11.3 Curves, Polygons and Symmetry


 Moris Hodge
 2 years ago
 Views:
Transcription
1 11.3 Curves, Polygons and Symmetry
2 Polygons
3 Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints.
4 Closed Definition A shape is closed if the endpoints meet.
5 Polygon Definition A polygon is a simple closed curve where all sides are line segments. There are no arcs allowed.
6 Concave v. Convex Definition A polygon is convex if any segment connecting any two points in the interior of the curve lies entirely inside the curve. Definition A polygon is concave if any segment connecting two points of the interior of a curve passes outside of the curve
7 Classification of Polygons by Sides Number of Sides 3 Polygon Name
8 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle
9 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4
10 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5
11 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6
12 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7
13 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8
14 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9
15 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10
16 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11
17 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 hendecagon 12
18 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 hendecagon 12 dodecagon n
19 Classification of Polygons by Sides Number of Sides Polygon Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 hendecagon 12 dodecagon n ngon
20 Regular Polygons Definition A regular polygon is a polygon where all sides and interior angles are congruent. What is the name of a regular triangle?
21 Regular Polygons Definition A regular polygon is a polygon where all sides and interior angles are congruent. What is the name of a regular triangle? What is the name of a regular quadrilateral?
22 Regular Polygons Definition A regular polygon is a polygon where all sides and interior angles are congruent. What is the name of a regular triangle? What is the name of a regular quadrilateral?
23 Exterior Angle Sum What is the exterior angle sum for a square?
24 Exterior Angle Sum What is the exterior angle sum for a square? What is the exterior angle sum for a pentagon?
25 Exterior Angle Sum What is the exterior angle sum for a square? What is the exterior angle sum for a pentagon? Conjecture?
26 Exterior Angle Sum What is the exterior angle sum for a square? What is the exterior angle sum for a pentagon? Conjecture? Exterior Angle Sum The exterior angle sum for a convex polygon is 360
27 Triangle Classifications We can classify triangles in two ways  by the number of congruent sides and by the types of angles. What types of triangles are there?
28 Triangle Classifications We can classify triangles in two ways  by the number of congruent sides and by the types of angles. What types of triangles are there? Types of Triangles By Side By Angle scalene no congruent sides acute all angles acute isosceles at least two congruent sides right one right angle equilateral all sides congruent obtuse one obtuse angle
29 Triangle Classifications We can classify triangles in two ways  by the number of congruent sides and by the types of angles. What types of triangles are there? Types of Triangles By Side By Angle scalene no congruent sides acute all angles acute isosceles at least two congruent sides right one right angle equilateral all sides congruent obtuse one obtuse angle Important to note: your book correctly states that a triangle that is equilateral is also isosceles. Some books incorrectly say that these are disjoint descriptions.
30 Quadrilateral Classifications That we want to do here is list all properties we know about the different quadrilaterals. Included in these properties we want to point out are: if opposite sides are parallel if opposite sides are congruent if opposite angles are congruent if adjacent angles are congruent if adjacent sides are perpendicular if diagonals bisect each other if diagonals are perpendicular if diagonals are congruent if there is at least one pair of parallel sides if there is at least one pair of congruent sides
31 Parallelogram
32 Parallelogram opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel
33 Rectangle
34 Rectangle opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel
35 Rectangle opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel diagonals are congruent adjacent sides are perpendicular
36 Rhombus
37 Rhombus opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel
38 Rhombus opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel adjacent sides congruent
39 Square
40 Square opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel diagonals are congruent adjacent sides are perpendicular
41 Square opposite sides congruent opposite angles are congruent diagonals bisect each other opposite sides are parallel diagonals are congruent adjacent sides are perpendicular adjacent sides congruent
42 Kite
43 Kite two pairs of congruent adjacent sides diagonals are perpendicular one pair of congruent angles
44 Trapezoid
45 Trapezoid at least one pair of parallel sides
46 Isosceles Trapezoid
47 Isosceles Trapezoid at least one pair of parallel sides
48 Isosceles Trapezoid at least one pair of parallel sides at least one pair of congruent sides base angles congruent
49 Hierarchy for Triangles For triangles, here is the relationship between them based on sides. Triangle Scalene Triangle Isosceles Triangle Equilateral Triangle
50 Hierarchy for Quadrilaterals Can you come up with a similar diagram for quadrilaterals?
51 Hierarchy for Quadrilaterals Can you come up with a similar diagram for quadrilaterals? Quadrilateral Kite Trapezoid Parallelogram Isosceles Trapezoid Rhombus Rectangle Square
52 Symmetries 1 Line symmetry 2 Rotational symmetry 3 Point symmetry
53 Line Symmetry Line Symmetry A figure has line symmetry if we can draw a line that divides the figure in half. We can think of this as the line over which we can fold the figure to make it fold onto itself.
54 How Many Lines of Symmetry?
55 How Many Lines of Symmetry?
56 Rotational Symmetry Rotational (Turn) Symmetry A figure has rotational symmetry if we can rotate the figure some number of degrees less than 360 and get the same exact polygon back in the same orientation. We describe the property as α degrees of turn symmetry.
57 Rotational Symmetry?
58 Rotational Symmetry?
59 Point Symmetry Point Symmetry Point symmetry is the term that we use when a figure has 180 turn symmetry. Which of our figures have point symmetry?
60 Diagonals Diagonal A diagonal is a line segment that joins to nonadjacenet vertices.
61 Diagonals Diagonal A diagonal is a line segment that joins to nonadjacenet vertices. The question is, how many diagonals does a convex polygon have?
62 Diagonals Diagonal A diagonal is a line segment that joins to nonadjacenet vertices. The question is, how many diagonals does a convex polygon have? Number of Diagonals A convex polygon with n sides we have n(n 3) 2 diagonals.
Geometry. Unit 6. Quadrilaterals. Unit 6
Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationUNIT H1 Angles and Symmetry Activities
UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)
More informationLine. A straight path that continues forever in both directions.
Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A
More information15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution
15 Polygons MEP Y8 Practice Book B 15.1 Angle Facts In this section we revise some asic work with angles, and egin y using the three rules listed elow: The angles at a point add up to 360, e.g. a c a +
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,
More informationA convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.
hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.
More informationPolygons are figures created from segments that do not intersect at any points other than their endpoints.
Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles
More information7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014
Chapter 7 Polygons Polygon 1. Closed Figure # of Sides Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 2. Straight sides/edges 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 15 Pentadecagon
More informationparallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect
parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross
More information1 of 69 Boardworks Ltd 2004
1 of 69 2 of 69 Intersecting lines 3 of 69 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are
More informationLEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.
Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the
More informationName: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work
Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work 1. An equilateral triangle always has three 60 interior angles. 2. A line segment
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationAnalysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 550 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website
Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 550 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra
More information61 Properties and Attributes of Polygons
61 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a threesided polygon. triangle 2. A? is a foursided polygon. quadrilateral Evaluate each expression
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationGeometry Vocabulary Booklet
Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular
More informationBegin recognition in EYFS Age related expectation at Y1 (secure use of language)
For more information  http://www.mathsisfun.com/geometry Begin recognition in EYFS Age related expectation at Y1 (secure use of language) shape, flat, curved, straight, round, hollow, solid, vertexvertices
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationPOLYGONS
POLYGONS 8.1.1 8.1.5 After studying triangles and quadrilaterals, students now extend their study to all polygons. A polygon is a closed, twodimensional figure made of three or more nonintersecting straight
More informationPage How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9
Acc. Geometery Name Polygon Review Per/Sec. Date Determine whether each of the following statements is always, sometimes, or never true. 1. A regular polygon is convex. 2. Two sides of a polygon are noncollinear.
More information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More informationGrade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse
More informationUnit 8. Ch. 8. "More than three Sides"
Unit 8. Ch. 8. "More than three Sides" 1. Use a straightedge to draw CONVEX polygons with 4, 5, 6 and 7 sides. 2. In each draw all of the diagonals from ONLY ONE VERTEX. A diagonal is a segment that joins
More informationPROPERTIES OF TRIANGLES AND QUADRILATERALS
Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 21 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS
More informationNovember 11, Polygons. poly means "many" gon means "angles" polygon means "many angles"
3.5 Polygons poly means "many" gon means "angles" polygon means "many angles" note that each polygon is formed by coplanar segments (called sides) such that: each segment intersects exactly 2 other segments,
More informationEstimating Angle Measures
1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle
More informationacute angle acute triangle Cartesian coordinate system concave polygon congruent figures
acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles
More informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
More information19. [Shapes] less than. The angle appears greater than 90. Check by placing the corner of a Maths Mate page inside the angle.
19. [Shapes] Skill 19.1 Comparing angles to a right angle. Place the corner of a page (which is a right angle) at the corner (vertex) of the angle. Align the base of the page with one line of the angle.
More informationGeometry. 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 informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
More informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More informationSu.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)
MA.912.G.2 Geometry: Standard 2: Polygons  Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures
More information115 Polygons ANSWER: ANSWER: ANSWER:
Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 1. 5. KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What
More informationA of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle?
8.1 Find Angle Measures in Polygons SWBAT: find interior and exterior angle measures in polygons. Common Core: G.CO.11, G.CO.13, G.SRT.5 Do Now Fill in the blank. A of a polygon is a segment that joins
More information1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?
1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional
More informationChapter Three. Parallel Lines and Planes
Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately
More informationAngle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationTEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements.
TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. The student will select an appropriate representation to solve
More informationMensuration Introduction
Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement
More information**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.
Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:
More informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationSHOW YOUR WORK CHECK YOUR WORK VALIDATE YOUR WORK! Unit 6: POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???
Unit 6: POLYGONS Are these polygons? Justify your answer by explaining WHY or WHY NOT??? a) b) c) Yes or No Why/Why not? Yes or No Why/Why not? Yes or No Why/Why not? a) What is a CONCAVE polygon? Use
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
More informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationTopic : Exterior Angles  Worksheet How many degrees are there in the sum of the exterior angles of a regular hexagon?
Topic : Exterior Angles  Worksheet 1 regular hexagon? polygon having 20 3. If each polygon contains 40 O how many each polygon having 16 angle of a regular polygon having 8 a 5 sided polygon? polygon
More informationChapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationThe angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons.
Interior Angles of Polygons The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. The sum of the measures of the interior angles of a triangle
More informationConstructing Symmetrical Shapes
07NEM5WBAnsCH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationActivity Set 4. Trainer Guide
Geometry and Measurement of Plane Figures Activity Set 4 Trainer Guide Int_PGe_04_TG GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set #4 NGSSS 3.G.3.1 NGSSS 3.G.3.3 NGSSS 4.G.5.1 NGSSS 5.G.3.1 Amazing
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More information(n = # of sides) One interior angle:
6.1 What is a Polygon? Regular Polygon Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n  2) Sum of the exterior angles of a polygon =
More informationUnit 8 Geometry QUADRILATERALS. NAME Period
Unit 8 Geometry QUADRILATERALS NAME Period 1 A little background Polygon is the generic term for a closed figure with any number of sides. Depending on the number, the first part of the word Poly is replaced
More informationGrade 4  Module 4: Angle Measure and Plane Figures
Grade 4  Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles
More information61 Angles of Polygons
Find the sum of the measures of the interior angles of each convex polygon. 1. decagon A decagon has ten sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationTons of Free Math Worksheets at:
Topic: Sum of Interior Angles Worksheet 1 a pentagon? nine 3. If the polygon equals 1080, then determine the 1620º? interior angles equals 6840s? n eighteen a Octagon? seventeen polygon equals 1980, how
More informationCLASSIFYING GEOMETRIC SHAPES
4 CLASSIFYING GEOMETRIC SHAPES INSTRUCTIONAL ACTIVITY Lesson 2 LEARNING GOAL Students will classify shapes according to single attributes. PRIMARY ACTIVITY Students will create groups of shapes that have
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationCLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS  SIMPLE CLOSED CURVE FIGURES AND POLYGONS
CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS  SIMPLE CLOSED CURVE FIGURES AND POLYGONS Material: Geometry Stick Box and Board A piece of string Paper and scissors Paper labels and pencil Presentation:
More informationGeometry Vocabulary. Created by Dani Krejci referencing:
Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More information7. 6 Justifying Constructions
31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties
More information2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206  Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
More informationII. Geometry and Measurement
II. Geometry and Measurement The Praxis II Middle School Content Examination emphasizes your ability to apply mathematical procedures and algorithms to solve a variety of problems that span multiple mathematics
More informationChapters 4 and 5 Notes: Quadrilaterals and Similar Triangles
Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is
More informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationFeatured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision.
Domain: Geometry 4.G Mathematical Content Standard: 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.
More informationGeometry Chapter 1 Vocabulary. coordinate  The real number that corresponds to a point on a line.
Chapter 1 Vocabulary coordinate  The real number that corresponds to a point on a line. point  Has no dimension. It is usually represented by a small dot. bisect  To divide into two congruent parts.
More information8.1 Find Angle Measures in Polygons
8.1 Find Angle Measures in Polygons Obj.: To find angle measures in polygons. Key Vocabulary Diagonal  A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon ABCDE has two
More informationPolygon Properties and Tiling
! Polygon Properties and Tiling You learned about angles and angle measure in Investigations and 2. What you learned can help you figure out some useful properties of the angles of a polygon. Let s start
More informationThe Polygon AngleSum Theorems
61 The Polygon AngleSum Theorems Common Core State Standards GSRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum
More informationSHAPE, SPACE AND MEASURES
SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions
More information(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationOverview of Geometry Map Project
Overview of Geometry Map Project The goal: To demonstrate your understanding of geometric vocabulary, you will be designing and drawing a town map that incorporates many geometric key terms. The project
More informationLesson 6: Polygons and Angles
Lesson 6: Polygons and Angles Selected Content Standards Benchmark Assessed: G.4 Using inductive reasoning to predict, discover, and apply geometric properties and relationships (e.g., patty paper constructions,
More informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More information22.1 Interior and Exterior Angles
Name Class Date 22.1 Interior and Exterior ngles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? Resource Locker Explore 1 Exploring Interior
More informationMaths Toolkit Teacher s notes
Angles turtle Year 7 Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. Use a ruler and protractor
More informationMath 6: Unit 7: Geometry Notes 2Dimensional Figures
Math 6: Unit 7: Geometry Notes Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons
More informationYear 10 Term 1 Homework
Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 10 Year 10 Term 1 Week 10 Homework 1 10.1 Deductive geometry.................................... 1 10.1.1 Basic
More informationQuadrilaterals Unit Review
Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of
More informationSTUDENT S BOOK. Geometry and measurement
STUDENT S BOOK IES Antoni Cumella (Granollers) Curs 20082009 2D shapes: Introduction, classification, properties. Before we start: Dimension and look around Worksheet 1: Names and definition of a polygon
More informationGeometry 81 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 81 ngles of Polygons 1. Interior angles  The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
More informationBASIC GEOMETRY GLOSSARY
BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationCircle Theorems. Angles at the circumference are equal. The angle in a semicircle is x The angle at the centre. Cyclic Quadrilateral
The angle in a semicircle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must
More informationSum of the interior angles of a (n  2)180 polygon ~, Sum of the exterior angles of a 360 polygon
Name Geometry Polygons Sum of the interior angles of a (n  2)180 polygon ~, Sum of the exterior angles of a 360 polygon Each interior angle of a regular (n  2)180 i polygon n Each exterior angle of a
More informationINFORMATION FOR TEACHERS
INFORMATION FOR TEACHERS The math behind DragonBox Elements  explore the elements of geometry  Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through
More information