THEOREM 8.1. Polygon Interior Angles Theorem. interior angles of a convex polygon with n sides is (n 2)p180.
|
|
|
- Bethany Marshall
- 7 years ago
- Views:
Transcription
1 Page of 7 8. ngles in Polygons Goal Find the measures of interior and exterior angles of polygons. The definitions for interior angles and exterior angles can be extended to include angles formed in any polygon. In the diagrams shown below, interior angles are red, and exterior angles are blue. Key Words interior angle p. 8 exterior angle p. 8 interior angles exterior angles ctivity 8. suggests the Polygon Interior ngles Theorem shown below. THORM 8. Polygon Interior ngles Theorem Words The sum of the measures of the interior angles of a convex polygon with n sides is (n )p80. Symbols ma ma... man (n )p80 6 n 6 XMPL Use the Polygon Interior ngles Theorem Find the sum of the measures of the interior angles of a convex heptagon. heptagon has 7 sides. Use the Polygon Interior ngles Theorem and substitute 7 for n. (n )p80 (7 )p80 Substitute 7 for n. p Simplify. Multiply. NSWR The sum of the measures of the interior angles of a convex heptagon is ngles in Polygons 7
2 Page of 7 XMPL Find the measure of a in the diagram. Find the Measure of an Interior ngle The polygon has 6 sides, so the sum of the measures of the interior angles is: (n )p80 (6 )p80 p F Student Help SKILLS RVIW To review solving an equation, see p. 67. dd the measures of the interior angles and set the sum equal to ma 70 The sum is ma 70 Simplify. ma Subtract 607. NSWR The measure of a is. XMPL Find the measure of an interior angle of a regular octagon. The sum of the measures of the interior angles of any octagon is: (n )p80 (8 )p80 6p ecause the octagon is regular, each angle has the same measure. So, divide 080 by 8 to find the measure of one interior angle Interior ngles of a Regular Polygon NSWR The measure of an interior angle of a regular octagon is. Find Measures of Interior ngles In xercises, find the measure of ag.. F G. H. H J J G F 0 0 G 8 H L M K K. Find the measure of an interior angle of a regular polygon with twelve sides. 8 hapter 8 Polygons and rea
3 Page of 7 xterior ngles The diagrams below show that the sum of the measures of the exterior angles of the convex polygon is 60. Visualize It! circle contains two straight angles. So, there are 80 80, or 60, in a circle or 60 Shade one exterior ut out the rrange the exterior angle at each vertex. exterior angles. angles to form The sum of the measures of the exterior angles of a convex polygon does not depend on the number of sides that the polygon has. THORM 8. Polygon xterior ngles Theorem Words The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 60. Symbols ma ma... man 60 n XMPL Find the value of x. Find the Measure of an xterior ngle Using the Polygon xterior ngles Theorem, set the sum of the measures of the exterior angles equal to Polygon xterior ngles Theorem 80 x 60 ombine like terms. x 80 NSWR The value of x is Subtract 80 from each side. x 60 ivide each side by. 8. ngles in Polygons 9
4 Page of 7 Find xterior ngle Measures Find the value of x xercises Guided Practice Vocabulary heck. Name an interior angle and an exterior angle of polygon shown at the right. G Skill heck. Write the formula that is used to find the sum of the measures of the interior angles of any convex polygon with n sides. F H. Use your answer from xercise to find the sum of the measures of the interior angles of a convex polygon with 9 sides. Write an equation to find the measure of a. o not solve the equation hapter 8 Polygons and rea
5 Page of 7 Practice and pplications xtra Practice See p Sum of Interior ngle Measures Find the sum of the measures of the interior angles of the convex polygon Polygons with n Sides Find the sum of the measures of the interior angles of the convex polygon with n sides.. n 0. n. n 0. n 0. n 6. n 00 Interior ngle Measures Find the measure of a F F IStudent Help I L S S Z O N. O M HOMWORK HLP xtra help with problem solving in xs. is at classzone.com Interior ngles of Regular Polygons Find the measure of an interior angle of the regular polygon.... Using lgebra Find the value of x. Homework Help xample : xs. 8 6 xample : xs. 7 0 xample : xs. xample : xs., ngles in Polygons
6 Page 6 of 7 Sports aseball home plate for a baseball field is a pentagon as shown. 6. Is the polygon regular? xplain why or why not. 7. What is the sum of the interior angles? 8. Find the measures of a and a. SLL Home plate is used to find the placement of the foul lines on the playing field. Visualize It! ut a strip of lined paper and tie it into an overhand knot as shown. Gently flatten the knot to form a pentagon. The pentagon should be regular. 9. Find the measure of an interior angle of a regular pentagon. 0. Measure the interior angles of your knot with a protractor. Use your answer to xercise 9 to determine whether your pentagon is regular. Logical Reasoning Select the word that makes the statement true.. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is (always, sometimes, never) 60.. The sum of the measures of the interior angles of a convex octagon is (always, sometimes, never) 0.. The measures of the exterior angles of a convex polygon are (always, sometimes, never) equal.. Outdoor Furniture You are constructing a regular hexagonal wooden bench like the one shown. On the bench, a ca. Find the measures of a and a so that you know what angle to use to cut the pieces of wood. hallenge Find the number of sides of the regular polygon with the given exterior angle measure hapter 8 Polygons and rea
7 Page 7 of 7 Standardized Test Practice Multiple hoice In xercises 9 and 0, use the diagram below. 9. What is the value of x? What is the measure of ap? P P 0 0 U R S 0 T F 9 G 78 H 6 J Mixed Review Using a entroid is the centroid of T. Find and. (Lesson.6). 6.. lgebra Skills bsolute Value valuate. (Skills Review, p. 66) Quiz ecide whether the polygon is regular. xplain your answer. (Lesson 8.)... Find the measure of a. (Lesson 8.) ngles in Polygons
4.7 Triangle Inequalities
age 1 of 7 4.7 riangle Inequalities Goal Use triangle measurements to decide which side is longest and which angle is largest. he diagrams below show a relationship between the longest and shortest sides
Angle Relationships in Parallel Lines and Triangles?
ngle Relationships in Parallel Lines and Triangles? MOUL 11 LSSON 11.1 Parallel Lines ut by a Transversal OMMON OR SSNTIL QUSTION How can you use angle relationships in parallel lines and triangles to
Which shapes make floor tilings?
Which shapes make floor tilings? Suppose you are trying to tile your bathroom floor. You are allowed to pick only one shape and size of tile. The tile has to be a regular polygon (meaning all the same
Measure and classify angles. Identify and use congruent angles and the bisector of an angle. big is a degree? One of the first references to the
ngle Measure Vocabulary degree ray opposite rays angle sides vertex interior exterior right angle acute angle obtuse angle angle bisector tudy ip eading Math Opposite rays are also known as a straight
Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain
Intermediate 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,
For the circle above, EOB is a central angle. So is DOE. arc. The (degree) measure of ù DE is the measure of DOE.
efinition: circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol to represent a circle. The a line segment from the center
Similar shapes. 33.1 Similar triangles CHAPTER. Example 1
imilar shapes 33 HTR 33.1 imilar triangles Triangle and triangle have the same shape but not the same size. They are called similar triangles. The angles in triangle are the same as the angles in triangle,
pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs.
age 1 of 5 6.5 rapezoids Goal Use properties of trapezoids. trapezoid is a quadrilateral with eactly one pair of parallel sides. he parallel sides are the bases. he nonparallel sides are the legs. leg
Geometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes
UNIT 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)
NAME DATE PERIOD. Study Guide and Intervention
opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. 5-1 M IO tudy Guide and Intervention isectors, Medians, and ltitudes erpendicular isectors and ngle isectors perpendicular bisector
Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find
Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
Areas of Circles and Sectors. GO for Help
-7 What You ll Learn To find the areas of circles, sectors, and segments of circles... nd Why To compare the area of different-size pizzas, as in Example reas of ircles and Sectors heck Skills You ll Need
2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
Shapes & Designs Notes
Problem 1.1 Definitions: regular polygons - polygons in which all the side lengths and angles have the same measure edge - also referred to as the side of a figure tiling - covering a flat surface with
Possible Stage Two Mathematics Test Topics
Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problem-solver with a strong mathematics background. It is based mainly on material
This is a tentative schedule, date may change. Please be sure to write down homework assignments daily.
Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (1-1) Points, Lines, & Planes Topic: (1-2) Segment Measure Quiz
Angle Vocabulary, Complementary & Supplementary Angles
ngle Vocabulary, omplementary & Supplementary ngles Review 1 1. What is the definition of an acute angle? 2. Name the angle shown. 3. What is the definition of complimentary angles? 4. What is the definition
of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
Target To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
Angles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
Lesson 1: Introducing Circles
IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed
GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
11-1 Lines that Intersect Circles Quiz
Name: lass: ate: I: 11-1 Lines that Intersect ircles Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b.
1.6. Solve Linear Inequalities E XAMPLE 1 E XAMPLE 2. Graph simple inequalities. Graph compound inequalities
.6 Solve Linear Inequalities Before You solved linear equations. Now You will solve linear inequalities. Why? So you can describe temperature ranges, as in Ex. 54. Key Vocabulary linear inequality compound
MATH STUDENT BOOK. 8th Grade Unit 6
MATH STUDENT BOOK 8th Grade Unit 6 Unit 6 Measurement Math 806 Measurement Introduction 3 1. Angle Measures and Circles 5 Classify and Measure Angles 5 Perpendicular and Parallel Lines, Part 1 12 Perpendicular
Geometry 8-1 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 8-1 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.
56 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
Unit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
10.2 45-45 -90 Triangles
Page of 6 0. --0 Triangles Goal Find the side lengths of --0 triangles. Key Words --0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. Geo-Activity Eploring an Isosceles Right
A discus thrower spins around in a circle one and a half times, then releases the discus. The discus forms a path tangent to the circle.
Page 1 of 6 11.2 Popeties of Tangents Goal Use popeties of a tangent to a cicle. Key Wods point of tangency p. 589 pependicula p. 108 tangent segment discus thowe spins aound in a cicle one and a half
Geometry Chapter 10 Study Guide Name
eometry hapter 10 Study uide Name Terms and Vocabulary: ill in the blank and illustrate. 1. circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center.
PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
Year 9 mathematics test
Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.
Geometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
Incenter and Circumcenter Quiz
Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of
Parallel and Perpendicular Lines
Trinity University Digital Commons @ Trinity Understanding by Design: Complete Collection Understanding by Design Summer 6-12-2014 Parallel and Perpendicular Lines Danielle R. Kendrick Trinity University,
1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
Applications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
Assessment Anchors and Eligible Content
M07.A-N The Number System M07.A-N.1 M07.A-N.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours Essential Question: LESSON 4 FINITE ARITHMETIC SERIES AND RELATIONSHIP TO QUADRATIC
Arc Length and Areas of Sectors
Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.
Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
Area. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
6.4 Factoring Polynomials
Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization
Exploring Geometric Figures Using Cabri Geometry II
Exploring Geometric Figures Using Cabri Geometry II Regular Polygons Developed by: Charles Bannister. Chambly County High School Linda Carre.. Chambly County High School Manon Charlebois Vaudreuil Catholic
Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations
Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane
Solve Quadratic Equations by the Quadratic Formula. The solutions of the quadratic equation ax 2 1 bx 1 c 5 0 are. Standardized Test Practice
10.6 Solve Quadratic Equations by the Quadratic Formula Before You solved quadratic equations by completing the square. Now You will solve quadratic equations using the quadratic formula. Why? So you can
Estimating 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
Triangle Similarity: AA, SSS, SAS Quiz
Name: lass: ate: I: Triangle Similarity:, SSS, SS Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Explain why the triangles are similar and write a
1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
Stop signs are constructed in the shape of a polygon with 8 sides of equal length The polygon has 8 sides A polygon with 8 sides is an octagon All sides of the polygon are congruent and all angles are
1-1. Nets and Drawings for Visualizing Geometry. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
1-1 Nets and Drawings for Visualizing Geometry Vocabulary Review Identify each figure as two-dimensional or three-dimensional. 1. 2. 3. three-dimensional two-dimensional three-dimensional Vocabulary uilder
Classifying Quadrilaterals
1 lassifying Quadrilaterals Identify and sort quadrilaterals. 1. Which of these are parallelograms?,, quadrilateral is a closed shape with 4 straight sides. trapezoid has exactly 1 pair of parallel sides.
Tessellating with Regular Polygons
Tessellating with Regular Polygons You ve probably seen a floor tiled with square tiles. Squares make good tiles because they can cover a surface without any gaps or overlapping. This kind of tiling is
CHAPTER 1 CEVA S THEOREM AND MENELAUS S THEOREM
HTR 1 V S THOR N NLUS S THOR The purpose of this chapter is to develop a few results that may be used in later chapters. We will begin with a simple but useful theorem concerning the area ratio of two
Chapter Review. 11-1 Lines that Intersect Circles. 11-2 Arcs and Chords. Identify each line or segment that intersects each circle.
HPTR 11-1 hapter Review 11-1 Lines that Intersect ircles Identify each line or segment that intersects each circle. 1. m 2. N L K J n W Y X Z V 3. The summit of Mt. McKinley in laska is about 20,321 feet
Duplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7
Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
Number Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
Section 7.1 Solving Right Triangles
Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,
Grade 7/8 Math Circles November 3/4, 2015. M.C. Escher and Tessellations
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Tiling the Plane Grade 7/8 Math Circles November 3/4, 2015 M.C. Escher and Tessellations Do the following
Grade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse
NF5-12 Flexibility with Equivalent Fractions and Pages 110 112
NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
Investigating Relationships of Area and Perimeter in Similar Polygons
Investigating Relationships of Area and Perimeter in Similar Polygons Lesson Summary: This lesson investigates the relationships between the area and perimeter of similar polygons using geometry software.
1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms - These words do not have formal definitions, but there is agreement aboutwhat they mean.
Objective: To distinguish between degree and radian measure, and to solve problems using both.
CHAPTER 3 LESSON 1 Teacher s Guide Radian Measure AW 3.2 MP 4.1 Objective: To distinguish between degree and radian measure, and to solve problems using both. Prerequisites Define the following concepts.
3.1. Angle Pairs. What s Your Angle? Angle Pairs. ACTIVITY 3.1 Investigative. Activity Focus Measuring angles Angle pairs
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Use Manipulatives Two rays with a common endpoint form an angle. The common endpoint is called the vertex. You can use a protractor to draw and measure
GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
SPRING UNIT 14. second half. Line symmetry and reflection. Measuring angles. Naming and estimating angles. Drawing angles
PART SPRING second half SHAPE AND SPACE SECTION Line symmetry and reflection SECTION Measuring angles SECTION Naming and estimating angles SECTION Drawing angles SECTION 5 Calculations involving angles
A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment
GEOMETRIC FIGURES, AREAS, AND VOLUMES
HPTER GEOMETRI FIGURES, RES, N VOLUMES carpenter is building a deck on the back of a house. s he works, he follows a plan that he made in the form of a drawing or blueprint. His blueprint is a model of
WORK SCHEDULE: MATHEMATICS 2007
, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check
5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle - A midsegment of a triangle is a segment that connects
G3-33 Building Pyramids
G3-33 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:
Shape 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
9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
Problem of the Month: William s Polygons
Problem of the Month: William s Polygons The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common
Advanced Euclidean Geometry
dvanced Euclidean Geometry What is the center of a triangle? ut what if the triangle is not equilateral?? Circumcenter Equally far from the vertices? P P Points are on the perpendicular bisector of a line
Roof Framing Geometry & Trigonometry for Polygons
Roof Framing Geometry & Trigonometry for Polygons section view polygon side length polygon center inscribed circle central angle plan angle working angle plan view plan view projection B angle B exterior
Prentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)
New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct
3D shapes. Level A. 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3-D shapes?
Level A 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite 2. What is another name for 3-D shapes? A) Polygon B) Polyhedron C) Point 3. A 3-D shape has four sides and a triangular
Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
Analytical Geometry (4)
Analytical Geometry (4) Learning Outcomes and Assessment Standards Learning Outcome 3: Space, shape and measurement Assessment Standard As 3(c) and AS 3(a) The gradient and inclination of a straight line
MEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.
MEP Pupil Text Number Patterns. Simple Number Patterns A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. Worked Example Write down the
12 Surface Area and Volume
12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
11.3 Sectors and Arcs Quiz
Name: lass: ate: I:.3 Sectors and rcs Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. ( point) Jenny s birthday cake is circular and has a 30 cm radius.
The Half-Circle Protractor
The Half-ircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a half-circle protractor to measure and draw
You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel IGCSE Mathematics B Paper 1 Centre Number Candidate Number Monday 6 June 2011 Afternoon Time: 1 hour 30 minutes Paper Reference 4MB0/01 You must have: Ruler
Elements of Plane Geometry by LK
Elements of Plane Geometry by LK These are notes indicating just some bare essentials of plane geometry and some problems to think about. We give a modified version of the axioms for Euclidean Geometry
Chapter 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
3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
Geometry Arcs And Central Angles Practice Key
Arcs And Central Angles Practice Key Free PDF ebook Download: Arcs And Central Angles Practice Key Download or Read Online ebook geometry arcs and central angles practice key in PDF Format From The Best
Circles in Triangles. This problem gives you the chance to: use algebra to explore a geometric situation
Circles in Triangles This problem gives you the chance to: use algebra to explore a geometric situation A This diagram shows a circle that just touches the sides of a right triangle whose sides are 3 units,
Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 4 6
Ma KEY STAGE 3 Mathematics test TIER 4 6 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
CAMI Education linked to CAPS: Mathematics
- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to