Section 1-1 Points, Lines, and Planes

Size: px
Start display at page:

Download "Section 1-1 Points, Lines, and Planes"

Transcription

1 Section 1-1 Points, Lines, and Planes

2 I CAN. Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in space.

3 Undefined Term- Words, usually readily understood, that are only explained using examples and descriptions. Point Line Plane

4 Point- A specific location. Drawn: as a dot Named by: a capital letter

5 Line- A straight path that continues forever in both directions. Drawn: with an arrowhead at each end Named by: the letters representing two points on the line or a lowercase script letter

6 Plane- A flat surface that extends indefinitely in all directions. Drawn: As a shaded, slanted 4-sided figure Named by: a capital script letter or by the letters naming three noncollinear points.

7 Collinear- Points that lie on the same line. Coplanar- Points that lie in the same plane.

8 Use the figure to name each of the following. a) A line containing point A b) A plane containing point C

9 Use the figure to name each of the following. a) A line containing point W b) A plane containing point X

10 Name the geometric terms modeled by each object. a) The long hand on a clock. b) A 10 X 12 patio c) The location where the corner of a driveway meets the road

11 Intersection A set of points common to two or more geometry figures. Two lines intersect at a point. Two planes intersect at a line.

12 Draw and label a figure for the relationship given. Point P represents the intersection of AB and CD

13 Draw and label a figure for the relationship given. TU lies in plane Q and contains point R.

14 Draw and label a figure for the relationship given. QR intersects plane T at point S.

15 Draw and label a figure for the relationship given. Lines GH and JK intersect at L for G(-1, -3), H(2, 3), J(-3, 2), and K(2, -3) on a coordinate plane. Point M is coplanar with these points, but not collinear with GH or JK

16 Draw and label a figure for the relationship given. Lines AB and CD intersect at E for A(-2, 4), B(0, -2), C(-3, 0), and D(3, 3) on a coordinate plane. Point F is coplanar with these points, but not collinear with AB or CD

17 Definitions (Defined Terms) terms that are explained using undefined terms and/or other defined terms. Space- A boundless three-dimensional set of all points.

18 A) How many planes appear in this figure? B) Name three points that are collinear. C) Are points G, A, B, and E coplanar? Explain. D) At what point do EF and intersect? AB

19 A) How many planes appear in this figure? B) Name three points that are collinear. C) Name the intersection of plane HDG with plane X. D) At what point do LM and EF intersect?

20 Section 1-2 Linear Measure

21 I CAN. Measure segments. Calculate with measures.

22 Line Segment (Segment)- A measurable part of a line that consists of two points, called endpoints, and all the points between them. The length or measure of a segment always includes a unit of measure, such as meter or inch. All measurements are approximations dependent upon the smallest unit of measure available on the measuring instrument.

23 *Metric measurements (centimeters, millimeters, etc.) are written as a decimal. *Standard measurements (inches, feet, etc.) are written as a fraction.

24 Find the length of CD using each ruler.

25 Find the length of CD using each ruler.

26 Find the length of AB using each ruler.

27 Find the length of AB using each ruler.

28 Find the length of AB using each ruler.

29 Find the length of AB using each ruler.

30 Find the length of CD using each ruler.

31 Find the length of CD using each ruler.

32 Between- For any two points, there is a point between them such that the two pieces add to equal to the whole piece. Point M is between points P and Q if and only if P, Q and M are collinear and PM + MQ = PQ

33 Find AC. Assume that the figure is not drawn to scale.

34 Find EG. Assume that the figure is not drawn to scale.

35 Find DE. Assume that the figure is not drawn to scale.

36 Find AB. Assume that the figure is not drawn to scale.

37 Find the length of LM if M lies between L and N, LN = 4 cm, and MN = 2.6 cm.

38 Find y and PQ if P is between Q and R, PQ = 2y, QR = 3y + 1, and PR = 21.

39 Find x and ST if T is between S and U, ST=7x, SU=45, and TU=5x 3.

40 Congruent- Having the same measure. Congruent Segments Segments that have the same measure. is read is congruent to. XY PQ Red slashes on the figure also indicates that segments are congruent.

41 In the graph, suppose a segment was drawn along the top of each bar. Which states have segments that are congruent? Explain.

42 Name the congruent segments in the sign shown.

43 Section 1-2 Extension Absolute Error and Relative Error

44 I CAN. Determine the absolute error of a measurement. Determine the relative error of a measurement.

45 Absolute Error one half the unit of measure for any measurement. 1 AE 2 smallest unit The smaller the unit of measure, the more precise the measurement.

46 Find the absolute error of each measurement. Then explain its meaning. A) 6.4 centimeters B) 4.2 meters

47 Find the absolute error of each measurement. Then explain its meaning. A) 2 ¼ inches B) 1 ½ inches

48 Significant Digits the digits that are used to express a measurement in precision. To determine whether digits are considered significant, use the following rules: Nonzero digits are always significant. In whole numbers, zeros are significant if they fall between nonzero digits. In decimal numbers greater than or equal to 1, every digit is significant. In decimal numbers less than 1, the first nonzero digit and every digit to the right are significant.

49 Determine the number of significant digits in each measurement. A) meters B) centimeters C) 779,000 mi D) 50,008 ft E) m

50 Relative Error RE Absolute Error Expected Measure

51 A manufacturer measures each part for a piece of equipment to be 23 centimeters in length. Find the relative error of this measurement.

52 Find the relative error of each measurement. A) 3.2 mi B) 1 ft C) 26 ft

53 Section 1-3 Distance and Midpoints

54 I CAN. Find the distance between two points. Find the midpoint of a segment.

55 The distance between two points is the length of the segment with those points as its endpoints. Distance on a Number Line Find the absolute values of the difference between their coordinates. Coordinate Plane Distance Formula d 2 2 x x y y

56 Use the number line to find CD.

57 Use the number line to find the length of the indicated segment. A) BE B) AC C) CF

58 Irrational Number a number that cannot be expressed as a terminating or repeating decimal.

59 Find the distance between R(5, 1) and S(-3, -3).

60 Find the distance between C(-4, -6) and D(5, -1).

61 Midpoint- The point halfway between the endpoints of a segment. Number Line x 1 x 2 2 Coordinate Plane Midpoint Formula x x y y 1 2,

62 Ex. Find Coordinates of Midpoint Find the coordinate of the midpoint of PQ

63 Find the coordinates of M, the midpoint of for P(-1, 2) and Q(6, 1). PQ

64 Find the coordinates of M, the midpoint of for S(-6, 3) and T(1, 0). ST

65 To Find a Missing Endpoint 1. Find a pattern from the endpoint to the midpoint. 2. Continue the pattern to find the missing endpoint.

66 Find the coordinates of X if Y(-2, 2) is the midpoint of and Z has coordinates (2, 8). XZ

67 Find the coordinates of D if E(-6, 4) is the midpoint of and F has coordinates (-5, -3) DF

68 Segment Bisector- A segment, line, or plane that cuts a segment into two equal pieces.

69 What is the measure of BC if B is the midpoint of AC?

70 What is the measure of PR if Q is the midpoint of PR?

71 Section 1-4 Angle Measure

72 I CAN. Measure and classify angles. Identify and use congruent angles and the bisector of an angle.

73 Ray A part of a line that has one endpoint and extends indefinitely in one direction. To name a ray always start with the endpoint.

74 Opposite Rays- Two rays that form a straight line. Since both rays share a common endpoint, opposite rays are collinear.

75 Angle- The intersection of two noncollinear rays at a common endpoint. Sides- The rays of an angle. Vertex- The point on an angle where the two rays intersect.

76 An angle divides a plane into three distinct parts. Points A, D and E lie on the angle. Points C and B lie in the interior of the angle. Points F and G lie in the exterior of the angle.

77 Interior- A point that does not lie on the angle itself and lies inside the angle. Exterior- A point that does not lie on the angle itself and lies outside the angle.

78 To name an angle: Naming Angles Use the number inside the angle Use the three points that make up the angle, always putting the vertex in the middle.

79 A) Name all angles that have W as a vertex. B) Name the sides of 1. C) Write another name for WYZ.

80 Use the map of a high school shown. A) Name all angles that have B as a vertex. B) Name the sides of 3. C) Write another name for GHL. D) Name a point in the interior of DBK.

81 Degree- A unit measure used in measuring angles and arcs. The degree results from dividing the distance around a circle into 360 parts.

82 To measure an angle, you can use a protractor. Angle PQR is a 65 degree angle. We say the degree measure or m PQR = 65

83 Right Angle- An angle with a degree measure of 90. Acute Angle- An angle with a degree measure less than 90.

84 Obtuse Angle- An angle with degree measure greater than 90 and less than 180.

85 Use a protractor to measure the angle to the nearest degree. Classify each angle as right, acute, or obtuse. A) PMQ B) PMR C) QMS

86 Congruent Angles Angles that have the same measure. Arcs on the figure also indicate which angles are congruent.

87 Angle Bisector- A ray that divides an angle into two congruent angles.

88 ABC DBF. If m ABC = 6x +2 and m DBF = 8x 14, find the actual measurements of ABC and DBF.

89 In the figure, and are opposite rays, and bisects JKL. If JKN 8x 13 and find m JKN. KJ KM KN m m NKL 6x 11

90 Section 1-5 Angle Relationships

91 I CAN. Identify and use special pairs of angles. Identify perpendicular lines.

92 Adjacent angles- Two angles beside each other, that share a side and a vertex. Examples Nonexample

93 Vertical angles- Two angles across from each other formed by intersecting lines.

94 Linear pair- Two angles that make a straight line.

95 Name an angle pair that satisfies each condition. A) Two obtuse vertical angles B) Two acute adjacent angles C) Name a linear pair

96 Complementary angles- Two angles with measures that have a sum of 90.

97 Supplementary angles- Two angles with measure that have a sum of 180.

98 Find the measures of two complementary angles if the difference in the measures of the two angles is 12.

99 Find the measures of two supplementary angles if the difference in the measures of the two angles is 18.

100 Perpendicular- Two lines that intersect at a 90 degree angle. Symbol: is read is perpendicular to. Perpendicular lines intersect to form four right angles. Perpendicular lines intersect to form congruent adjacent angles. Segments and rays can be perpendicular to lines or other line segments and rays. The right angle symbol in the figure indicates that the lines are perpendicular.

101 Find x and y so that BE and AD are perpendicular.

102 Find x and y so that PR and SQ are perpendicular.

103 Determine whether each statement can be assumed from the figure. A) LPM and MPO are adjacent. B) OPQ and LPM are complementary. C) LPO and QPO are a linear pair.

104 Determine whether each statement can be assumed from the figure. A) KHJ and GHM are complementary. B) GHK and JHK are a linear pair. HL HM C) and are perpendicular.

105 Section 1-6 Two-Dimensional Figures

106 I CAN. Identify and name polygons. Find perimeter, circumference, and area of two-dimensional figures.

107 Polygon- A closed figure formed by a finite number of coplanar segments called sides. The sides that have a common endpoint are noncollinear, and Each side intersects exactly two other sides, but only at their endpoints, called the vertices. Vertex the point where two sides intersect.

108

109 Concave- A polygon for which there is a line containing a side of the polygon that also contains a point in the interior of the polygon. On a concave polygon, part of the figure caves in.

110 Convex- A polygon for which there is no line that contains both a side of the polygon and a point in the interior of the polygon.

111 n-gon- A polygon with n sides. Number of Sides Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

112 Regular polygon- A convex polygon in which all of the sides are congruent and all of the angles are congruent. Octagon PQRSTUVW is a regular octagon.

113 Irregular polygon- A polygon in which all the sides are not congruent, or all the angles are not congruent, or a polygon that is concave.

114 Name each polygon by its name of sides. Then classify it as convex or concave and regular or irregular.

115 Name each polygon by its name of sides. Then classify it as convex or concave and regular or irregular.

116 Perimeter- The sum of the lengths of the sides of a polygon. Circumference- The distance around a circle. Area- The number of square units needed to cover a surface.

117 Perimeter, Circumference, and Area

118 Find the perimeter or circumference and area of the figure.

119 Find the perimeter or circumference and area of the figure.

120 Yolanda has 26 centimeters of cording to frame a photograph in her scrapbook. Which of these shapes would use most or all of the cording and enclose the largest area? A) right triangle with each leg about 7 cm long B) Circle with a radius of about 4 cm C) Rectangle with a length of 8 cm and a width of 4.5 cm D) Square with side length of 6 cm

121 Find the perimeter and area of triangle PQR if P(-1, 3), Q(-3, -1), and R(4, -1). 2 Use the Distance Formula d x x y y1

122 Section 1-7 Three-Dimensional Figures

123 I CAN. Identify and name three-dimensional figures. Find surface area and volume.

124 Polyhedron Closed three-dimensional figures made up of flat polygonal regions. Face A flat surface of a polygon. Edges The line segments where the faces intersect. Vertices The point where three or more edges intersect.

125 Solids that are Polyhedrons Prism A polyhedron with two parallel congruent faces called bases connected by parallelogram faces. Pyramid A polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex.

126 Polyhedrons or polyhedra are named by the shape of their bases.

127 Solids that are not Polyhedrons Cylinder A solid with congruent parallel circular bases connected by a curved surface. Cone A solid with a circular base connected by a curved surface to a singular vertex. Sphere A set of points in space that are the same distance from a given point.

128 Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

129 Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

130 Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

131 Regular polyhedron A polyhedron in which all of the faces are regular congruent polygons. Platonic solids The five regular polyhedra: tetrahedron, hexahedron, octahedron, dodecahedron, or icosahedron.

132 Surface Area A two-dimensional measurement of the surface of a solid. Volume The measure of the amount of space enclosed by a solid figure.

133 Surface Area and Volume

134 Find the surface area and volume of the square pyramid.

135 Find the surface area and volume of the cylinder.

136 The diameter of the pool Mr. Sato purchased is 8 feet. The height of the pool is 20 inches. Find each measure to the nearest tenth. A) Surface Area of Pool B) Volume of Pool

Geometry Reasons for Proofs Chapter 1

Geometry Reasons for Proofs Chapter 1 Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms

More information

Geometry 1-1. Non-collinear Points not on the same line. Need at least 3 points to be non-collinear since two points are always collinear

Geometry 1-1. Non-collinear Points not on the same line. Need at least 3 points to be non-collinear since two points are always collinear Name Geometry 1-1 Undefined terms terms which cannot be defined only described. Point, line, plane Point a location in space Line a series of points that extends indefinitely in opposite directions. It

More information

Date Name of Lesson Assignments & Due Dates

Date Name of Lesson Assignments & Due Dates Date Name of Lesson Assignments & Due Dates Basic Terms Points, Lines and Planes Constructions (Copy Angle and Segment) Distance Formula Activity for Distance Formula Midpoint Formula Quiz Angle Measure

More information

Dear Parents/Students,

Dear Parents/Students, Dear Parents/Students, In the summer time, many necessary mathematical skills are lost due to the absence of daily exposure. The loss of skills may result in a lack of success and unnecessary frustration

More information

Geometry. Chapter 1 Points, Lines, Planes, and Angles

Geometry. Chapter 1 Points, Lines, Planes, and Angles Geometry Chapter 1 Points, Lines, Planes, and Angles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** Algebraic Equations Review Keystone Vocabulary

More information

Geometry Semester 1 Final Exam Study Guide FCS, Mr. Garcia

Geometry Semester 1 Final Exam Study Guide FCS, Mr. Garcia Name Date Period This is your semester 1 exam review study guide. It is designed for you to do a portion each day until the day of the exam. You may use the following formula to calculate your semester

More information

Geometry Practice. 1. Angles located next to one another sharing a common side are called angles.

Geometry Practice. 1. Angles located next to one another sharing a common side are called angles. Geometry Practice Name 1. Angles located next to one another sharing a common side are called angles. 2. Planes that meet to form right angles are called planes. 3. Lines that cross are called lines. 4.

More information

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance

More information

Term Definition Figure

Term Definition Figure Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do

More information

Lines Plane A flat surface that has no thickness and extends forever.

Lines Plane A flat surface that has no thickness and extends forever. Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that

More information

Reteach. Understanding Points, Lines, and Planes. P point P

Reteach. Understanding Points, Lines, and Planes. P point P Name Date Class 1-1 Understanding Points, Lines, and Planes A point has no size. It is named using a capital letter. All the figures below contain points. line Figure Characteristics Diagram Words and

More information

Moore Catholic High School Math Department

Moore Catholic High School Math Department Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during

More information

SHAPE AND STRUCTURE. Shape and Structure. An explanation of Mathematical terminology

SHAPE AND STRUCTURE. Shape and Structure. An explanation of Mathematical terminology Shape and Structure An explanation of Mathematical terminology 2005 1 POINT A dot Dots join to make lines LINE A line is 1 dimensional (length) A line is a series of points touching each other and extending

More information

Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26)

Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26) Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26) Learning Target: At the end of today s lesson we will be able to successfully name and sketch geometric figures.

More information

pine cone Ratio = 13:8 or 8:5

pine cone Ratio = 13:8 or 8:5 Chapter 10: Introducing Geometry 10.1 Basic Ideas of Geometry Geometry is everywhere o Road signs o Carpentry o Architecture o Interior design o Advertising o Art o Science Understanding and appreciating

More information

Geometry Vocabulary. Name Class

Geometry Vocabulary. Name Class Geometry Vocabulary Name Class Definition/Description Symbol/Sketch 1 point An exact location in space. In two dimensions, an ordered pair specifies a point in a coordinate plane: (x,y) 2 line 3a line

More information

Geometry ~ Chapter 1 Capacity Matrix

Geometry ~ Chapter 1 Capacity Matrix Geometry ~ Chapter 1 Capacity Matrix Learning Targets 1. Drawing and labeling the Geometry Vocabulary 2. Using the distance and midpoint formula 3. Classifying triangles and polygons Section Required Assignments

More information

Unit 10 Study Guide: Plane Figures

Unit 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 information

NORTH HAVEN HIGH SCHOOL. Geometry (Level 2 and Level 3) Summer Assignment 2016

NORTH HAVEN HIGH SCHOOL. Geometry (Level 2 and Level 3) Summer Assignment 2016 221 Elm Street NORTH HAVEN HIGH SCHOOL North Haven, CT 06473 June 2016 Geometry (Level 2 and Level 3) Summer Assignment 2016 Dear Parent(s) or Guardian(s): Your child is currently scheduled to take Geometry

More information

NORTH HAVEN HIGH SCHOOL. Applied Geometry (Level 1) Summer Assignment 2017

NORTH HAVEN HIGH SCHOOL. Applied Geometry (Level 1) Summer Assignment 2017 NORTH HAVEN HIGH SCHOOL 221 Elm Street North Haven, CT 06473 June 2017 Applied Geometry (Level 1) Summer Assignment 2017 Dear Parents, Guardians, and Students, The Geometry curriculum builds on geometry

More information

There are two ways to name a line. What are the two ways?

There are two ways to name a line. What are the two ways? Geometry: 1-1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the two

More information

Chapter 1-2 Points, Lines, and Planes

Chapter 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 information

Grade VIII. Mathematics Geometry Notes. #GrowWithGreen

Grade VIII. Mathematics Geometry Notes. #GrowWithGreen Grade VIII Mathematics Geometry Notes #GrowWithGreen Polygons can be classified according to their number of sides (or vertices). The sum of all the interior angles of an n -sided polygon is given by,

More information

Geometry 10 and 11 Notes

Geometry 10 and 11 Notes Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into

More information

Mrs. Daniel s Geometry Vocab List

Mrs. Daniel s Geometry Vocab List Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Reflectional Symmetry

More information

GEOMETRY is the study of points in space

GEOMETRY 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 information

Moore Catholic High School Math Department

Moore Catholic High School Math Department Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

Index COPYRIGHTED MATERIAL. Symbols & Numerics

Index COPYRIGHTED MATERIAL. Symbols & Numerics Symbols & Numerics. (dot) character, point representation, 37 symbol, perpendicular lines, 54 // (double forward slash) symbol, parallel lines, 54, 60 : (colon) character, ratio of quantity representation

More information

Class Generated Review Sheet for Math 213 Final

Class Generated Review Sheet for Math 213 Final Class Generated Review Sheet for Math 213 Final Key Ideas 9.1 A line segment consists of two point on a plane and all the points in between them. Complementary: The sum of the two angles is 90 degrees

More information

Geometry - Chapter 1 - Corrective #1

Geometry - Chapter 1 - Corrective #1 Class: Date: Geometry - Chapter 1 - Corrective #1 Short Answer 1. Sketch a figure that shows two coplanar lines that do not intersect, but one of the lines is the intersection of two planes. 2. Name two

More information

BENCHMARK Name Points, Lines, Segments, and Rays. Name Date. A. Line Segments BENCHMARK 1

BENCHMARK Name Points, Lines, Segments, and Rays. Name Date. A. Line Segments BENCHMARK 1 A. Line Segments (pp. 1 5) In geometry, the words point, line and plane are undefined terms. They do not have formal definitions but there is agreement about what they mean. Terms that can be described

More information

Test Review: Geometry I TEST DATE: ALL CLASSES TUESDAY OCTOBER 6

Test Review: Geometry I TEST DATE: ALL CLASSES TUESDAY OCTOBER 6 Test Review: Geometry I TEST DATE: ALL CLASSES TUESDAY OCTOBER 6 Notes to Study: Notes A1, B1, C1, D1, E1, F1, G1 Homework to Study: Assn. 1, 2, 3, 4, 5, 6, 7 Things it would be a good idea to know: 1)

More information

25. How would you make the octahedral die shown below?

25. How would you make the octahedral die shown below? 304450_ch_08_enqxd 12/6/06 1:39 PM Page 577 Chapter Summary 577 draw others you will not necessarily need all of them. Describe your method, other than random trial and error. How confident are you that

More information

Mrs. Daniel s Geometry Vocab List

Mrs. Daniel s Geometry Vocab List Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Refectional Symmetry Definition:

More information

1-1. Points, Lines, and Planes. Lesson 1-1. What You ll Learn. Active Vocabulary

1-1. Points, Lines, and Planes. Lesson 1-1. What You ll Learn. Active Vocabulary 1-1 Points, Lines, and Planes What You ll Learn Scan the text in Lesson 1-1. Write two facts you learned about points, lines, and planes as you scanned the text. 1. Active Vocabulary 2. New Vocabulary

More information

Math 6, Unit 8 Notes: Geometric Relationships

Math 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

Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK

Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK [acute angle] [acute triangle] [adjacent interior angle] [alternate exterior angles] [alternate interior angles] [altitude] [angle] [angle_addition_postulate]

More information

Geometry Chapter 1 TEST * Required

Geometry Chapter 1 TEST * Required Geometry Chapter 1 TEST * Required Vocabulary Match each word with the correct definition or description. 1. Plane * A flat surface extending indefinitely The two rays that from an angle Exactly one of

More information

NAME DATE PERIOD. Study Guide and Intervention

NAME DATE PERIOD. Study Guide and Intervention NM T IO 1-5 tudy Guide and Intervention ngle elationships airs of ngles djacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.

More information

Geometry Semester 1 Final Exam Study Guide FCS, Mr. Garcia 12/8/14

Geometry Semester 1 Final Exam Study Guide FCS, Mr. Garcia 12/8/14 Name Date Period This is your semester 1 exam review study guide. It is designed for you to do a portion each day until the day of the exam on Thursday of next week. Topics that we have covered on chapters

More information

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers 1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible

More information

1.1 Understanding the Undefined Terms

1.1 Understanding the Undefined Terms 1.1 Understanding the Undefined Terms Undefined Terms There are three undefined terms in geometry, these words do not have a formal definition. The undefined terms are:,, and. Naming Points, Lines, and

More information

Chapter 1. Essentials of Geometry

Chapter 1. Essentials of Geometry Chapter 1 Essentials of Geometry 1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures so you can use geometry terms in the real world. Essential Question: How do you name

More information

Objectives: (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes

Objectives: (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes Geometry Chapter 1 Outline: Points, Lines, Planes, & Angles A. 1-1 Points, Lines, and Planes (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting

More information

Maintaining Mathematical Proficiency

Maintaining 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 information

HONORS GEOMETRY CHAPTER 1 WORKBOOK

HONORS GEOMETRY CHAPTER 1 WORKBOOK HONORS GEOMETRY CHAPTER 1 WORKBOOK FALL 2016 0 Honors Geometry Skills Review Worksheet For numbers 1 3, solve each equation. 1. 8x 2 = 9 + 7x 2. 12 = 4( 6x 3) 3. 5(1 5x) + 5( 8x 2) = 4x 8x For numbers

More information

TOURNAMENT OF THE TOWNS, Glossary

TOURNAMENT OF THE TOWNS, Glossary TOURNAMENT OF THE TOWNS, 2003 2004 Glossary Absolute value The size of a number with its + or sign removed. The absolute value of 3.2 is 3.2, the absolute value of +4.6 is 4.6. We write this: 3.2 = 3.2

More information

Postulates, Theorems, and Corollaries. Chapter 1

Postulates, Theorems, and Corollaries. Chapter 1 Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a

More information

The radius for a regular polygon is the same as the radius of the circumscribed circle.

The radius for a regular polygon is the same as the radius of the circumscribed circle. Perimeter and Area The perimeter and area of geometric shapes are basic properties that we need to know. The more complex a shape is, the more complex the process can be in finding its perimeter and area.

More information

Geometry Vocabulary. acute angle-an angle measuring less than 90 degrees

Geometry Vocabulary. acute angle-an angle measuring less than 90 degrees Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that

More information

Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume

Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and

More information

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence. Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity

More information

1.1 Building Blocks of Geometry

1.1 Building Blocks of Geometry 1.1 uilding locks of Geometry Name Definition Picture Short Rorm Point A location in space The point P Line An infinite number of points extending in two directions. A line only has length. T M TM Ray

More information

Geometry Final Exam - Study Guide

Geometry Final Exam - Study Guide Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are

More information

Polygons. 5 sides 5 angles. pentagon. no no R89. Name

Polygons. 5 sides 5 angles. pentagon. no no R89. Name Lesson 11.1 Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number of angles

More information

B. Section 1.1. Chapter 1 Review Booklet A. Vocabulary Match the vocabulary term with its definition. 3. A pair of opposite rays on line p.

B. Section 1.1. Chapter 1 Review Booklet A. Vocabulary Match the vocabulary term with its definition. 3. A pair of opposite rays on line p. A. Vocabulary Match the vocabulary term with its definition. Point Polygon Angle Sides Postulate Collinear Opposite Rays Vertical angles Coplanar Linear Pair Complementary Vertex Line Adjacent Plane Distance

More information

CARDSTOCK MODELING Math Manipulative Kit. Student Activity Book

CARDSTOCK MODELING Math Manipulative Kit. Student Activity Book CARDSTOCK MODELING Math Manipulative Kit Student Activity Book TABLE OF CONTENTS Activity Sheet for L.E. #1 - Getting Started...3-4 Activity Sheet for L.E. #2 - Squares and Cubes (Hexahedrons)...5-8 Activity

More information

Pre-Algebra, Unit 10: Measurement, Area, and Volume Notes

Pre-Algebra, Unit 10: Measurement, Area, and Volume Notes Pre-Algebra, Unit 0: Measurement, Area, and Volume Notes Triangles, Quadrilaterals, and Polygons Objective: (4.6) The student will classify polygons. Take this opportunity to review vocabulary and previous

More information

Name Date Period. 1.1 Understanding the Undefined Terms

Name Date Period. 1.1 Understanding the Undefined Terms Name Date Period Lesson Objective: 1.1 Understanding the Undefined Terms Naming Points, Lines, and Planes Point Line Plane Collinear: Coplanar: 1. Give 2 other names for PQ and plane R. 2. Name 3 points

More information

Polygons. 5 sides 5 angles. pentagon. Name

Polygons. 5 sides 5 angles. pentagon. Name Lesson 11.1 Reteach Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number

More information

Geometry Workbook WALCH PUBLISHING

Geometry Workbook WALCH PUBLISHING Geometry Workbook WALCH PUBLISHING Table of Contents To the Student..............................vii Unit 1: Lines and Triangles Activity 1 Dimensions............................. 1 Activity 2 Parallel

More information

1-1 Understanding Points, Lines, and Planes (pp. 6 11) Vocabulary EXERCISES

1-1 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 information

Polygons and Convexity

Polygons and Convexity Geometry Week 4 Sec 2.5 to ch. 2 test Polygons and Convexity section 2.5 convex set has the property that any two of its points determine a segment contained in the set concave set a set that is not convex

More information

Department: Course: Chapter 1

Department: Course: Chapter 1 Department: Course: 2016-2017 Term, Phrase, or Expression Simple Definition Chapter 1 Comprehension Support Point Line plane collinear coplanar A location in space. It does not have a size or shape The

More information

Unit 3. Chapter 1. Foundations of Geometry. Name. Hour

Unit 3. Chapter 1. Foundations of Geometry. Name. Hour Unit 3 Chapter 1 Foundations of Geometry Name Hour 1 Geometry Unit 3 Foundations of Geometry Chapter 1 Monday October 1 Tuesday October 2 1.1 Understanding Points, Lines, & Planes 1.2 Linear Measure DHQ

More information

Geometry Vocabulary Math Fundamentals Reference Sheet Page 1

Geometry Vocabulary Math Fundamentals Reference Sheet Page 1 Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and

More information

Math 7, Unit 8: Geometric Figures Notes

Math 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 information

Math 7, Unit 08: Geometric Figures Notes

Math 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 information

OC 1.7/3.5 Proofs about Parallel and Perpendicular Lines

OC 1.7/3.5 Proofs about Parallel and Perpendicular Lines (Segments, Lines & Angles) Date Name of Lesson 1.5 Angle Measure 1.4 Angle Relationships 3.6 Perpendicular Bisector (with Construction) 1.4 Angle Bisectors (Construct and Measurements of Angle Bisector)

More information

Geometry First Semester Practice Final (cont)

Geometry First Semester Practice Final (cont) 49. Determine the width of the river, AE, if A. 6.6 yards. 10 yards C. 12.8 yards D. 15 yards Geometry First Semester Practice Final (cont) 50. In the similar triangles shown below, what is the value of

More information

Chapter 1 Tools of Geometry. Section 1-1 Points, Lines and Planes. Definitions

Chapter 1 Tools of Geometry. Section 1-1 Points, Lines and Planes. Definitions Chapter 1 Tools of Geometry Section 1-1 Points, Lines and Planes Definitions Undefined terms - terms that are explained using examples and descriptions Defined terms - terms explained using undefined terms

More information

SEVENTH EDITION and EXPANDED SEVENTH EDITION

SEVENTH EDITION and EXPANDED SEVENTH EDITION SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 9-1 Chapter 9 Geometry 9.1 Points, Lines, Planes, and Angles Basic Terms A line segment is part of a line between two points, including the endpoints.

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

More information

Lesson Polygons

Lesson Polygons Lesson 4.1 - Polygons Obj.: classify polygons by their sides. classify quadrilaterals by their attributes. find the sum of the angle measures in a polygon. Decagon - A polygon with ten sides. Dodecagon

More information

Any questions about the material so far? About the exercises?

Any questions about the material so far? About the exercises? Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:

More information

Course: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days

Course: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days Geometry Curriculum Chambersburg Area School District Course Map Timeline 2016 Units *Note: unit numbers are for reference only and do not indicate the order in which concepts need to be taught Suggested

More information

M2 GEOMETRY REVIEW FOR MIDTERM EXAM

M2 GEOMETRY REVIEW FOR MIDTERM EXAM M2 GEOMETRY REVIEW FOR MIDTERM EXAM #1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle.

More information

HS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume

HS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume HS Pre-Algebra Notes Unit 0: Measurement, Area, and Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (5.6) The student will classify polygons. (5.5) The student will validate conclusions

More information

Vocabulary. Term Page Definition Clarifying Example. cone. cube. cylinder. edge of a threedimensional. figure. face of a polyhedron.

Vocabulary. Term Page Definition Clarifying Example. cone. cube. cylinder. edge of a threedimensional. figure. face of a polyhedron. CHAPTER 10 Vocabulary The table contains important vocabulary terms from Chapter 10. As you work through the chapter, fill in the page number, definition, and a clarifying example. cone Term Page Definition

More information

Geometry Foundations Planning Document

Geometry Foundations Planning Document Geometry Foundations Planning Document Unit 1: Chromatic Numbers Unit Overview A variety of topics allows students to begin the year successfully, review basic fundamentals, develop cooperative learning

More information

Indiana State Math Contest Geometry

Indiana State Math Contest Geometry Indiana State Math Contest 018 Geometry This test was prepared by faculty at Indiana University - Purdue University Columbus Do not open this test booklet until you have been advised to do so by the test

More information

PLANE GEOMETRY SKILL BUILDER ELEVEN

PLANE 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 information

Section 1.1 Notes. Points - have no size or dimension and named using capital letters A

Section 1.1 Notes. Points - have no size or dimension and named using capital letters A Section 1.1 Notes Building Blocks of Geometry Undefined Terms: Points - have no size or dimension and named using capital letters A Lines - have no thickness (1D) and extend forever. Named using 2 points

More information

Point A location in geometry. A point has no dimensions without any length, width, or depth. This is represented by a dot and is usually labelled.

Point A location in geometry. A point has no dimensions without any length, width, or depth. This is represented by a dot and is usually labelled. Test Date: November 3, 2016 Format: Scored out of 100 points. 8 Multiple Choice (40) / 8 Short Response (60) Topics: Points, Angles, Linear Objects, and Planes Recognizing the steps and procedures for

More information

Chapter 6 Review. Find MG and NG. In Exercises 1 4, find the indicated measure. State how you know. 1. AD 2. GJ. 3. PQ 4. m

Chapter 6 Review. Find MG and NG. In Exercises 1 4, find the indicated measure. State how you know. 1. AD 2. GJ. 3. PQ 4. m Name Date Chapter 6 Review In Exercises 1 4, find the indicated measure. State how you know. 1. AD 2. GJ 3. PQ 4. m DGF 5.In the figure at the right, what value of x makes G the incenter of JKL? 6. LG

More information

FGCU Invitational Geometry Individual 2014

FGCU Invitational Geometry Individual 2014 All numbers are assumed to be real. Diagrams are not drawn to scale. For all questions, NOTA represents none of the above answers is correct. For problems 1 and 2, refer to the figure in which AC BC and

More information

EOC Review: Practice: 1. In the circle below, AB = 2BC. What is the probability of hitting the shaded region with a random dart?

EOC Review: Practice: 1. In the circle below, AB = 2BC. What is the probability of hitting the shaded region with a random dart? EOC Review: Focus Areas: Trigonometric Ratios Area and Volume including Changes in Area/Volume Geometric Probability Proofs and Deductive Reasoning including Conditionals Properties of Polygons and Circles

More information

Math-in-CTE Lesson Plan Template

Math-in-CTE Lesson Plan Template Lesson Development Math-in-CTE Lesson Plan Template Lesson Title: Basic Geometric Concepts Lesson # Author(s): Phone Number(s): E-mail Address(es): Juan Carlos Martínez jcmartinez@dadeschoolsnet Bergman

More information

heptagon; not regular; hexagon; not regular; quadrilateral; convex concave regular; convex

heptagon; not regular; hexagon; not regular; quadrilateral; convex concave regular; convex 10 1 Naming Polygons A polygon is a plane figure formed by a finite number of segments. In a convex polygon, all of the diagonals lie in the interior. A regular polygon is a convex polygon that is both

More information

Example: The following is an example of a polyhedron. Fill the blanks with the appropriate answer. Vertices:

Example: The following is an example of a polyhedron. Fill the blanks with the appropriate answer. Vertices: 11.1: Space Figures and Cross Sections Polyhedron: solid that is bounded by polygons Faces: polygons that enclose a polyhedron Edge: line segment that faces meet and form Vertex: point or corner where

More information

3. Write a conditional statement ( If.., then ) from the sentence: A whole number is an integer. If, then.

3. Write a conditional statement ( If.., then ) from the sentence: A whole number is an integer. If, then. Geometry: Spring Semester Final Exam Review Worksheet Name Hour Score /30 1. Refer to the diagram at the right. a. Name 2 lines in the diagram. b. Name the intersection of WY and XZ. b. Name the intersection

More information

Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review

Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review Geometry H Final Exam Review Chapter 1-3 Parallel Lines, Vocab, and Linear Equations Review 1. Use the figure at the right to answer the following questions. a. How many planes are there in the figure?

More information

Jumpstarters for Geometry. Table of Contents. Table of Contents

Jumpstarters for Geometry. Table of Contents. Table of Contents Table of Contents Table of Contents Introduction to the Teacher...1 Lines, Rays, and Line Segments...2 Classifying Angles...3 Measuring and Drawing Angles...4 Classifying Pairs of Lines...5 Special Pairs

More information

1. Revision Description Reflect and Review Teasers Recall basics of geometrical shapes.

1. Revision Description Reflect and Review Teasers Recall basics of geometrical shapes. 1. Revision Description Reflect and Review Teasers Recall basics of geometrical shapes. A book, a birthday cap and a dice are some examples of 3-D shapes. 1) Write two examples of 2-D shapes and 3-D shapes

More information

Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND

Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 2 WHAT YOU WILL LEARN Points, lines, planes, and

More information

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second

More information

Answer Key: Three-Dimensional Cross Sections

Answer Key: Three-Dimensional Cross Sections Geometry A Unit Answer Key: Three-Dimensional Cross Sections Name Date Objectives In this lesson, you will: visualize three-dimensional objects from different perspectives be able to create a projection

More information

1) Draw line m that contains the points A and B. Name two other ways to name this line.

1) Draw line m that contains the points A and B. Name two other ways to name this line. 1) Draw line m that contains the points A and B. Name two other ways to name this line. 2) Find the next 3 terms in the sequence and describe the pattern in words. 1, 5, 9, 13,,, 3) Find the next 3 terms

More information

Dear Parents and Students,

Dear Parents and Students, Dear Parents and Students, Mathematics is a discipline that constantly builds on previous knowledge. Students entering Honors Geometry will be expected to recall and apply the material that they learned

More information