Lines, angles, triangles, and More
|
|
- Clinton Harper
- 6 years ago
- Views:
Transcription
1 Unit 8 eaumont Middle School 8th Grade, Introduction to lgebra Name: P R U T S Q Lines, angles, triangles, and More I can define key terms and identify types of angles and adjacent angles. I can measure angles. I can identify vertical, supplementary and complementary angles. I can determine the measure of an interior angle of a triangle given two angle measurements. I can determine an interior angle of a triangle given an interior and eterior angle measurement. I can use the angle relationships involving parallel lines and transversals to determine the measures of corresponding angles, alternate interior angles, alternate eterior angles.
2 ~~ Unit 8, Page 2 ~~ Lines Segments, and Rays Draw the diagram that goes with each geometric term below, and then write a definition. ngle Diagonal line segment Horizontal line segment Intersecting line segments Line Line segment Parallel Perpendicular Point Ray Skew Verte (Vertices is plural) Vertical line segment
3 ~~ Unit 8, Page 3 ~~ ngles ngles are made up of two rays with a common endpoint, called the verte. Rays are named starting with the endpoint and then another point on the ray. Ray and ray share a common endpoint (). Notice that both rays are named starting with. Point is called the: The sides of the angle are: and ngles are usually named by three capital letters. The middle letter names the. If only one angle is located at a verte, then the angle can be named using the verte letter alone. nd if there is a lower case letter between the two sides, the angle can also be referred to using the lower case letter. The angle above can be named: NGLE MESURES protractor is used to measure angles. The protractor is divided evenly into a half circle of 180 degrees (180 ). When the middle of the bottom of the protractor is placed on the verte, and one of the rays of the angle is lined up with 0, the other ray of the angle crosses the protractor at the measure of the angle. The angle below has the ray pointing left lined up with 0 (the outside numbers), and the other ray of the angle crossed the protractor at 55. Types of ngles Type Type Type Type Measure Measure Measure Measure
4 ~~ Unit 8, Page 4 ~~ Using the protractor below, find the measure of the following angles. Then, tell what type of angle it is using the information above. # Question Measure Type of ngle 1 What is the measure of RF? 2 What is the measure of RF? 3 What is the measure of DRF? 4 What is the measure of RD? djacent ngles djacent ngles - djacent angles are two angles that have the same verte and share one ray as a side. They do not share space inside the angles. Figure D ) D is adjacent to D. However, D is not adjacent to D because adjacent angles do not share any space inside the angle. Figure ) These two angles are not adjacent. They share a common ray but do not share the same verte. N S O T M Figure ) NOT is not adjacent to SOM. They share space inside the angles. (overlap)
5 ~~ Unit 8, Page 5 ~~ For each diagram below, name the angle that is adjacent to it. D 1) D is adjacent T U V Z 2) TUV is adjacent R S T P 3) SRP is adjacent J R Q P 4) PQR is adjacent to to to to Independent Practice Part 1: ircle the correct choice for each question.?
6 ~~ Unit 8, Page 6 ~~ Part 2: Fill in the blanks with the correct geometric term. 1) 2) 3) 4) 5) 6) 7) The verte of in the drawing above is point 8) 9) 10) Two acute angles in the figure are and Part 3: Find the measure of each angle. # Question Measure Type of ngle 1 What is the measure of RF? 2 What is the measure of ERF? 3 What is the measure of R? 4 What is the measure of KR? 5 What is the measure of R? 6 What is the measure of FR?
7 ~~ Unit 8, Page 7 ~~ Part 4: For each angle, circle the best estimate. Part 5: For each diagram below, name the angle that is adjacent to it. Y O Y Z G D P F V X V 1) YOP is adjacent 2) XVY is adjacent 3) DF is adjacent J K L M 4) JKL is adjacent to to to to
8 ~~ Unit 8, Page 8 ~~ Vertical ngles When two lines intersect, two pairs of VERTIL NGLES are formed. Vertical angles are not adjacent. Vertical angles are located across from each other, they share a common verte, and the sides of the angles are composed of opposite rays. Use a straight edge. Draw ray opposite to ray, and then draw ray opposite to ray. Use what you ve learned about the measure of straight angles to prove that the figure contains two pairs of congruent angles. OD O 45 D O Pairs of vertical angles always have the same measure. Vertical angles are (symbol hint ) ongruent means they have the. Set : In the diagram, name the second angle in each pair of vertical angles. Y Q R 1) YPV 4) VPT 2) QPR 5) RPT 3) SPT 6) VPS V P T S Set : Use the information given in the diagram to find the measure of each unknown vertical angle Set Questions G 50 1) m F = H 130 D 2) m = F J K 6) Figure above is a 7) The proper notation for the figure is 3) m KJ = 4) m G = 5) m J = 18) m = 8) The sum of the angles in figure is + + =
9 ~~ Unit 8, Page 9 ~~ omplementary and Supplementary ngles Two angles are complementary if the sum of their angles measure 90. Two angles are supplementary if the sum of their angles measure 180. omplementary and supplementary angle pairs may be adjacent, but do not need to be. linear pair is a pair of adjacent angles that are supplementary. elow, the angles marked 32 and 148 are a linear pair. Together, these angle pairs form a Sum = Sum = Sum = 148 Sum = Sum = Sum = These angles are: These angles are: PRTIE: alculate the measure of each unknown angle b a 140 c d 119 h e f g G F H O E D The sum of all the central angles = SET The sum of angles e + d + c = SET 1) m a = 5) m e = 2) m b = 6) m f = 9) m O = 10) m OD = 3)m c = 7) m g = 11)m EOF = 4) m d = 8) m h = 12) m OH =
10 ~~ Unit 8, Page 10 ~~ Independent Practice Part 1: In the diagram below, name the second angle in each pair of vertical angles. Set K M 1) MLN 4) GLM L N 2) KLH 5) KLM J H G 3) GLN 6) HLG Use the information given in the diagram to find the measure of each unknown vertical angle. Set 7) m = y m p z w ) m y = 9) m z = 10) m w = 11) m m = 12) m p = 13) + y = 14) m + p = 15) w + z = 16) Each of the angle pairs in questions above are angles because their sum is. 17) The sum of the four angles located around every point in the figure above =
11 Part 2: ~~ Unit 8, Page 11 ~~
12 ~~ Unit 8, Page 12 ~~ Review: Lines and ngles Notes: Identify each type of triangle by its angles and by its sides y y y sides: sides: sides: y y y angles: angles: angles: Part 1: Find the measure of the angles below. K 1) What is the measure of DR? D 2) What is the measure of RF? 3) What is the measure of R? E 4) What is the measure of R? 5) What is the measure of KR? R F Use the following diagram for questions H D E F Z Y W X V G 6) Which angle is supplementary angle to EDF? 7) What is the measure of GDF? 13) What is the measure of D? 8) Which two angles are right angles? and 9) What is the measure of EDF? 14) Which angles are adjacent to ED? 10) Which angle is adjacent to D? and 11) Which angle is a complementary angle to HD? 12) What is the measure of H?
13 ~~ Unit 8, Page 13 ~~ Part 2: Use what you know about complementary and supplementary angles to find the measures of the following angles. SET S 1) m RMS = R Q 21 M P V 50 T 2) m VMT = 3)m QMN = 4) m WPQ = N W The sum of angles located above = SET D 49 D J 55 K L H G 5) m JK = 6) m KD = 7)m FKH = F 8) m L = The sum of angles located below = Part 3: lassify each triangle two ways. 1) 2) 3) 4) 5) 6)
14 ~~ Unit 8, Page 14 ~~ Interior ngles of a Triangle FT: The three interior angles of a triangle always add up to ⁰. Eample 1: 45⁰ 30⁰ 60⁰ 45⁰ 60⁰ 60⁰ 60⁰ 45⁰ + 45⁰ + = 30⁰ + 60⁰ + = 60⁰ + 60⁰ + 60⁰ = 3( ) = Eample 2: Find the missing angle in the triangle. 20⁰ Solution: Step 1: Write equation. 20⁰ + 125⁰ + = Step 2: ombine like terms. + = 180⁰ Step 3: Isolate. 125⁰ 145⁰ + = 180⁰ Step 4: State the solution. = Step 5: Use solution to answer the original question. The missing angle is Eample 3: Find the missing angle in the triangle. 42⁰
15 ~~ Unit 8, Page 15 ~~ Independent Practice Find the missing angle in the triangles. For each problem, show an equation and solve. 1) 40⁰ 2) 3) 80⁰ 32⁰ 45⁰ 4) 5) 6) 78⁰ 55⁰ 15⁰ 25⁰ 7) 8) 9) 60⁰ 36⁰ 30⁰ 30⁰ 10) Two equations required 11) 12) Two equations required 22⁰ y z 38⁰ (2)⁰ (3 4)⁰ ( + 10)⁰ w 32⁰ y 38⁰ z w: y: z: : : : : : y: z:
16 ~~ Unit 8, Page 16 ~~ Eterior ngles The eterior angle of a triangle is always equal to the sum of the opposite interior angles. Eample 1: Eamine the figures below. Find the measure of the missing angle. Figure Figure 62⁰ 60⁰ 58⁰ z 40⁰ 50⁰ y 1) Sum s in triangle = 2) = 3) Sum of interior angles opposite of angle = + = 1) = 2) y = z = 3) Sum of interior angles opposite of angle y = Sum of interior angles opposite of angle z = Eample 2: Find the measure of and y. Step 1: Use the rule for eterior angles to write equation. 120⁰ = + 120⁰ = 75⁰ + 75⁰ y 120⁰ 45⁰ = Step 2: The sum of the interior angles of a triangle equals 180⁰, and supplements D, so either equation: SUM of INTERIOR NGLES 180⁰ = 75⁰ + 45⁰ + y 180⁰ = 75⁰ + 45⁰ + y SUPPLEMENTL NGLES 180⁰ = 120⁰ + y 60⁰ = y 180⁰ = 120⁰ + y 60⁰ = y
17 ~~ Unit 8, Page 17 ~~ Independent Practice Part 1: Find the measure of the missing angle measures. Show an equation for each angle. 1) 2) 102⁰ 50⁰ 105⁰ y y 38⁰ 3) 4) 28⁰ y 55⁰ 110⁰ 81⁰ y 5) 6) 33⁰ 122⁰ 39⁰ y y 119⁰ 7) w z (2y 3) y v 133⁰ 8) (2 + 45) y 82⁰ 9) 64⁰ y 84⁰ (y + 25) w v
18 ~~ Unit 8, Page 18 ~~ Follow-up, review assignment for homework after p ) Find the missing angle. 2) Solve for. Then solve for each of the triangle's interior angles. 42⁰ 120⁰ 2 3 3) Find the measures for and y. 4) Find the measures for and y. y 110⁰ 145⁰ 55⁰ 65⁰ y 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19)
19 ~~ Unit 8, Page 19 ~~ orresponding, lternate Interior, and lternate Eterior ngles If two parallel lines are intersected by another line, how many angles are formed? Number them on the diagram. P T Q R U S The etra arrows on two of the lines mean they are. The line that intersects the two lines is called a. The number of angles formed is. The angles formed when parallel lines are cut by a transversal line have special relationships and are named according to those relationships with one another. ORRESPONDING NGLES Definition: Name the corresponding angles for the following. 1) 1 corresponds with 2) 2 corresponds with 3) 3 corresponds with 4) 4 corresponds with What do you notice about the angle pairs above? omplete the sentence: If two angles are corresponding angles, then they are:
20 ~~ Unit 8, Page 20 ~~ LTERNTE INTERIOR NGLES Word attack To alternate means INterior means: Definition: Name the alternate interior angle for the following angles. 1) 3 is an alternate interior angle with 2) 4 is an alternate interior angle with How many pairs of alternate interior angles are possible? What do you notice about the angle pairs above? omplete the sentence: If two angles are alternate interior angles, then they are: LTERNTE EXTERIOR NGLES Word attack To alternate means Eterior means: Definition: Name the alternate eterior angle for the following angles. 1) 1 is an alternate eterior angle with 2) 2 is an alternate eterior angle with How many pairs of alternate eterior angles are possible? What do you notice about the angle pairs above? omplete the sentence: If two angles are alternate eterior angles, then they are: Look at the diagram below. For each pair of angles, state whether they are corresponding (), alternate interior (I), alternate eterior (E), vertical (V), or supplementary (S). y s u w z F v E t D 1) u, 6) t, 11) t, u 2) w, s 7) w, z 12) w, 3) t, y 8) v, w 13) w, s 4) s, t 9) v, z 14) s, v 5) w, y 10) s, z 15), z 16) If m s = 110⁰, find the measure of the remaining angles. m v = m t = m u = m w = m = m y = m z =
21 Parallel Lines ut by a Transversal ~~ Unit 8, Page 21 ~~ s eplained in the previous section, when two parallel lines are intersected, or cut, by a transversal, eight angles are formed. ny two angles are either congruent or supplementary! Given the measure of just one of the eight angles, the other seven can be determined. Eample: Lines a and b are parallel. Line m intersects both line a and b. The eight resulting angles are labeled 1 8, and m 1 is given to be 25⁰. Find all angle measures. m 25⁰ a Step 1: Notice the relationships b 1 and 4 are vertical angles and therefore, so m 4 = 25⁰. Other pairs of vertical angles are 2 and 3, 5 and 8, 6 and 7. 1 is supplementary to 2; so the m 2 = 180⁰ - 1 = ⁰ = 155⁰. 1 is also supplementary to 3; so the m 3 is also 155⁰. Notice that 2 and 3are vertical angles, and would have to be to each other. Step 2: orresponding angles have the same relative position, like 1 and 5 are both in the upper left section of the intersecting lines. orresponding angles are always congruent, so m 1and m 5are both 25⁰. 5 and 8 are vertical angles, so m 8 = 25⁰. 6 and 8 form a linear pair, so m 6 = 180⁰ - 25⁰ = 155⁰. 6 and 7 are vertical angles, so m 7 is also 155⁰. nswer: m 1, m 4, m 5 and m 8 (all) = and are angles m 2, m 3, m 6 and m 7 (all) = and are angles
22 ~~ Unit 8, Page 22 ~~ INDEPENDENT PRTIE Part 1: 1) Parallel lines and when cut by transversal form eight angles, as shown in the diagram below. Use the diagram to find the measures of each of the angles ⁰ 1) m 1 = 3) m 3 = 5) m 5 = 7) m 7 = 2) m 2 = 4) m 4 = 6) m 6 = 8) m 8 = 108⁰ 2) Parallel lines and when cut by transversal form eight angles, as shown in the diagram below. Use the diagram to find the measures of each of the angles ⁰ 1 2 9) m 1 = 11) m 2 = 13) m 3 = 15) m 4 = 63⁰ 10) m 5 = 12) m 6 = 14) m 7 = 16) m 8 =
23 ~~ Unit 8, Page 23 ~~ Part 2: For each pair of angles, state whether they are corresponding (), alternate interior (I), alternate eterior (E), vertical (V), or supplementary (S) angles ) 1 and 4 6) 6 and 5 11) 3 and 6 2) 2 and 6 7) 2 and 7 12) 4 and 8 3) 1 and 3 8) 1 and 2 13) 1 and 5 4) 5 and 8 9) 4 and 5 14) 2 and 3 5) 5 and 7 10) 6 and 8 15) 6 and 7 Parallel lines and when cut by transversal form eight angles, as shown in the diagram below. Use the diagram below for problems 16 and ) m 2 = 17) m 4 = 121⁰ Parallel lines and when cut by transversals and. Find all of the unknown angle measures. 18) m 18 = 19) m 19 = 20) m 20 = 21) m 21 = 22) m 22 = 23) m 23 = 24) m 24 = 25) m 25 = 26) m 26 = 27) m 27 = 28) m 28 = 29) m 29 =
24 Finding Unknown ngle Measures ~~ Unit 8, Page 24 ~~ We will use the angle relationships that are formed when two parallel lines are intersected by a transversal to find the measures of missing angles. ll of the angle relationships will either be supplementary or congruent. Eample : The pair of angles are either vertical angles, alternate interior angles, alternate eterior angles, or corresponding angles; so they are congruent. ll you have to do is set up and solve an equation where the epressions are congruent. Once you have solved for, substitute that value back into each epression to find the measure of each angle. #1 Relationship: Equation: = = = #2 Relationship: Equation: = = = Eample : Each pair of angles are supplementary to each other, which means the angles add up to 180 o. ll you have to do is set up and solve an equation where the epressions add up to equal 180 o. Once you have solved for, substitute that value back into each epression to find the measure of each angle. #3 Relationship: Equation: = = =
25 ~~ Unit 8, Page 25 ~~ INDEPENDENT PRTIE Part 1: Find the measure of each missing angle in the parallel lines and transversals. Each pair of angles is either supplementary or congruent (vertical angles, alternate interior angles, alternate eterior angles, or corresponding angles). State the relationship, set up an appropriate equation and solve for. Once you've solved for, substitute that value back into each epression to find the measure of each angle. Relationship: 1) Equation: 2) = = = Relationship: Equation: = = = 3) Relationship: Equation: = = = 4) Relationship: Equation: = = =
26 ~~ Unit 8, Page 26 ~~ 5) Relationship: Equation: = = = 6) Relationship: Equation: = = = 7) Relationship: Equation: = = = 8) Relationship: Equation: = = =
27 ~~ Unit 8, Page 27 ~~ Part 2: The following problems are multiple choice. ircle the letter indicating the best answer for each question. 1) 2) 3) 4) 5) 6)
28 ~~ Unit 8, Page 28 ~~ Review for Unit Test Part 1: Key Terms, Types of ngles, Measuring ngles and djacent ngles N S T D 1) D is adjacent W 2) NWS is adjacent M 3) The verte is: to to G Use the protractor to measure each angle. Indicate whether it is acute, obtuse, right, or straight. R S 4) = ; 5) = ; 6) = ; 7) = ; E F N 8) = ; The following questions are multiple choice. ircle the letter net to the best answer. 9) 10) Which of the following is a correct name for the angle indicated below with the question mark??... D.
29 ~~ Unit 8, Page 29 ~~ Part 2: Vertical, Supplementary and omplementary ngles Find the measure of angle b and classify the angle relationship. 1) 2) 3) lassification: b: lassification: b: lassification: b: Part 3: Interior and Eterior ngles of a Triangle Find the value of in each of the following diagrams. Equation: 1) 2) Equation: : : 3) Equation: 4) Equation: : : 5) Equation: :
30 ~~ Unit 8, Page 30 ~~ Part 5: Parallel Lines and Transversals [orresponding ngles, lternate Interior ngles, lternate Eterior ngles] Find the missing angle measurement. Identify the relationship of the angles. corresponding (), alternate interior (I), alternate eterior (E), vertical (V), or supplementary (S) angles. 1) 2) 3) : Relationship: 4) : Relationship: 5) 6) : Relationship: : Relationship: : Relationship: : Relationship: Identify the relationship of the angles. corresponding (), alternate interior (I), alternate eterior (E), vertical (V), or supplementary (S) angles. Write an equation to solve for. Solve. 7) Relationship: 8) Equation Relationship: Equation : :
31 ~~ Unit 8, Page 31 ~~ Identify the relationship of the angles. corresponding (), alternate interior (I), alternate eterior (E), vertical (V), or supplementary (S) angles. Write an equation to solve for. Solve. 9) Relationship: Equation 10) (4 + 2) Relationship: Equation : : 11) Identify the measures of the indicated angles. The following questions are multiple choice. ircle the letter net to the best answer. 12) 13) 14)
Name: Unit 8 Beaumont Middle School 8th Grade, Advanced Algebra I T Q R U
Unit 8 eaumont Middle School 8th Grade, 2015-2016 dvanced lgebra I Name: P T Q R U S I can define ke terms and identif tpes of angles and adjacent angles. I can identif vertical, supplementar and complementar
More informationWhen two (or more) parallel lines are cut by a transversal, the following angle relationships are true:
Lesson 8: Parallel Lines Two coplanar lines are said to be parallel if they never intersect. or any given point on the first line, its distance to the second line is equal to the distance between any other
More informationAngles. Problems: A.! Name the vertex of the angle. What rays are the sides of the angle? C.! Give three other names of LJK.
ngles page # Problems:. ngles. Name the vertex of the angle.. What rays are the sides of the angle? J. Give three other names of LJK.. Name the following angles with three letters: = = N M The remaining
More informationLine: It s a straight arrangement of points that extends indefinitely in opposite directions.
More Terminology and Notation: Plane: It s an infinitely large flat surface. Line: It s a straight arrangement of points that extends indefinitely in opposite directions. ollinear Points: Points that lie
More informationAre You Ready? Conditional Statements
SKILL 88 onditional Statements Teaching Skill 88 Objective Determine whether a conditional statement is true, write its converse, and determine whether the converse is true. Review with students the different
More informationSummer Dear Geometry Students and Parents:
Summer 2018 Dear Geometry Students and Parents: Welcome to Geometry! For the 2018-2019 school year, we would like to focus your attention to the prerequisite skills and concepts for Geometry. In order
More informationIntroduction to Geometry
Introduction to Geometry Objective A: Problems involving lines and angles Three basic concepts of Geometry are: Points are a single place represented by a dot A Lines are a collection of points that continue
More informationParallel Lines: Two lines in the same plane are parallel if they do not intersect or are the same.
Section 2.3: Lines and Angles Plane: infinitely large flat surface Line: extends infinitely in two directions Collinear Points: points that lie on the same line. Parallel Lines: Two lines in the same plane
More informationNovember 10, 2004 : Fax:
Honors Geometry Issue Super Mathter November 0, 004 : 30-0-6030 Fax: 30--864 For class info, visit www.mathenglish.com irect your questions and comments to rli@smart4micro.com Name: Peter Lin Peter Lin
More informationLesson 1: Complementary and Supplementary Angles
lasswork Opening As we begin our study of unknown angles, let us review key definitions. Term Definition Two angles and, with a common side, are angles if is in the interior of. When two lines intersect,
More informationGeo Final Review 2014
Period: ate: Geo Final Review 2014 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. n angle measures 2 degrees more than 3 times its complement. Find the
More informationLet s use a more formal definition. An angle is the union of two rays with a common end point.
hapter 2 ngles What s the secret for doing well in geometry? Knowing all the angles. s we did in the last chapter, we will introduce new terms and new notations, the building blocks for our success. gain,
More informationLesson 4-1: Angles Notation and Types of Angles
Name: Date: Lesson 4-1: Angles Notation and Types of Angles Learning Goals: 1. What are a right angle, acute angle, and obtuse angle? 2. How do I name an angle? 3. How can we use special angle pair definitions
More informationIdentify parallel lines, skew lines and perpendicular lines.
Learning Objectives Identify parallel lines, skew lines and perpendicular lines. Parallel Lines and Planes Parallel lines are coplanar (they lie in the same plane) and never intersect. Below is an example
More informationWhat is an angle? The space between two intersecting lines.
Name: Date: Lesson 4-1: Angles Notation and Types of Angles Learning Goals: 1. What are a right angle, acute angle, and obtuse angle? 2. How do I name an angle? 3. How can we use special angle pair definitions
More informationMath 7, Unit 08: Geometric Figures Notes
Math 7, Unit 08: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My
More informationMath 7, Unit 8: Geometric Figures Notes
Math 7, Unit 8: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My guess
More informationWarm-Up Based on upper. Based on lower boundary of 1. m 1 m 2 m 3 m What do you notice about these angles?
Warm-Up 1.8.1 Metalbro is a construction company involved with building a new skyscraper in ubai. The diagram below is a rough sketch of a crane that Metalbro workers are using to build the skyscraper.
More informationObjective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms
Unit 1 asics of Geometry Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically looks
More informationG7-3 Measuring and Drawing Angles and Triangles
G7-3 Measuring and Drawing ngles and Triangles right angle acute angles obtuse angles 90 less than 90 more than 90 and less than 180 1. Without using a protractor, identify each angle as acute or obtuse.
More informationPoints, Lines, and Planes 1.1
Points, Lines, and Planes 1.1 Point a location ex. write as: Line made up of points and has no thickness or width. ex. c write as:, line c ollinear points on the same line. Noncollinear points not on the
More information2 and 6 4 and 8 1 and 5 3 and 7
Geo Ch 3 Angles formed by Lines Parallel lines are two coplanar lines that do not intersect. Skew lines are that are not coplanar and do not intersect. Transversal is a line that two or more lines at different
More informationUnit 8 Plane Geometry
Unit 8 Plane Geometry Grade 9 pplied Lesson Outline *Note: This unit could stand alone and be placed anywhere in the course. IG PITURE Students will: investigate properties of geometric objects using dynamic
More informationTriangle Geometry Isometric Triangles Lesson 1
Triangle eometry Isometric Triangles Lesson 1 Review of all the TORMS in OMTRY that you know or soon will know!. Triangles 1. The sum of the measures of the interior angles of a triangle is 180º (Triangle
More informationChapter 1-2 Points, Lines, and Planes
Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines
More informationBasics of Geometry Unit 1 - Notes. Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes.
asics of Geometry Unit 1 - Notes Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically
More informationParallel Lines cut by a Transversal Notes, Page 1
Angle Relationships Review 2 When two lines intersect, they form four angles with one point in 1 3 common. 4 Angles that are opposite one another are VERTIAL ANGLES. Some people say instead that VERTIAL
More informationGeometry. Points, Lines, Planes & Angles. Part 2. Slide 1 / 185. Slide 2 / 185. Slide 3 / 185. Table of Contents
Slide 1 / 185 Slide 2 / 185 Geometry Points, Lines, Planes & ngles Part 2 2014-09-20 www.njctl.org Part 1 Introduction to Geometry Table of ontents Points and Lines Planes ongruence, istance and Length
More informationMath-2. Lesson 7-4 Properties of Parallelograms And Isosceles Triangles
Math-2 Lesson 7-4 Properties of Parallelograms nd Isosceles Triangles What sequence of angles would you link to prove m4 m9 3 1 4 2 13 14 16 15 lternate Interior Corresponding 8 5 7 6 9 10 12 11 What sequence
More informationUnit III: SECTION #1 - Angles & Lines
1/16 Name Period An angle is made up of two rays that meet at a point called the vertex. Kinds of Angles 1) Acute Angle the angle s measure is between 0ᵒ and 90ᵒ 2) Right Angle the angle s measure is 90ᵒ
More informationGeometry Definitions, Postulates, and Theorems. Chapter 4: Congruent Triangles. Section 4.1: Apply Triangle Sum Properties
Geometry efinitions, Postulates, and Theorems Key hapter 4: ongruent Triangles Section 4.1: pply Triangle Sum Properties Standards: 12.0 Students find and use measures of sides and of interior and exterior
More informationa triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
More information9.1 Angle Relationships
? LESSON 9.1 ngle Relationships ESSENTIL QUESTION How can you use angle relationships to solve problems? Equations, epressions, and relationships 7.11. Write and solve equations using geometry concepts,
More informationGeometry. Slide 1 / 190. Slide 2 / 190. Slide 3 / 190. Angles. Table of Contents
Slide 1 / 190 Slide 2 / 190 Geometry ngles 2015-10-21 www.njctl.org Table of ontents click on the topic to go to that section Slide 3 / 190 ngles ongruent ngles ngles & ngle ddition Postulate Protractors
More informationAre You Ready? Triangle Sum Theorem
SKILL 30 Triangle Sum Theorem Teaching Skill 30 Objective Use the Triangle Sum Theorem to find the measures of missing angles. Have students read the Triangle Sum Theorem. Point out that the theorem is
More informationUnit 9 Study Guide. Multiple Choice (2 points) Identify the choice that best completes the statement or answers the question.
Unit 9 Study Guide Multiple hoice (2 points) Identify the choice that best completes the statement or answers the question. Find the perimeter of each rectangle. 1. 38 m 18 m a. 684 m c. 56 m b. 94 m d.
More informationMath 6, Unit 8 Notes: Geometric Relationships
Math 6, Unit 8 Notes: Geometric Relationships Points, Lines and Planes; Line Segments and Rays As we begin any new topic, we have to familiarize ourselves with the language and notation to be successful.
More information(Current Re nweb Grade)x.90 + ( finalexam grade) x.10 = semester grade
2//2 5:7 PM Name ate Period This is your semester exam which is worth 0% of your semester grade. You can determine grade what-ifs by using the equation below. (urrent Re nweb Grade)x.90 + ( finalexam grade)
More informationReview Test 1 Chapters 1 & 2 and Appendix L
Math 61 pring 2009 Review Test 1 hapters 1 & 2 and ppendix L www.timetodare.com 1 To prepare for the test, learn all definitions, be familiar with all theorems and postulates, study all exercises and theorems
More informationName Class Date 1 C REFLECT. m 1 m 2 m 3 m 4 m 1 + m 2 m 2 + m 3 m 3 + m 4 m 4 + m 1
Name lass Date 1-4 Pairs of ngles Going Deeper Essential question: How can you use angle pairs to solve problems? Recall that two rays with a common endpoint form an angle. The two rays form the sides
More informationAngle Geometry. Lesson 18
Angle Geometry Lesson 18 Lesson Eighteen Concepts Specific Expectations Determine, through investigation using a variety of tools, and describe the properties and relationships of the interior and exterior
More informationWhat could be the name of the plane represented by the top of the box?
hapter 02 Test Name: ate: 1 Use the figure below. What could be the name of the plane represented by the top of the box? E F I 2 Use the figure below. re points,, and E collinear or noncollinear? noncollinear
More informationUnit 8 Chapter 3 Properties of Angles and Triangles
Unit 8 Chapter 3 Properties of Angles and Triangles May 16 7:01 PM Types of lines 1) Parallel Lines lines that do not (and will not) cross each other are labeled using matching arrowheads are always the
More informationGeometry. Points, Lines, Planes & Angles. Part 2. Angles. Slide 1 / 185 Slide 2 / 185. Slide 4 / 185. Slide 3 / 185. Slide 5 / 185.
Slide 1 / 185 Slide 2 / 185 eometry Points, ines, Planes & ngles Part 2 2014-09-20 www.njctl.org Part 1 Introduction to eometry Slide 3 / 185 Table of ontents Points and ines Planes ongruence, istance
More informationGeometry. Points, Lines, Planes & Angles. Part 2. Slide 1 / 185. Slide 2 / 185. Slide 3 / 185. Table of Contents
Slide 1 / 185 Slide 2 / 185 Geometry Points, Lines, Planes & ngles Part 2 2014-09-20 www.njctl.org Part 1 Introduction to Geometry Table of ontents Points and Lines Planes ongruence, istance and Length
More informationPoints, Lines, Planes, & Angles
Points, Lines, Planes, and ngles Points, Lines, Planes, & ngles www.njctl.org Table of ontents Points, Lines, & Planes Line Segments Simplifying Perfect Square Radical Expressions Rational & Irrational
More informationParallel Lines and Triangles. Objectives To use parallel lines to prove a theorem about triangles To find measures of angles of triangles
-5 Parallel Lines and Triangles ommon ore State Standards G-O..0 Prove theorems about triangles... measures of interior angles of a triangle sum to 80. MP, MP, MP 6 Objectives To use parallel lines to
More informationCCM Unit 10 Angle Relationships
CCM6+7+ Unit 10 Angle Relationships ~ Page 1 CCM6+7+ 2015-16 Unit 10 Angle Relationships Name Teacher Projected Test Date Main Concepts Page(s) Unit 10 Vocabulary 2-6 Measuring Angles with Protractors
More informationReteaching Exploring Angles of Polygons
Name Date lass Eploring Angles of Polygons INV X 3 You have learned to identify interior and eterior angles in polygons. Now you will determine angle measures in regular polygons. Interior Angles Sum of
More informationPLANE GEOMETRY SKILL BUILDER ELEVEN
PLANE GEOMETRY SKILL BUILDER ELEVEN Lines, Segments, and Rays The following examples should help you distinguish between lines, segments, and rays. The three undefined terms in geometry are point, line,
More informationWarm up Exercise. 1. Find the missing angle measure in the figures below: Lesson 54 Angle Relationships & Lesson 55 Nets.notebook.
Warm up Exercise 1. Find the missing angle measure in the figures below: 45 o 29 o 30 o a d 49 o b c 1 Lesson 54: Angle Relationships Intersecting lines form pairs of adjacent angles and pairs of opposite
More informationGEOMETRY R Unit 2: Angles and Parallel Lines
GEOMETRY R Unit 2: Angles and Parallel Lines Day Classwork Homework Friday 9/15 Unit 1 Test Monday 9/18 Tuesday 9/19 Angle Relationships HW 2.1 Angle Relationships with Transversals HW 2.2 Wednesday 9/20
More informationChapter 3: Congruent to Similar Figures (Triangles) Angles. Opposite Angles: Corresponding Angles: Alternate Interior Angles
h. 3 n g l e s, T r i a n g l e s a n d M e t r i c R e l a t i o n s P a g e 1 hapter 3: ongruent to Similar Figures (Triangles) ngles Name the following angles: omplementary ngles Supplementary ngles
More information7.1 Interior and Exterior Angles
Name Class Date 7.1 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
More informationSAMPLE. Classification of angles: Answer: Answer: Answer: Answer: Answer:
SMPL The ancient Romans are famous for their achievements in architecture and engineering. One of ancient Rome s greatest accomplishments was the Roman aqueduct system. The aqueducts brought clean water
More informationGeometry. Slide 1 / 190 Slide 2 / 190. Slide 4 / 190. Slide 3 / 190. Slide 5 / 190. Slide 5 (Answer) / 190. Angles
Slide 1 / 190 Slide 2 / 190 Geometry ngles 2015-10-21 www.njctl.org Slide 3 / 190 Table of ontents click on the topic to go to that section Slide 4 / 190 Table of ontents for Videos emonstrating onstructions
More informationNaming Angles. One complete rotation measures 360º. Half a rotation would then measure 180º. A quarter rotation would measure 90º.
Naming Angles What s the secret for doing well in geometry? Knowing all the angles. An angle can be seen as a rotation of a line about a fixed point. In other words, if I were mark a point on a paper,
More informationMaintaining Mathematical Proficiency
Name Date Chapter 1 Maintaining Mathematical Proficiency Simplify the expression. 1. 3 + ( 1) = 2. 10 11 = 3. 6 + 8 = 4. 9 ( 1) = 5. 12 ( 8) = 6. 15 7 = + = 8. 5 ( 15) 7. 12 3 + = 9. 1 12 = Find the area
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name ate onstellations Naming, Measuring, and lassifying ngles Vocabulary Write the term from the box that best completes each statement. point line segment
More informationUnit 1, Lesson 1: Moving in the Plane
Unit 1, Lesson 1: Moving in the Plane Let s describe ways figures can move in the plane. 1.1: Which One Doesn t Belong: Diagrams Which one doesn t belong? 1.2: Triangle Square Dance m.openup.org/1/8-1-1-2
More information3-1 Study Guide Parallel Lines and Transversals
3-1 Study Guide Parallel Lines and Transversals Relationships Between Lines and Planes When two lines lie in the same plane and do not intersect, they are parallel. Lines that do not intersect and are
More informationIf lines m and n are parallel, we write. Transversal: A line that INTERSECTS two or more lines at 2
Unit 4 Lesson 1: Parallel Lines and Transversals Name: COMPLEMENTARY are angles to add up to 90 SUPPLEMENTARY are angles to add up to 180 These angles are also known as a LINEAR PAIR because they form
More informationdescribes a ray whose endpoint is point A. TRUE g. A plane has no thickness. TRUE h. Symbols XY and YX describe the same line. TRUE i.
Geometry Ms. H. Ray, 010 NSWRS TO TH RVIW FOR TH GOMTRY MITRM XM. 1. True or False? e prepared to explain your answer. a. efinitions and theorems are very important in mathematics but every mathematical
More informationUnit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
More informationAngle Unit Definitions
ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers
More informationSummer Review for incoming Geometry students (all levels)
Name: 2017-2018 Mathematics Teacher: Summer Review for incoming Geometry students (all levels) Please complete this review packet for the FIRST DAY OF CLASS. The problems included in this packet will provide
More information5 and Parallel and Perpendicular Lines
Ch 3: Parallel and Perpendicular Lines 3 1 Properties of Parallel Lines 3 Proving Lines Parallel 3 3 Parallel and Perpendicular Lines 3 Parallel Lines and the Triangle Angles Sum Theorem 3 5 The Polgon
More informationb) A ray starts at one point on a line and goes on forever. c) The intersection of 2 planes is one line d) Any four points are collinear.
Name: Review for inal 2016 Period: eometry 22 Note to student: This packet should be used as practice for the eometry 22 final exam. This should not be the only tool that you use to prepare yourself for
More informationCCGPS UNIT 1A Semester 1 ANALYTIC GEOMETRY Page 1 of 35. Similarity Congruence and Proofs Name:
GPS UNIT 1 Semester 1 NLYTI GEOMETRY Page 1 of 35 Similarity ongruence and Proofs Name: Date: Understand similarity in terms of similarity transformations M9-12.G.SRT.1 Verify experimentally the properties
More informationExample 1. Find the angle measure of angle b, using opposite angles.
2..1 Exploring Parallel Lines Vertically opposite angles are equal When two lines intersect, the opposite angles are equal. Supplementary angles add to 180 Two (or more) adjacent angles on the same side
More informationGeometry Basics * Rory Adams Free High School Science Texts Project Mark Horner Heather Williams. 1 Introduction. 2 Points and Lines
OpenStax-NX module: m31494 1 Geometry asics * Rory dams Free High School Science Texts Project Mark Horner Heather Williams This work is produced by OpenStax-NX and licensed under the reative ommons ttribution
More informationGEOMETRY is the study of points in space
CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of
More informationLesson 13: Angle Sum of a Triangle
Student Outcomes Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum
More information7.1 Interior and Exterior Angles
Name Class Date 7.1 Interior and Exterior ngles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? G.6.D Verify theorems about the relationships
More informationGeometry Definitions, Postulates, and Theorems. Chapter 3: Parallel and Perpendicular Lines. Section 3.1: Identify Pairs of Lines and Angles.
Geometry Definitions, Postulates, and Theorems Chapter : Parallel and Perpendicular Lines Section.1: Identify Pairs of Lines and Angles Standards: Prepare for 7.0 Students prove and use theorems involving
More informationUnit 10 Angles. Name: Teacher: Grade:
Unit 10 Angles Name: Teacher: Grade: 1 Lesson 1 Classwork Complementary Angles Complementary Angles: ** Using the above definition, the word sum tells us that we are using addition to set up an equation.
More informationLesson 1.9.1: Proving the Interior Angle Sum Theorem Warm-Up 1.9.1
NME: SIMILRITY, CONGRUENCE, ND PROOFS Lesson 9: Proving Theorems bout Triangles Lesson 1.9.1: Proving the Interior ngle Sum Theorem Warm-Up 1.9.1 When a beam of light is reflected from a flat surface,
More informationGeometry Notes - Unit 4 Congruence
Geometry Notes - Unit 4 ongruence Triangle is a figure formed by three noncollinear points. lassification of Triangles by Sides Equilateral triangle is a triangle with three congruent sides. Isosceles
More information9-1. Translations. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
9- Translations Vocabular Review. Underline the correct word to complete the sentence. If two triangles are congruent, corresponding angle measures are the same/ different and corresponding side lengths
More informationGeometry Review. Line CD is drawn perpendicular to Line BC.
Geometry Review Geometry is the original mathematics! Way before x and y s and all that algebra stuff! You will find that geometry has many definitions and exact vocabulary! Knowing the meaning of words
More informationAdditional Practice. Name Date Class. 1. Which of these angles are acute, which are obtuse, and which are right? a. b. c. d. e. f. Shapes and Designs
Additional Practice Investigation 1 1. Which of these angles are acute, which are obtuse, and which are right? a. b. c. d. e. f. 1 Additional Practice (continued) Investigation 1 2. Use the diagram of
More informationCh 1 Note Sheet L2 Key.doc 1.1 Building Blocks of Geometry
1.1 uilding locks of Geometry Read page 28. It s all about vocabulary and notation! To name something, trace the figure as you say the name, if you trace the figure you were trying to describe you re correct!
More informationSmart s Mill Middle School
Smart s Mill Middle School Geometry Semester Exam Review 0 03 You must show your work to receive credit! Mrs. nderson and Mrs. ox note to remember, for this review N the actual exam: It is always helpful
More informationGeometry Short Cycle 1 Exam Review
Name: lass: ate: I: Geometry Short ycle 1 Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name a plane that contains. a. plane R c. plane WRT
More information14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. Using the space below, draw at least right triangles, each of which has one
More informationClassifying Angles and Triangles
6 1 NAMING AND CLASSIFYING ANGLES AND TRIANGLES 6 1 Naming and Classifying Angles and Triangles Points, Lines, and Rays In the world of math, it is sometimes necessary to refer to a specific point in space.
More information1-1 Understanding Points, Lines, and Planes (pp. 6 11) Vocabulary EXERCISES
Vocabulary acute angle.................. 1 adjacent angles.............. 8 angle....................... 0 angle bisector............... 3 area........................ 36 base........................ 36
More informationPoints that live on the same line are. Lines that live on the same plane are. Two lines intersect at a.
For points through E, plot and label the points on the coordinate plane and then state the quadrant each point is located in. If the point does not live in a quadrant, state where it falls. LOTION (-3,
More informationMs. Campos 7 th Grade. Unit 14- Angles
Ms. Campos 7 th Grade Unit 14- Angles 2017-2018 Date Lesson Topic Homework 3 W 5/16 1 Complementary Angles Lesson 1 - Page 5 4 T 5/17 2 Supplementary Angles Lesson 2 Page 9 5 F 5/18 3 Vertical Angles Lesson
More informationGeometry Unit 4a - Notes Triangle Relationships
Geometry Unit 4a - Notes Triangle Relationships This unit is broken into two parts, 4a & 4b. test should be given following each part. Triangle - a figure formed by three segments joining three noncollinear
More informationGrade 6 Math Circles February 29, D Geometry
1 Universit of Waterloo Facult of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Feruar 29, 2012 2D Geometr What is Geometr? Geometr is one of the oldest ranches in
More informationdescribes a ray whose endpoint is point A. g. A plane has no thickness. h. Symbols XY and YX describe the same line. i. Symbols AB
RVIW FOR TH GOMTRY MITRM XM. 1. True or False? e prepared to explain your answer. a. efinitions and theorems are very important in mathematics but every mathematical system must contain some undefined
More informationBoardworks Ltd KS3 Mathematics. S1 Lines and Angles
1 KS3 Mathematics S1 Lines and Angles 2 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons 3 Lines In Mathematics,
More informationChapter 8. Properties of Triangles and Quadrilaterals. 02/2017 LSowatsky
Chapter 8 Properties of Triangles and Quadrilaterals 02/2017 LSowatsky 1 8-1A: Points, Lines, and Planes I can Identify and label basic geometric figures. LSowatsky 2 Vocabulary: Point: a point has no
More informationName Period Date GRADE 7: MATHEMATICS COMMON CORE SUPPLEMENT ANGLES, DRAWINGS, AND ALGEBRAIC CONNECTIONS
Name Period Date 7-CORE3.1 Geometric Figures Measure and draw angles using a protractor. Review facts about interior angles of triangles and quadrilaterals. Find missing angle measures in geometric diagrams.
More informationSTEPS FOR FULL CREDIT 1. Complete, show all work 2. Check 3. Correct. Study all geometry vocabulary words from your chapter packet.
ccelerated Review 9: Geometric Relationships Name: 1. 2. STEPS FOR FULL REIT 1. omplete, show all work 2. heck 3. orrect Study all geometry vocabulary words from your chapter packet. aleb drew a quadrilateral
More informationProving Lines Parallel
Proving Lines Parallel Proving Triangles ongruent 1 Proving Triangles ongruent We know that the opposite sides of a parallelogram are congruent. What about the converse? If we had a quadrilateral whose
More information1. Measuring Angles (4).notebook October 21, 2014
IWBAT estimate, classify, measure and draw acute, obtuse, right, straight, 180+, complementary, supplementary, and vertical angles. 1 Angles are measured in degrees! 2 Please Create a Vocabulary section
More informationUnit. Key Words. In this unit you will learn to: segment. vertex. acute. obtuse. estimate. regular polygon. eight
1 Unit a s n e d l g Polygons n Key Words The Eiffel Tower in Paris, France, is 324 m tall. It was built in 1889 and was the tallest structure in the world for 41 years. It is one of the most famous monuments
More informationGeometry Definitions, Postulates, and Theorems
Geometry efinitions, Postulates, and Theorems hapter : Similarity Section.1: Ratios, Proportions, and the Geometric ean Standards: Prepare for 8.0 Students know, derive, and solve problems involving the
More information