, and ngles Essential Question How can you identify and draw points, lines, line segments, rays, and angles? MHEMIL PROEE 4.1., 4.1.E Unlock the Problem

### 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

1 lassifying Quadrilaterals Identify and sort quadrilaterals. 1. Which of these are parallelograms?,, quadrilateral is a closed shape with 4 straight sides. trapezoid has exactly 1 pair of parallel sides.

### 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.

### 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

### 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

### 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

### 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

### 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,

### Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. are rectangles used in tennis?

ectangles Vocabulary rectangle ecognize and apply properties of rectangles. etermine whether parallelograms are rectangles. are rectangles used in tennis? any sports are played on fields marked by parallel

### 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.)

### A Different Look at Trapezoid Area Prerequisite Knowledge

Prerequisite Knowledge Conditional statement an if-then statement (If A, then B) Converse the two parts of the conditional statement are reversed (If B, then A) Parallel lines are lines in the same plane

### 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

### A segment that joins two nonconsecutive vertices of a polygon is called a diagonal. Polygon PQRST has two diagonals from vertex R, RP &* and RT&*.

age of 6 6. olygons Goal Identify and classify polygons. Find angle measures of quadrilaterals. Each traffic sign below is an example of a polygon. Notice that each sign is formed with straight lines.

### 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

### 1-4 Angle Measure. Use the figure at the right. 1. Name the vertex of SOLUTION: 2. Name the sides of SOLUTION: 3. What is another name for SOLUTION:

Use the figure at the right. 6. 1. Name the vertex of U 2. Name the sides of 7. AFD is an obtuse angle. The measure of AFD is 150. 3. What is another name for XYU, UYX 4. What is another name for 1, YXU

### 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:

### 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

### 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

### Mathematics Geometry Unit 1 (SAMPLE)

Review the Geometry sample year-long scope and sequence associated with this unit plan. Mathematics Possible time frame: Unit 1: Introduction to Geometric Concepts, Construction, and Proof 14 days This

### 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

### 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

### 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

### 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

### 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)

### 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

### 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

### 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

### Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon.

ngles of Polygons Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. Vocabulary diagonal does a scallop shell illustrate

### 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

### 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

### 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

### 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,

### A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.

### 3.1. Angle Pairs. What s Your Angle? Angle Pairs. ACTIVITY 3.1 Investigative. Activity Focus Measuring angles Angle pairs

SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Use Manipulatives Two rays with a common endpoint form an angle. The common endpoint is called the vertex. You can use a protractor to draw and measure

### 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

### Angle Vocabulary, Complementary & Supplementary Angles

ngle Vocabulary, omplementary & Supplementary ngles Review 1 1. What is the definition of an acute angle? 2. Name the angle shown. 3. What is the definition of complimentary angles? 4. What is the definition

### Euclidean Geometry. We start with the idea of an axiomatic system. An axiomatic system has four parts:

Euclidean Geometry Students are often so challenged by the details of Euclidean geometry that they miss the rich structure of the subject. We give an overview of a piece of this structure below. We start

### 22.1 Interior and Exterior Angles

Name Class Date 22.1 Interior and Exterior ngles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? Resource Locker Explore 1 Exploring Interior

### Grade 4 - Module 4: Angle Measure and Plane Figures

Grade 4 - Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles

### 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.

### CK-12 Geometry: Perpendicular Bisectors in Triangles

CK-12 Geometry: Perpendicular Bisectors in Triangles Learning Objectives Understand points of concurrency. Apply the Perpendicular Bisector Theorem and its converse to triangles. Understand concurrency

### Use algebra to write two-column proofs. Use properties of equality in geometry proofs. is mathematical evidence similar to evidence in law?

lgebraic Proof Use algebra to write two-column proofs. Use properties of equality in geometry proofs. Vocabulary deductive argument two-column proof formal proof is mathematical evidence similar to evidence

### Angles 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,

### Practical Geometry. Chapter Introduction

Practical Geometry Chapter 14 14.1 Introduction We see a number of shapes with which we are familiar. We also make a lot of pictures. These pictures include different shapes. We have learnt about some

### Unit 6 Grade 7 Geometry

Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson

### G7-3 Measuring and Drawing Angles and Triangles Pages

G7-3 Measuring and Drawing Angles and Triangles Pages 102 104 Curriculum Expectations Ontario: 5m51, 5m52, 5m54, 6m48, 6m49, 7m3, 7m4, 7m46 WNCP: 6SS1, review, [T, R, V] Vocabulary angle vertex arms acute

### 4 Mathematics Curriculum

Common Core 4 Mathematics Curriculum G R A D E GRADE 4 MODULE 4 Table of Contents GRADE 4 MODULE 4 Angle Measure and Plane Figures Module Overview... i Topic A: Lines and Angles... 4.A.1 Topic B: Angle

### Scaffolding Task: Angle Tangle

Fourth Grade Mathematics Unit Scaffolding Task: Angle Tangle STANDARDS FOR MATHEMATICAL CONTENT MCC4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint,

### **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:

### EXPECTED BACKGROUND KNOWLEDGE

MOUL - 3 oncurrent Lines 12 ONURRNT LINS You have already learnt about concurrent lines, in the lesson on lines and angles. You have also studied about triangles and some special lines, i.e., medians,

### 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

### Inscribed Angle Theorem and Its Applications

: Student Outcomes Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle. Recognize and use different

### Lesson 2: Circles, Chords, Diameters, and Their Relationships

Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct

### 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

Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper

### circumscribed circle Vocabulary Flash Cards Chapter 10 (p. 539) Chapter 10 (p. 530) Chapter 10 (p. 538) Chapter 10 (p. 530)

Vocabulary Flash ards adjacent arcs center of a circle hapter 10 (p. 539) hapter 10 (p. 530) central angle of a circle chord of a circle hapter 10 (p. 538) hapter 10 (p. 530) circle circumscribed angle

### 4.7 Triangle Inequalities

age 1 of 7 4.7 riangle Inequalities Goal Use triangle measurements to decide which side is longest and which angle is largest. he diagrams below show a relationship between the longest and shortest sides

### Activity Set 4. Trainer Guide

Geometry and Measurement of Plane Figures Activity Set 4 Trainer Guide Int_PGe_04_TG GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set #4 NGSSS 3.G.3.1 NGSSS 3.G.3.3 NGSSS 4.G.5.1 NGSSS 5.G.3.1 Amazing

### 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.

### Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line.

Chapter 1 Vocabulary coordinate - The real number that corresponds to a point on a line. point - Has no dimension. It is usually represented by a small dot. bisect - To divide into two congruent 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

### 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

### 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.

### half-line the set of all points on a line on a given side of a given point of the line

Geometry Week 3 Sec 2.1 to 2.4 Definition: section 2.1 half-line the set of all points on a line on a given side of a given point of the line notation: is the half-line that contains all points on the

### 55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.

Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit

### 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

### 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,

### 6. Angles. a = AB and b = AC is called the angle BAC.

6. Angles Two rays a and b are called coterminal if they have the same endpoint. If this common endpoint is A, then there must be points B and C such that a = AB and b = AC. The union of the two coterminal

### Line. A straight path that continues forever in both directions.

Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A

### Lesson 1: Introducing Circles

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

### 12-1. Tangent Lines. Vocabulary. Review. Vocabulary Builder HSM11_GEMC_1201_T Use Your Vocabulary

1-1 Tangent Lines Vocabulary Review 1. ross out the word that does NT apply to a circle. arc circumference diameter equilateral radius. ircle the word for a segment with one endpoint at the center of a

### 2.1. Inductive Reasoning EXAMPLE A

CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers

### 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,