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

Save this PDF as:

Size: px
Start display at page:

## Transcription

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

2 Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 2

3 WHAT YOU WILL LEARN Points, lines, planes, and angles Polygons, similar figures, and congruent figures Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 3

4 Section 1 Points, Lines, Planes, and Angles Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 4

5 Basic Terms A point, line, and plane are three basic terms in geometry that are NOT given a formal definition, yet we recognize them when we see them. A line is a set of points. Any two distinct points determine a unique line. Any point on a line separates the line into three parts: the point and two half lines. A ray is a half line including the endpoint. A line segment is part of a line between two points, including the endpoints. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 5

6 Basic Terms Description Diagram Symbol Line AB A B AB Ray AB A B AB Ray BA A B BA Line segment AB A B AB Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 6

7 Plane We can think of a plane as a two-dimensional surface that extends infinitely in both directions. Any three points that are not on the same line (noncollinear points) determine a unique plane. A line in a plane divides the plane into three parts, the line and two half planes. Any line and a point not on the line determine a unique plane. The intersection of two distinct, non-parellel planes is a line. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 7

8 Angles An angle is the union of two rays with a common endpoint; denoted. The vertex is the point common to both rays. The sides are the rays that make the angle. There are several ways to name an angle: ABC, CBA, B Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 8

9 Angles The measure of an angle is the amount of rotation from its initial to its terminal side. Angles can be measured in degrees, radians, or gradients. Angles are classified by their degree measurement. Right Angle is 90 Acute Angle is less than 90 Obtuse Angle is greater than 90 but less than 180 Straight Angle is 180 Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 9

10 Types of Angles Adjacent Angles-angles that have a common vertex and a common side but no common interior points. Complementary Angles-two angles whose sum of their measures is 90 degrees. Supplementary Angles-two angles whose sum of their measures is 180 degrees. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 10

11 Example C A B m ABC m CBD D Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 11

12 More definitions Vertical angles are the nonadjacent angles formed by two intersecting straight lines. Vertical angles have the same measure. A line that intersects two different lines, at two different points is called a transversal. Special angles are given to the angles formed by a transversal crossing two parallel lines. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 12

13 Special Names Alternate interior angles Alternate exterior angles Corresponding angles Interior angles on the opposite side of the transversal have the same measure Exterior angles on the opposite sides of the transversal have the same measure One interior and one exterior angle on the same side of the transversal have the same measure Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 13

14 Section 2 Polygons Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 14

15 Polygons Polygons are named according to their number of sides. Number of Sides 3 Name Triangle Number of Sides 8 Name Octagon 4 Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Hexagon 12 Dodecagon 7 Heptagon 20 Icosagon Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 15

16 Polygons (continued) The sum of the measures of the interior angles of an n-sided polygon is (n 2)180. Example: A certain brick paver is in the shape of a regular octagon. Determine the measure of an interior angle and the measure of one exterior angle. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 16

17 Polygons (continued) Determine the sum of the interior angles. S ( n 2)180 (8 2)(180 ) 6(180 ) 1080 The measure of one interior angle is The exterior angle is supplementary to the interior angle, so the measure of one exterior angle is = 45 Copyright 2009 Pearson Education, Inc. Chapter 9 Section 2 Slide 17

18 Types of Triangles Acute Triangle All angles are acute. Obtuse Triangle One angle is obtuse. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 18

19 Types of Triangles (continued) Right Triangle One angle is a right angle. Isosceles Triangle Two equal sides. Two equal angles. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 19

20 Types of Triangles (continued) Equilateral Triangle Three equal sides. Three equal angles, 60º each. Scalene Triangle No two sides are equal in length. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 20

21 Similar Figures Two polygons are similar if their corresponding angles have the same measure and the lengths of their corresponding sides are in proportion Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 21

22 Example Catherine Johnson wants to measure the height of a lighthouse. Catherine is 5 feet tall and determines that when her shadow is 12 feet long, the shadow of the lighthouse is 75 feet long. How tall is the lighthouse? x Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 22

23 Example (continued) ht. lighthouse length of lighthouse's shadow = ht. Catherine length of Catherine's shadow x 75 = x = 375 x = x Therefore, the lighthouse is feet tall. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 2 Slide 23

24 Congruent Figures If corresponding sides of two similar figures are the same length, the figures are congruent. Corresponding angles of congruent figures have the same measure. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 24

25 Quadrilaterals Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360. Quadrilaterals may be classified according to their characteristics. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 25

26 Classifications Trapezoid Parallelogram Two sides are parallel. Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 2 Slide 26

27 Classifications (continued) Rhombus Rectangle Both pairs of opposite sides are parallel. The four sides are equal in length. Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. The angles are right angles. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 2 Slide 27

28 Classifications (continued) Square Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles. Copyright 2009 Pearson Education, Inc. Chapter 9 Section 2 Slide 28

### Points, lines, angles

Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in

### 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.

### 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

### 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

### 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

### Unit 3 Geometry. Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D

Unit 3 Geometry Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D Chapter 7 Outline Section Subject Homework Notes Lesson and Homework Complete

### 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

### Polygons - Part 1. Triangles

Polygons - Part 1 Triangles Introduction Complementary Angles: are two angles that add up to 90 Example: degrees A ADB = 65 degrees Therefore B + ADB BDC 65 deg 25 deg D BDC = 25 degrees C 90 Degrees Introduction

### Angle 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

### 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

### UNIT 6: Connecting Algebra & Geometry through Coordinates

TASK: Vocabulary UNIT 6: Connecting Algebra & Geometry through Coordinates Learning Target: I can identify, define and sketch all the vocabulary for UNIT 6. Materials Needed: 4 pieces of white computer

### 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

### U4 Polygon Notes January 11, 2017 Unit 4: Polygons

Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides

### Convex polygon - a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

Chapter 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.

### Mgr. ubomíra Tomková GEOMETRY

GEOMETRY NAMING ANGLES: any angle less than 90º is an acute angle any angle equal to 90º is a right angle any angle between 90º and 80º is an obtuse angle any angle between 80º and 60º is a reflex angle

### 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

### MPM1D Page 1 of 6. length, width, thickness, area, volume, flatness, infinite extent, contains infinite number of points. A part of a with endpoints.

MPM1D Page 1 of 6 Unit 5 Lesson 1 (Review) Date: Review of Polygons Activity 1: Watch: http://www.mathsisfun.com/geometry/dimensions.html OBJECT Point # of DIMENSIONS CHARACTERISTICS location, length,

### 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

### 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

### Show all work on a separate sheet of paper.

Sixth Grade Review 15: Geometric Shapes & Angles Name: Show all work on a separate sheet of paper. Geometry Word Bank Obtuse Angle Right Angle Acute Angle Straight Angle Pentagon Octagon Decagon Scalene

### Yimin Math Centre. 6.1 Properties of geometrical figures Recognising plane shapes... 1

Yimin Math Centre Student Name: Grade: Date: Score: Table of Contents 6 Year 7 Term 3 Week 6 Homework 1 6.1 Properties of geometrical figures............................ 1 6.1.1 Recognising plane shapes...........................

### Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º.

Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º. Definition: Convex polygon A convex polygon is a polygon in which the measure of

### Angle Unit Definition Packet

ngle Unit Definition Packet Name lock Date Term Definition Notes Sketch djacent ngles Two angles with a coon, a coon you normay name and, and no coon interior points. 3 4 3 and 4 Vertical ngles Two angles

### Geometry/Trigonometry Unit 5: Polygon Notes Period:

Geometry/Trigonometry Unit 5: Polygon Notes Name: Date: Period: # (1) Page 270 271 #8 14 Even, #15 20, #27-32 (2) Page 276 1 10, #11 25 Odd (3) Page 276 277 #12 30 Even (4) Page 283 #1-14 All (5) Page

### Polygons, Congruence, Similarity Long-Term Memory Review Grade 8 Review 1

Review 1 1. In the diagram below, XYZ is congruent to CDE XYZ CDE. Y D E X Z C Complete the following statements: a) C b) XZ c) CDE d) YZ e) Z f) DC 2. In the diagram below, ABC is similar to DEF ABC DEF.

### Reteaching Transversals and Angle Relationships

Name Date Class Transversals and Angle Relationships INV Transversals A transversal is a line that intersects two or more coplanar lines at different points. Line a is the transversal in the picture to

### 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.

### Geometry Chapter 8 Test Review

Geometry Chapter 8 Test Review Short Answer 1. Find the sum of the measures of the interior angles of the indicated convex polygon. Decagon 2. Find the sum of the measures of the interior angles of the

### Polygons. L E S S O N 1.4

Page 1 of 5 L E S S O N 1.4 Polygons A polygon is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each line segment

### Unit 3: Triangles and Polygons

Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following

### 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

### Answer Key. 1.1 Basic Geometric Definitions. Chapter 1 Basics of Geometry. CK-12 Geometry Concepts 1

1.1 Basic Geometric Definitions 1. WX, XW, WY, YW, XY, YX and line m. 2. Plane V, Plane RST, Plane RTS, Plane STR, Plane SRT, Plane TSR, and Plane TRS. 3. 4. A Circle 5. PQ intersects RS at point Q 6.

### TOPIC 2 Building Blocks of Geometry. Good Luck To

Good Luck To Period Date PART I DIRECTIONS: Use the Terms (page 2), Definitions (page 3), and Diagrams (page 4) to complete the table Term (capital letters) 1. Chord 2. Definition (roman numerals) Pictures

### PROPERTIES OF TRIANGLES AND QUADRILATERALS (plus polygons in general)

Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 15 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS

### Videos, Constructions, Definitions, Postulates, Theorems, and Properties

Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording

### ACT Math and Science - Problem Drill 11: Plane Geometry

ACT Math and Science - Problem Drill 11: Plane Geometry No. 1 of 10 1. Which geometric object has no dimensions, no length, width or thickness? (A) Angle (B) Line (C) Plane (D) Point (E) Polygon An angle

### 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

### Closed shapes with straight sides

41 Unit 6 and 7 Properties of 2D shapes Activity 1 Closed shapes with straight sides (polygons). Let s revise the 2D shapes you learnt about in Grade 5 Closed shapes with straight sides triangle quadrilateral

### Angle 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

### Lesson 7.1. Angles of Polygons

Lesson 7.1 Angles of Polygons Essential Question: How can I find the sum of the measures of the interior angles of a polygon? Polygon A plane figure made of three or more segments (sides). Each side intersects

### 8.1 Find Angle Measures in Polygons

VOCABULARY 8.1 Find Angle Measures in Polygons DIAGONAL Review: EQUILATERAL EQUIANGULAR REGULAR CLASSIFYING POLYGONS Polygon Interior Angle Theorem: The sum of the measures of the interior angles of a

### 1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons:

1. Revision Recall of basics of triangles, polygons etc. The minimum number of line segments required to form a polygon is 3. 1) Name the polygon formed with 4 line segments of equal length. 1) Square

### If two sides and the included angle of one triangle are congruent to two sides and the included angle of 4 Congruence

Postulates Through any two points there is exactly one line. Through any three noncollinear points there is exactly one plane containing them. If two points lie in a plane, then the line containing those

### An Approach to Geometry (stolen in part from Moise and Downs: Geometry)

An Approach to Geometry (stolen in part from Moise and Downs: Geometry) Undefined terms: point, line, plane The rules, axioms, theorems, etc. of elementary algebra are assumed as prior knowledge, and apply

### MATH DICTIONARY. Number Sense. Number Families. Operations. Counting (Natural) Numbers The numbers we say when we count. Example: {0, 1, 2, 3, 4 }

Number Sense Number Families MATH DICTIONARY Counting (Natural) Numbers The numbers we say when we count Example: {1, 2, 3, 4 } Whole Numbers The counting numbers plus zero Example: {0, 1, 2, 3, 4 } Positive

### Developmental Math An Open Program Unit 7 Geometry First Edition

Developmental Math An Open Program Unit 7 Geometry First Edition Lesson 1 Basic Geometric Concepts and Figures TOPICS 7.1.1 Figures in 1 and 2 Dimensions 1 Identify and define points, lines, line segments,

### 15. First make a parallelogram by rotating the original triangle. Then tile with the Parallelogram.

Shapes and Designs: Homework Examples from ACE Investigation 1: Question 15 Investigation 2: Questions 4, 20, 24 Investigation 3: Questions 2, 12 Investigation 4: Questions 9 12, 22. ACE Question ACE Investigation

### 7) Are HD and HA the same line?

Review for Exam 2 Math 123 SHORT ANSWER. You must show all work to receive full credit. Refer to the figure to classify the statement as true or false. 7) Are HD and HA the same line? Yes 8) What is the

### ACT SparkNotes Test Prep: Plane Geometry

ACT SparkNotes Test Prep: Plane Geometry Plane Geometry Plane geometry problems account for 14 questions on the ACT Math Test that s almost a quarter of the questions on the Subject Test If you ve taken

### November 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

### Thomas Jefferson High School for Science and Technology Program of Studies TJ Math 1

Course Description: This course is designed for students who have successfully completed the standards for Honors Algebra I. Students will study geometric topics in depth, with a focus on building critical

### Section 1-1 Points, Lines, and Planes

Section 1-1 Points, Lines, and Planes I CAN. Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in space. Undefined Term- Words, usually

### Mathematics Assessment Anchor Glossary Grades 3 & 4

Mathematics Assessment Anchor Glossary Grades 3 & 4 The definitions for this glossary were taken from one or more of the following sources: Webster s Dictionary, various mathematics dictionaries, the PA

### MATH STUDENT BOOK. 7th Grade Unit 8

MATH STUDENT BOOK 7th Grade Unit 8 Unit 8 Geometry Math 708 Geometry Introduction 3 1. Basic Geometry 5 Introduction to Geometry 5 Special Pairs of Angles 12 Polygons 20 Circles 27 Self Test 1: Basic Geometry

### Review Interior Angle Sum New: Exterior Angle Sum

Review Interior Angle Sum New: Exterior Angle Sum QUIZ: Prove that the diagonal connecting the vertex angles of a kite cut the kite into two congruent triangles. 1 Interior Angle Sum Formula: Some Problems

### 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

### GEOMETRY POSTULATES AND THEOREMS. Postulate 1: Through any two points, there is exactly one line.

GEOMETRY POSTULATES AND THEOREMS Postulate 1: Through any two points, there is exactly one line. Postulate 2: The measure of any line segment is a unique positive number. The measure (or length) of AB

### Euclid s Muse Directions

Euclid s Muse Directions First: Draw and label three columns on your chart paper as shown below. Name Picture Definition Tape your cards to the chart paper (3 per page) in the appropriate columns. Name

### Naming 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,

### Angles, Polygons, Circles

Page 1 of 5 Part One Last week we learned about the angle properties of circles and used them to solve a simple puzzle. This week brings a new puzzle that will make us use our algebra a bit more. But first,

### 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

### PROPERTIES OF TRIANGLES AND QUADRILATERALS

Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 22 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS

### Geometry. Released Test Questions. 2 In the diagram below,! 1 "!4. Consider the arguments below.

1 Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition defining mathematical terms

### Right Angle Triangle. Square. Opposite sides are parallel

Triangles 3 sides ngles add up to 18⁰ Right ngle Triangle Equilateral Triangle ll sides are the same length ll angles are 6⁰ Scalene Triangle ll sides are different lengths ll angles are different Isosceles

### 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

### CORRELATION TO GEORGIA QUALITY CORE CURRICULUM FOR GEOMETRY (GRADES 9-12)

CORRELATION TO GEORGIA (GRADES 9-12) SUBJECT AREA: Mathematics COURSE: 27. 06300 TEXTBOOK TITLE: PUBLISHER: Geometry: Tools for a Changing World 2001 Prentice Hall 1 Solves problems and practical applications

### Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?

Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each

### ACCELERATED MATHEMATICS CHAPTER 9 GEOMETRIC PROPERTIES PART II TOPICS COVERED:

ACCELERATED MATHEMATICS CHAPTER 9 GEOMETRIC PROPERTIES PART II TOPICS COVERED: Measuring angles Complementary and supplementary angles Triangles (sides, angles, and side-angle relationships) Angle relationships

### Number and Operations - Fractions

NF.1.3c Number and Operations - Fractions NF.1.3 NF.1.2b NF.1.2a Understand Fractions February 3 - February 20 NF.1.2 NF.1.1 Math! Lessons Develop understanding of fractions as numbers. Understand a fraction

### AngLegs Activity Cards Written by Laura O Connor & Debra Stoll

LER 4340/4341/4342 AngLegs Activity Cards Written by Laura O Connor & Debra Stoll Early Elementary (K-2) Polygons Activity 1 Copy Cat Students will identify and create shapes. AngLegs Pencil Paper 1. Use

### Math Handbook of Formulas, Processes and Tricks. Geometry

Math Handbook of Formulas, Processes and Tricks (www.mathguy.us) Prepared by: Earl L. Whitney, FSA, MAAA Version 3.1 October 3, 2017 Copyright 2010 2017, Earl Whitney, Reno NV. All Rights Reserved Handbook

### Ready to Go On? Skills Intervention Building Blocks of Geometry

8-1 Ready to Go On? Skills Intervention Building Blocks of Geometry A point is an exact location. A line is a straight path that extends without end in opposite directions. A plane is a flat surface that

### 1. 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

### Name: Second semester Exam Honors geometry Agan and Mohyuddin. May 13, 2014

Name: Second semester Exam Honors geometry Agan and Mohyuddin May 13, 2014 1. A circular pizza has a diameter of 14 inches and is cut into 8 equal slices. To the nearest tenth of a square inch, which answer

### 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

### Squares and Rectangles

LESSON.1 Assignment Name Date Squares and Rectangles Properties of Squares and Rectangles 1. In quadrilateral VWXY, segments VX and WY bisect each other, and are perpendicular and congruent. Is this enough

### Geometry Unit 5 - Notes Polygons

Geometry Unit 5 - Notes Polygons Syllabus Objective: 5.1 - The student will differentiate among polygons by their attributes. Review terms: 1) segment 2) vertex 3) collinear 4) intersect Polygon- a plane

### Elementary Planar Geometry

Elementary Planar Geometry What is a geometric solid? It is the part of space occupied by a physical object. A geometric solid is separated from the surrounding space by a surface. A part of the surface

### Prime Time (Factors and Multiples)

CONFIDENCE LEVEL: Prime Time Knowledge Map for 6 th Grade Math Prime Time (Factors and Multiples). A factor is a whole numbers that is multiplied by another whole number to get a product. (Ex: x 5 = ;

Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as

### CCM 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

### Draw and Classify 3-Dimensional Figures

Introduction to Three-Dimensional Figures Draw and Classify 3-Dimensional Figures Identify various three-dimensional figures. Course 2 Introduction to Three-Dimensional Figures Insert Lesson Title Here

### 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

### Name: Date: Period: CLASS MONDAY (9/19) TUESDAY (9/20) WEDNESDAY (9/21) THURSDAY (9/22) FRIDAY (9/23) Practice with finding the apothem

Homework 2 nd Hour 1 st Hour Name: Date: Period: This week, we will learn how to find the area and angles of regular polygons. We will end the week reviewing how to solve proportions. CLASS MONDAY (9/19)

### 6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles

6.1: Date: Geometry Polygon Number of Triangles Sum of Interior Angles Triangle: # of sides: # of triangles: Quadrilateral: # of sides: # of triangles: Pentagon: # of sides: # of triangles: Hexagon: #

### What 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

### COURSE OBJECTIVES LIST: GEOMETRY

COURSE OBJECTIVES LIST: GEOMETRY Geometry Honors is offered. PREREQUISITES: All skills from Algebra I are assumed. A prerequisites test is given during the first week of class to assess knowledge of these

### In this chapter, you will learn:

In this chapter, you will learn: > Find the measurements of missing angles made by a line that intersects parallel lines. > Find unknown angles inside and outside of triangles. > Determine if two triangles

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

STANDARDS OF LEARNING CONTENT REVIEW NOTES 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 for

CHAPTER Properties of Quadrilaterals The earliest evidence of quilting is an ivory carving from the 35th century BC. It shows the king of the Egyptian First Dynasty wearing a quilted cloak. You will examine

### Name 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.

### Consolidation of Grade 6 EQAO Questions Geometry and Spatial Sense

Consolidation of Grade 6 EQAO Questions Geometry and Spatial Sense SE2 Families of Schools Year GV1 GV2 GV3 Spring 2006 Spring 2007 Spring 2008 MC14 MC24 MC13 OR9 MC17 OR30 OR9 MC21 MC18 MC3 MC23 OR30

Understanding Quadrilaterals Parallelogram: A quadrilateral with each pair of opposite sides parallel. Properties: (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one

### Tessellations: Wallpapers, Escher & Soccer Balls. Robert Campbell

Tessellations: Wallpapers, Escher & Soccer Balls Robert Campbell Tessellation Examples What Is What is a Tessellation? A Tessellation (or tiling) is a pattern made by copies of one or

### Grade 8 Math WORKBOOK UNIT 1 : POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???

Grade 8 Math WORKBOOK UNIT 1 : 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

### Explore 2 Exploring Interior Angles in Polygons

Explore 2 Exploring Interior Angles in Polygons To determine the sum of the interior angles for any polygon, you can use what you know about the Triangle Sum Theorem by considering how many triangles there

### Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook

Unit 2: Triangles and Quadrilaterals Lesson 2.1 pply Triangle Sum Properties Lesson 4.1 from textbook Objectives Classify angles by their sides as equilateral, isosceles, or scalene. Classify triangles

### Pre-AICE 2: Unit 5 Exam - Study Guide

Pre-AICE 2: Unit 5 Exam - Study Guide 1 Find the value of x. (The figure may not be drawn to scale.) A. 74 B. 108 C. 49 D. 51 2 Find the measure of an interior angle and an exterior angle of a regular