VideoText Interactive
|
|
|
- Joshua Mosley
- 5 years ago
- Views:
Transcription
1 VideoText Interactive Homescool and Independent Study Sampler Print Materials for Geometry: A Complete Course Unit I, Part C, Lesson 3 Triangles Course Notes ( pages) Student WorkText (3 pages) Solutions Manual ( pages) Quizzes Forms A and B (6 pages) Quiz Solutions (6 pages) 006
2 COURSE NOTE 9 Measuring Polygons (cont.) Triangle Perimeter (P) 4 in 7 in 9 in P in Pa++c 006 VideoTextInteractive Inc. Unit I, Part C, Lesson 3a
3 COURSE NOTE 30 Measuring Polygons (cont.) Rigt Triangle Area (A) Area (A) metod metod 6 in 6 in in in 6 in 6 in in in 006 VideoTextInteractive Inc. 6 in in A 6 in in A sqin 36sqin Unit I, Part C, Lesson 3
4 COURSE NOTE 3 Measuring Polygons (cont.) Acute Triangle Area (A) 006 VideoTextInteractive Inc. A A Unit I, Part C, Lesson 3c
5 COURSE NOTE 3 Measuring Polygons (cont.) Isosceles Triangle Area (A) 006 VideoTextInteractive Inc. A A Unit I, Part C, Lesson 3d
6 COURSE NOTE 33 Measuring Polygons (cont.) Otuse Triangle Area (A) 006 VideoTextInteractive Inc. A A Unit I, Part C, Lesson 3e
7 Unit I Te Structure of Geometry Part C Measurement Lesson 3 Triangles Ojective: To understand, and demonstrate, te concepts of area and perimeter, as tey relate to triangles. Important Terms: Triangle A polygon made wit tree line segments. Rigt Triangle A triangle in wic one of te angles is a rigt angle (90 o ). Perimeter Intuitively, te measure of te distance around a simple closed plane curve. Formally, te perimeter of a polygon is simply te sum of te measures of its sides. Perimeter of a Triangle Formally, te perimeter of a triangle can e found y adding te measures of all tree sides, as long as all of te sides are measured in te same units. Tere really is no standard formula for tis relationsip except to express it symolically as P a + + c were a,, and c are te measures of te tree sides. Area Intuitively, te numer of non-overlapping unit squares, and parts of unit squares, wic can e fit into te interior of a simple closed plane curve. Area of a Triangle Formally, te area A of a triangle, can e found y multiplying te measure of te ase y one-alf of te measure of te eigt on tat ase, as long as te ase and eigt are measured in te same units. Tis is represented y te formula A i i or, more commonly, A i i. Unit I Te Structure of Geometry
8 Example : Find te perimeter and te area of te triangle illustrated elow, using te indicated measures. 3m 8m m m Solution: First, te perimeter of tis triangle can e found intuitively, y adding te measures of all of its sides. P meters Formally, te solution is te same since te formula tells us we must add te measures of all tree sides. P a + + c meters Second, it is difficult, intuitively, to find te area of tis triangle witout cutting it up in pieces and rearranging, so we will find it formally, y using te formula for te area of a triangle. A i i i i 8 84 square meters Lesson 3 Exercises: Find te area and perimeter of eac of te triangles in exercises troug Part C Measurement 3
9 Lesson 3 Exercises: (cont d) m 6m m 8m cm 3 cm cm cm 8. cm 6 3. cm Find te area of eac of te triangles in exercises 9 troug. Express your answer in terms of t. 9. 3t 0.. 3t 8t t t 7 t + 7. Find te area of te given rigt triangle if te measure of te line segment AB is 3 inces and te measure of line segment BC is inces. B 3 C A 4 Unit I Te Structure of Geometry
10 3. Perimeter Sum of te lengts of te sides Ai 4. 3 k+ k+ 3 k+ k 3 k+ 3 k+ k+ k ( ) i k+( + ) i k ( + 3 ) i k+(+ ) i k ik+ ik 3 ( 3 + ) i k ( 3 k) i ( k) i 3 k i i k i i 3 k i k i ikik 3i k squareunits Perimeter Sum of te lengts of te sides k+k+k+k (+++) i k 0k units Ai k i (k+4) kik+ki4 k + i4 ik k + 0k (k + 0k) units ( i 3 + i 3 i 3 ) i i k ( ) i k k i k Unit I Te Structure of Geometry Part C Measurement p. 3 Lesson 3 Triangles.. 3. Area i i Area i i i7fti4ft i8 in. i6 in. i 7 ii i i4 i6 i i 4sq.ft or4 ft 4sq.in. or 4 in Area i i i8mi6m i i 4 i 6 i 4sq.mor4m Perimeter Sum of te lengts of te sides 3 ft + 7 ft + 6 ft 0ft+6 ft 6 ft Perimeter Sum of te lengts of te sides 6in.+8in.+0 in. 4in.+0in. 4in. Perimeter Sum of te lengts of te sides 8 m+4 m+m m+m 33 meters Area i i Area i i 3 i cm i cm i (6 in.+ 8 in.) i 8 in. i i i 3 i 4 i 8 ii ii ii7 i8 3 cm ii 4 6 sq.in. or 6 in Area i i (0ft+ft) ft i i i i ii ii6 i ii 30sq. ft or 30 ft Perimeter Sum of te lengts of te sides cm+cm+cm 30cm+cm 4cm Perimeter Sum of te lengts of te sides 0in.+ 6 in.+ 8 in.+ in. 6 in.+ 8 in.+ in. 4 in.+ in. 3inces Perimeter Sum of te lengts of te sides ft +0 ft + ft + 7 ft ft + 9 ft 30 feet 0 Unit I Te Structure of Geometry
11 Area i i Area i i i cm i cm i in. i. in. i i6 i iin. i ii in. 7sq.cm or 7 cm i in. i in. Perimeter Sum of te lengts of te sides i i ii cm+cm+ cm (4 cm+ ) cm 4 sq.in.or 6 4 in Area i i i(8t) i(3t) i i4 it i3it ii 4 it i3it 4i3itit t sq.units Perimeter Sum of te lengts of tesides in.+3in.+6in. 8in.+6in. 4in Area i i Area PytagoreanTriangle for rigt triangles i i a + c i(t) i(3t - ) i(t + 7) i(t - 7) + 3 i (t) i (3t - ) (t + 7) (t - 7) + 69 i i ii (t)(3t) +(t)(-) i (t + 7) (t - 7) i ii t - t (t + 7) (t - 7) ( )sq.units 44 (t + 7)(t) + (t - 7)(-7) t it + 7 it +(t)(-7) +(7)(-7) ( - )( +) 0 t + 7t + -7t or t +(7+-7)t t +0i t -49 inces ( cannot e negative) t Area i t -49 i ( )sq.units i in. i in. i ii6 ii 30sq.in. Part C Measurement
12 Quiz Form A Class Date Score Unit I - Te Structure of Geometry Part C - Measurement Lesson 3 - Triangles Find te area and perimeter of te given triangles in exercises troug 3. (Note: You may first ave to use te Pytagorean Teorem (a + c ) to find some missing parts.. Area: Area: VideoTextInteractive Geometry: A Complete Course 49
13 Unit I, Part C, Lesson 3, Quiz Form A Continued 3. Area: Find te area of a triangle wit ase (x + 3) units and eigt (4x - ) units. Area: VideoTextInteractive Geometry: A Complete Course
14 Unit I, Part C, Lesson 3, Quiz Form A Continued. Find te area and perimeter of te given triangle. 9 yds Area: yds 3 yds _ 6. Find te area and perimeter of te saded square in te given figure. 4 Area: 4 _ VideoTextInteractive Geometry: A Complete Course
15 Quiz Form B Class Date Score Unit I - Te Structure of Geometry Part C - Measurement Lesson 3 - Triangles Find te area and perimeter of te given triangles in exercises troug 3. Note: You may first ave to use te Pytagorean Teorem (a + c ) to find some missing parts.. Area: 6. Area: VideoTextInteractive Geometry: A Complete Course 3
16 Unit I, Part C, Lesson 3, Quiz Form B Continued 3. Area: 9 cm 6 cm 4. Find te area of a triangle wit ase (x - 4) units and eigt (x - ) units Area: VideoTextInteractive Geometry: A Complete Course
17 Unit I, Part C, Lesson 3, Quiz Form B Continued. Find te area and perimeter of te given figure. Area: 0. cm 6.3 cm 8.4 cm 6. Find te area and perimeter of te given figure. Area: 6m 3m 4m 006 VideoTextInteractive Geometry: A Complete Course
18 Quiz Form A Class Date Score Unit I - Te Structure of Geometry Part C - Measurement Lesson 3 - Triangles Find te area and perimeter of te given triangles in exercises troug 3. [Note: You may first ave to use te Pytagorean Teorem (a + c ) to find some missing parts.]. Area: 84 sq. units units Area ase eigt Perimeter Sum of lengts of te sides ( + 6) ( + ) units square units. Area: sq. inces inces 3 6 Area ase eigt square inces Perimeter Sum of Lengts of te Sides Perimeter Perimeter 0 inces Pytagorean Teorem a + c c c c c 006 VideoTextInteractive Geometry: A Complete Course 49
19 Unit I, Part C, Lesson 3, Quiz Form A Continued 3. Area: 0 sq. inces ( ) units 6 8 Area ase eigt square units Pytagorean Teorem a + c + x 4 + x 9 x 9 x 6 + y 36 + y 6 y 6 y Perimeter Sum of Lengts of te Sides ( ) Perimeter units 4. Find te area of a triangle wit ase (x + 3) units and eigt (4x - ) units. Area ase eigt ( x + ) x 3 4 ( ) ( )( ) x x x 4x + 3 4x + x ( ) + 3 ( ) 8x + x + 4x + 6 8x + 8x 6 4 ( x + 4x 3) ( ) 4x + 4x 3 square units ( ) 4x + 4x 3 square units Area: VideoTextInteractive Geometry: A Complete Course
20 Unit I, Part C, Lesson 3, Quiz Form A Continued. Find te area and perimeter of te given triangle. 9 yds Area: 8 sq. yards yds 3 yds Area ase eigt a a a a 4 3 a 9 a 8 square yards _ yards Perimeter Sum of lengts of te sides or yards 6. Find te area and perimeter of te saded square in te given figure. 4 Area: 4 sq. units _ 4 4units Area of Larger Square: Pytagorean Teorem elps us find c. Area ( + 4) ( + 4) a + c c 8 square units 6 + c 4 c 4 c c) Area of Saded Square d) Perimeter is te sum of te lengts of te sides. Area 4 4 Perimeter ( ) square units 4 4units 006 VideoTextInteractive Geometry: A Complete Course
21 Quiz Form B Class Date Score Unit I - Te Structure of Geometry Part C - Measurement Lesson 3 - Triangles Find te area and perimeter of te given triangles in exercises troug 3. Note: You may first ave to use te Pytagorean Teorem (a + c ) to find some missing parts.. Area: 90 sq. inces 6 49 inces Area ase eigt Perimeter Sum of Lengts of te Sides inces square inces 3 sq. feet. Area: Area ase eigt a ( + ) feet Pytagorean Teorem a + c Two Missing Pieces: a 9 3 a 7 or 3 square feet x x x 3 + y 9 + y 34 y x x 34 y Perimeter Sum of Lengts of te Sides ( ) ( 4 34 ) feet feet 006 VideoTextInteractive Geometry: A Complete Course 3
22 Unit I, Part C, Lesson 3, Quiz Form B Continued 3. Area: 7 sq. sm 6 cm 9 cm ( ) cm Area ase eigt Pytagorean Teorem a + c c c 39 7 c 7 c 7 square cm 3 3 c 3 3 c Perimeter Sum of Lengts of te Sides ( ) cm 4. Find te area of a triangle wit ase (x - 4) units and eigt (x - ) units Area ase eigt x + 3 4x 8x + 8x 6 8x + 8x 6 4 ( x + 4x 3) ( )( ) ( ) + Area: ( 4 4 3) 4x + 4x 3 square units x x square units VideoTextInteractive Geometry: A Complete Course
23 Unit I, Part C, Lesson 3, Quiz Form B Continued. Find te area and perimeter of te given figure. Area: 6.46 cm 0. cm 8.4 cm 6.3 cm _. cm Area ase eigt Perimeter Sum of Lengts of te Sides a 84 ( 63) (.).. cm ( 84. )( 63. ) a ( 4. ) ( 6. 3) a a cm 6. Find te area and perimeter of te given figure. Area: sq. meters 3m 6m 4m Pytagorean Teorem a) find c. ) Find x: a + c c c c c ( )meters a + x 6 + x 36 + x 6 x 6 x c) Perimeter is: d) Area is alf te ase times te eigt Perimeter Area ase eigt + ase Perimeter ( 3 + 6) meters Area Area + Area 6 + Area square meters 006 VideoTextInteractive Geometry: A Complete Course
NOTES: A quick overview of 2-D geometry
NOTES: A quick overview of 2-D geometry Wat is 2-D geometry? Also called plane geometry, it s te geometry tat deals wit two dimensional sapes flat tings tat ave lengt and widt, suc as a piece of paper.
19.2 Surface Area of Prisms and Cylinders
Name Class Date 19 Surface Area of Prisms and Cylinders Essential Question: How can you find te surface area of a prism or cylinder? Resource Locker Explore Developing a Surface Area Formula Surface area
Measuring Length 11and Area
Measuring Lengt 11and Area 11.1 Areas of Triangles and Parallelograms 11.2 Areas of Trapezoids, Romuses, and Kites 11.3 Perimeter and Area of Similar Figures 11.4 Circumference and Arc Lengt 11.5 Areas
Areas of Triangles and Parallelograms. Bases of a parallelogram. Height of a parallelogram THEOREM 11.3: AREA OF A TRIANGLE. a and its corresponding.
11.1 Areas of Triangles and Parallelograms Goal p Find areas of triangles and parallelograms. Your Notes VOCABULARY Bases of a parallelogram Heigt of a parallelogram POSTULATE 4: AREA OF A SQUARE POSTULATE
Read pages in the book, up to the investigation. Pay close attention to Example A and how to identify the height.
C 8 Noteseet L Key In General ON LL PROBLEMS!!. State te relationsip (or te formula).. Sustitute in known values. 3. Simplify or Solve te equation. Use te order of operations in te correct order. Order
Areas of Parallelograms and Triangles. To find the area of parallelograms and triangles
10-1 reas of Parallelograms and Triangles ommon ore State Standards G-MG..1 Use geometric sapes, teir measures, and teir properties to descrie ojects. G-GPE..7 Use coordinates to compute perimeters of
12.2 Investigate Surface Area
Investigating g Geometry ACTIVITY Use before Lesson 12.2 12.2 Investigate Surface Area MATERIALS grap paper scissors tape Q U E S T I O N How can you find te surface area of a polyedron? A net is a pattern
When the dimensions of a solid increase by a factor of k, how does the surface area change? How does the volume change?
8.4 Surface Areas and Volumes of Similar Solids Wen te dimensions of a solid increase by a factor of k, ow does te surface area cange? How does te volume cange? 1 ACTIVITY: Comparing Surface Areas and
Lecture 4: Geometry II
Lecture 4: Geometry II LPSS MATHCOUNTS 19 May 2004 Some Well-Known Pytagorean Triples A Pytagorean triple is a set of tree relatively prime 1 natural numers a,, and c satisfying a 2 + 2 = c 2 : 3 2 + 4
Classify solids. Find volumes of prisms and cylinders.
11.4 Volumes of Prisms and Cylinders Essential Question How can you find te volume of a prism or cylinder tat is not a rigt prism or rigt cylinder? Recall tat te volume V of a rigt prism or a rigt cylinder
THANK YOU FOR YOUR PURCHASE!
THANK YOU FOR YOUR PURCHASE! Te resources included in tis purcase were designed and created by me. I ope tat you find tis resource elpful in your classroom. Please feel free to contact me wit any questions
Geometry Chapter 11 Areas of Circles and Polygons HOMEWORK Name: Period:
Geometry Capter 11 Areas of Circles and Polygons HOMEWORK Name: Period: 1 Free Plain Grap Paper from ttp://incompetec.com/grappaper/plain/ Free Plain Grap Paper from ttp://incompetec.com/grappaper/plain/
You Try: A. Dilate the following figure using a scale factor of 2 with center of dilation at the origin.
1 G.SRT.1-Some Tings To Know Dilations affect te size of te pre-image. Te pre-image will enlarge or reduce by te ratio given by te scale factor. A dilation wit a scale factor of 1> x >1enlarges it. A dilation
VOLUMES. The volume of a cylinder is determined by multiplying the cross sectional area by the height. r h V. a) 10 mm 25 mm.
OLUME OF A CYLINDER OLUMES Te volume of a cylinder is determined by multiplying te cross sectional area by te eigt. r Were: = volume r = radius = eigt Exercise 1 Complete te table ( =.14) r a) 10 mm 5
Algebra Area of Triangles
LESSON 0.3 Algera Area of Triangles FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards Learning Ojective 6.G.A. Find te area of rigt triangles, oter triangles, special quadrilaterals,
All truths are easy to understand once they are discovered; the point is to discover them. Galileo
Section 7. olume All truts are easy to understand once tey are discovered; te point is to discover tem. Galileo Te main topic of tis section is volume. You will specifically look at ow to find te volume
MAC-CPTM Situations Project
raft o not use witout permission -P ituations Project ituation 20: rea of Plane Figures Prompt teacer in a geometry class introduces formulas for te areas of parallelograms, trapezoids, and romi. e removes
PART ONE: Learn About Area of a Parallelogram
13 Lesson AREA PART ONE: Learn About Area of a Parallelogram? How can you use a rectangle to find the area of a parallelogram? Area (A) tells how much surface a two-dimensional figure covers. You can use
VideoText Interactive
VideoText Interactive Homeschool and Independent Study Sampler Print Materials for Geometry: A Complete Course Unit I, Part B, Lesson 1 Undefined Terms ------------------------------------------ Course
2 The Derivative. 2.0 Introduction to Derivatives. Slopes of Tangent Lines: Graphically
2 Te Derivative Te two previous capters ave laid te foundation for te study of calculus. Tey provided a review of some material you will need and started to empasize te various ways we will view and use
Piecewise Polynomial Interpolation, cont d
Jim Lambers MAT 460/560 Fall Semester 2009-0 Lecture 2 Notes Tese notes correspond to Section 4 in te text Piecewise Polynomial Interpolation, cont d Constructing Cubic Splines, cont d Having determined
Review: What is the definition of a parallelogram? What are the properties of a parallelogram? o o o o o o
Geometry CP Lesson 11-1: Areas of Parallelograms Page 1 of 2 Objectives: Find perimeters and areas of parallelograms Determine whether points on a coordinate plane define a parallelogram CA Geometry Standard:
Areas of Rectangles and Parallelograms
CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson, you Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover
Section 2.3: Calculating Limits using the Limit Laws
Section 2.3: Calculating Limits using te Limit Laws In previous sections, we used graps and numerics to approimate te value of a it if it eists. Te problem wit tis owever is tat it does not always give
Section 3. Imaging With A Thin Lens
Section 3 Imaging Wit A Tin Lens 3- at Ininity An object at ininity produces a set o collimated set o rays entering te optical system. Consider te rays rom a inite object located on te axis. Wen te object
EXERCISES 6.1. Cross-Sectional Areas. 6.1 Volumes by Slicing and Rotation About an Axis 405
6. Volumes b Slicing and Rotation About an Ais 5 EXERCISES 6. Cross-Sectional Areas In Eercises and, find a formula for te area A() of te crosssections of te solid perpendicular to te -ais.. Te solid lies
Chapter K. Geometric Optics. Blinn College - Physics Terry Honan
Capter K Geometric Optics Blinn College - Pysics 2426 - Terry Honan K. - Properties of Ligt Te Speed of Ligt Te speed of ligt in a vacuum is approximately c > 3.0µ0 8 mês. Because of its most fundamental
10-2. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the unknown side lengths in each special right triangle. 1. a 30-60 -90 triangle with hypotenuse 2 ft 2. a 45-45 -90 triangle with leg length
What is a tessellation???? Give an example... Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =?
Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =? 36 74 0 78 0 154 o 44 48 54 o y x 154 o 78 0 12 74 0 9 1. 8 ft 2. 21m 3. 21 ft 4. 30cm 5. 6mm 6. 16 in 7. yes 9 = 7
AREA OF POLYGONS
AREA OF POLYGONS 5.3.1 5.3.4 Area is the number of non-overlapping square units needed to cover the interior region of a twodimensional figure or the surface area of a three-dimensional figure. For example,
Notes: Dimensional Analysis / Conversions
Wat is a unit system? A unit system is a metod of taking a measurement. Simple as tat. We ave units for distance, time, temperature, pressure, energy, mass, and many more. Wy is it important to ave a standard?
THE POSSIBILITY OF ESTIMATING THE VOLUME OF A SQUARE FRUSTRUM USING THE KNOWN VOLUME OF A CONICAL FRUSTRUM
THE POSSIBILITY OF ESTIMATING THE VOLUME OF A SQUARE FRUSTRUM USING THE KNOWN VOLUME OF A CONICAL FRUSTRUM SAMUEL OLU OLAGUNJU Adeyemi College of Education NIGERIA Email: lagsam04@aceondo.edu.ng ABSTRACT
4.1 Tangent Lines. y 2 y 1 = y 2 y 1
41 Tangent Lines Introduction Recall tat te slope of a line tells us ow fast te line rises or falls Given distinct points (x 1, y 1 ) and (x 2, y 2 ), te slope of te line troug tese two points is cange
4-8 Similar Figures and Proportions. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Find the cross products, and then tell whether the ratios are equal. 1. 16, 40 6 15 2. 3. 3 8, 18 46 8, 24 9 27 4. 28, 42 12 18 240
Note Sheets Chapter 8: Area
Ch 8 Notesheet L Key V3 Note Sheets Chapter 8: rea In General ON LL PROBLEMS!!. State the relationship (or the formula).. Sustitute in known values. 3. Simplify or Solve the equation. Use the order of
Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume
Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and
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
Tier 2: GEOMETRY INTRODUCTION TO GEOMETRY Lessons Abbreviation Key Table... 7 G1 LESSON: WHAT IS GEOMETRY?... 8 G1E... 9 G1EA...
Craig Hane, Ph.D., Founder Tier 2: GEOMETRY INTRODUCTION TO GEOMETRY... 6 1.1 Lessons Abbreviation Key Table... 7 G1 LESSON: WHAT IS GEOMETRY?... 8 G1E... 9 G1EA... 10 G2 LESSON: STRAIGHT LINES AND ANGLES...
1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd
Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second
Vocabulary for Geometry. Line (linea) a straight collection of points extending in opposite directions without end.
Vocabulary for Geometry Line (linea) a straight collection of points extending in opposite directions without end. A line AB or line BA B Symbol for a line is AB Jan 27 2:56 PM Line Segment (linea segmento)
Name: Class: Date: 2. I have four vertices. I have four right angles and all my sides are the same length.
1. Circle the right triangles. Use the corner of a piece of paper to check. 2. I have four vertices. I have four right angles and all my sides are the same length. What am I? 3. I have four vertices. All
Lesson Plan #39. 2) Students will be able to find the sum of the measures of the exterior angles of a triangle.
Lesson Plan #39 Class: Geometry Date: Tuesday December 11 th, 2018 Topic: Sum of the measures of the interior angles of a polygon Objectives: Aim: What is the sum of the measures of the interior angles
MATH 5a Spring 2018 READING ASSIGNMENTS FOR CHAPTER 2
MATH 5a Spring 2018 READING ASSIGNMENTS FOR CHAPTER 2 Note: Tere will be a very sort online reading quiz (WebWork) on eac reading assignment due one our before class on its due date. Due dates can be found
Extra Practice 1. Name Date. Lesson 1: Exploring Triangles
Master 6.36 Extra Practice 1 Lesson 1: Exploring Triangles 1. Draw 3 different triangles. Measure and label the side lengths. Name each triangle as equilateral, isosceles, or scalene. 2. Name each triangle
MTH-112 Quiz 1 - Solutions
MTH- Quiz - Solutions Words in italics are for eplanation purposes onl (not necessar to write in te tests or. Determine weter te given relation is a function. Give te domain and range of te relation. {(,
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
Bounding Tree Cover Number and Positive Semidefinite Zero Forcing Number
Bounding Tree Cover Number and Positive Semidefinite Zero Forcing Number Sofia Burille Mentor: Micael Natanson September 15, 2014 Abstract Given a grap, G, wit a set of vertices, v, and edges, various
6 Mathematics Curriculum
New York State Common Core 6 Mathematics Curriculum GRADE GRADE 6 MODULE 5 Table of Contents 1 Area, Surface Area, and Volume Problems... 3 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)...
Linear Interpolating Splines
Jim Lambers MAT 772 Fall Semester 2010-11 Lecture 17 Notes Tese notes correspond to Sections 112, 11, and 114 in te text Linear Interpolating Splines We ave seen tat ig-degree polynomial interpolation
Chapter Test Form A. 173 Holt Geometry. Name Date Class. 1. Find the area of the triangle.
Form A 1. Find the area of the triangle. 6. A square has a perimeter of 8 inches. Find the area of the square. cm 7. Find the circumference of C in terms of.. Find the area of the parallelogram. 11 cm
Surface Area of Prisms 8.7.B
? LESSON 10.1 ESSENTIAL QUESTION Surface Area of Prisms How do you find the surface area of a prism? Expressions, equations, and relationships make connections to the formulas for lateral and total surface
Mathematics Curriculum
6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...
POLYGONS
POLYGONS 8.1.1 8.1.5 After studying triangles and quadrilaterals, the students now extend their knowledge to all polygons. A polygon is a closed, two-dimensional figure made of three or more non-intersecting
Notes: Geometry (6.G.1 4)
Perimeter Add up all the sides (P =s + s + s...) Square A = side 2 A = S 2 Perimeter The distance around a polygon. Rectangle w s L A = Length x Width A = lw Parallelogram A = Base x Height A = h h Triangle
Name Date Teacher Practice A
Practice A Triangles Identify each triangle by its angles and sides. 1. 2. 3. Find each angle measure. 4. Find x in the acute 5. Find y in the right 6. Find r in the obtuse 7. Find x in the acute 8. Find
Recalling Quadrilaterals
Recalling Quadrilaterals Play Area Lesson 23-1 Recalling Quadrilaterals Learning Targets: Define and classify quadrilaterals based on their properties. Use properties of quadrilaterals to determine missing
Area. Domain 4 Lesson 25. Getting the Idea
Domain 4 Lesson 5 Area Common Core Standard: 7.G.6 Getting the Idea The area of a figure is the number of square units inside the figure. Below are some formulas that can be used to find the areas of common
Algebra Area of Parallelograms
Lesson 10.1 Reteach Algebra Area of Parallelograms The formula for the area of a parallelogram is the product of the base and height. The formula for the area of a square is the square of one of its sides.
13.5 DIRECTIONAL DERIVATIVES and the GRADIENT VECTOR
13.5 Directional Derivatives and te Gradient Vector Contemporary Calculus 1 13.5 DIRECTIONAL DERIVATIVES and te GRADIENT VECTOR Directional Derivatives In Section 13.3 te partial derivatives f x and f
Math 6: Unit 7: Geometry Notes 2-Dimensional 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
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
Numerical Derivatives
Lab 15 Numerical Derivatives Lab Objective: Understand and implement finite difference approximations of te derivative in single and multiple dimensions. Evaluate te accuracy of tese approximations. Ten
Unit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
MATH STUDENT BOOK. 10th Grade Unit 8
MATH STUDENT BOOK 10th Grade Unit 8 Unit 8 Area and Volume MATH 1008 Area and Volume INTRODUCTION 3 1. POLYGONS 5 AREA CONCEPTS 5 RECTANGLE 8 PARALLELOGRAM 1 TRIANGLE 14 TRAPEZOID 17 REGULAR POLYGON 19
"Unpacking the Standards" 4th Grade Student Friendly "I Can" Statements I Can Statements I can explain why, when and how I got my answer.
0406.1.1 4th Grade I can explain why, when and how I got my answer. 0406.1.2 I can identify the range of an appropriate estimate. I can identify the range of over-estimates. I can identify the range of
9-1. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry
9-1 9-1 Warm Up Lesson Presentation Lesson Quiz Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 3. a = 20, c = 52 c =
HS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume
HS Pre-Algebra Notes Unit 0: Measurement, Area, and Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (5.6) The student will classify polygons. (5.5) The student will validate conclusions
Geometry 10 and 11 Notes
Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into
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.
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
Fault Localization Using Tarantula
Class 20 Fault localization (cont d) Test-data generation Exam review: Nov 3, after class to :30 Responsible for all material up troug Nov 3 (troug test-data generation) Send questions beforeand so all
For Questions 1 through 13, use the figure above. The measure of 1 is 135. Complete each statement.
Assignment Assignment for Lesson 9.1 Name Date Figuring All of the Angles Angles and Angle Pairs 5 6 7 8 1 2 3 4 For Questions 1 through 13, use the figure above. The measure of 1 is 135. Complete each
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.
2. A circle is inscribed in a square of diagonal length 12 inches. What is the area of the circle?
March 24, 2011 1. When a square is cut into two congruent rectangles, each has a perimeter of P feet. When the square is cut into three congruent rectangles, each has a perimeter of P 6 feet. Determine
Chapter 11 Areas of Polygons and Circles
Section 11-1: Areas of Parallelograms and Triangles SOL: G.14 The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, and
To find the surface area and volume of a sphere
To find the surface area and volume of a sphere Sphere set of all points in space equidistant from a given point called the center. Surface Area Formula: S.A. = 4πr 2 r Volume Formula: V = 4 πr 3 3 Great
Unit 1, Lesson 1: Tiling the Plane
Unit 1, Lesson 1: Tiling the Plane Let s look at tiling patterns and think about area. 1.1: Which One Doesn t Belong: Tilings Which pattern doesn t belong? 1 1.2: More Red, Green, or Blue? m.openup.org//6-1-1-2
OHS GEOMETRY SUMMER ASSIGNMENT
OHS GEOMETRY SUMMER ASSIGNMENT Name: Date Started: Complete each of the following exercises in this formative assessment. To receive full credit for this assignment, you must show your work in this packet,
Any questions about the material so far? About the exercises?
Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:
Geometry - Additional Questions: Sheet 1
Geometry - Additional Questions: Sheet 1 Parallel Lines Eercises (G3E) e g f h L1 L1 L2 1.) How many angles do you need to know in order to replace the letters in the diagram to the left? b c a d L2 2.)
Unit 2: Geometric Figures
Unit 2: Geometric Figures This lesson describes elementary geometric figures as : 1. Circles. 2. Triangles. 3. Quadrilaterals. 4. Polygons. The circle (p. 31) Human brain is very good doing shape recognition.
January Regional Geometry Team: Question #1. January Regional Geometry Team: Question #2
January Regional Geometry Team: Question #1 Points P, Q, R, S, and T lie in the plane with S on and R on. If PQ = 5, PS = 3, PR = 5, QS = 3, and RT = 4, what is ST? 3 January Regional Geometry Team: Question
3.6 Directional Derivatives and the Gradient Vector
288 CHAPTER 3. FUNCTIONS OF SEVERAL VARIABLES 3.6 Directional Derivatives and te Gradient Vector 3.6.1 Functions of two Variables Directional Derivatives Let us first quickly review, one more time, te
2.3 Additional Relations
3 2.3 Additional Relations Figure 2.3 identiies additional relations, indicating te locations o te object and image, and te ratio o teir eigts (magniication) and orientations. Ray enters te lens parallel
Polygons. 5 sides 5 angles. pentagon. Name
Lesson 11.1 Reteach Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number
Polygon Practice. E90 Grade 5. Name
Lesson 11.1 Polygon Practice Write the number of sides and the number of angles that each polygon has. Then match each description to one of the polygons drawn below. Label the polygon with the exercise
Practice Test - Chapter 11. Find the area and perimeter of each figure. Round to the nearest tenth if necessary.
Find the area and perimeter of each figure. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Use the Pythagorean Theorem to find the
Getting Ready to Teach Unit 6
Getting Ready to Teach Unit 6 Learning Path in the Common Core Standards In this unit, students study the attributes of triangles, quadrilaterals, and other polygons. They find perimeter and area of various
HPISD Curriculum: Grade 4 TAG Math
Unit Overview HPISD Curriculum: Grade 4 TAG Math Title Estimated Duration 9 Weeks Geometry and Measurement 8 weeks 1 2 3 4 Properties/attributes of polygons, triangles, quadrilaterals Area and perimeter
Mathematics - LV 5 (with QuickTables)
Mathematics - LV 5 (with QuickTables) Correlation of the ALEKS Course Mathematics LV 5 to the California Mathematics Content Standards for Grade 5 (1998) Number Sense: NS1.1: NS1.2: NS1.3: NS1.4: TD =
Algebra Summer Math HW check
Lesson Practice 1 a) Integers, rational numbers, real numbers b) Rational numbers, real numbers c) Irrational numbers, real numbers Whole numbers; Sample: There can be d) no people or any number of people.
Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a
GM1.1 Answers 1 a b 2 Shape Name Regular Irregular Convex Concave A Decagon B Octagon C Pentagon D Quadrilateral E Heptagon F Hexagon G Quadrilateral H Triangle I Triangle J Hexagon Original Material Cambridge
GM1 End-of-unit Test. 1 Calculate the size of angles a, b and c. 2 ABC is a right-angled triangle. Work out the size of the marked angles.
GM End-of-unit Test Calculate the size of angles a, and c. 2 ABC is a right-angled triangle. a = = c = 3 marks Work out the size of the marked angles. p = q = r = 3 marks Original material Camridge University
6 th Grade Mathematics Instructional Week 25 Develop and Use Formulas to Determine the Volume and Surface Area of Rectangular Prisms Paced Standards:
6 th Grade Mathematics Instructional Week 25 Develop and Use Formulas to Determine the Volume and Surface Area of Rectangular Prisms Paced Standards: 6.GM.4: Find the area of complex shapes composed of
The scale factor between the blue diamond and the green diamond is, so the ratio of their areas is.
For each pair of similar figures, find the area of the green figure. 1. The scale factor between the blue diamond and the green diamond is, so the ratio of their areas is. The area of the green diamond
Pre-Algebra. Tests and Resources. Author: Shelly Chittam, M.S. Managing Editor: Alan Christopherson, M.S.
Pre-Algebra Tests and Resources Author: Shelly Chittam, M.S. Managing Editor: Alan Christopherson, M.S. Editors: Laura Messner, B.A. Rachelle Wiersma, M.A. Graphic Design & Illustration: Ron A. Hartmann,
Haar Transform CS 430 Denbigh Starkey
Haar Transform CS Denbig Starkey. Background. Computing te transform. Restoring te original image from te transform 7. Producing te transform matrix 8 5. Using Haar for lossless compression 6. Using Haar
MATH Student Book. 5th Grade Unit 10
MATH Student Book 5th Grade Unit 10 Unit 10 PERIMETER, AREA, AND VOLUME MATH 510 PERIMETER, AREA, AND VOLUME Introduction 3 1. Perimeter...4 Polygons 5 Regular Polygons 10 Circumference 16 Self Test 1:
Vocabulary. Term Page Definition Clarifying Example. apothem. center of a circle. center of a regular polygon. central angle of a regular polygon
CHAPTER 9 Vocabulary The table contains important vocabulary terms from Chapter 9. As you work through the chapter, fill in the page number, definition, and a clarifying example. apothem Term Page Definition
Instructional. Essential Standards. Materials. Envision Topic 1 1-1; 1-2; 1-3; 1-4. Envision Topic 2 2-2; 2-3. Envision Topic 2 2-4; 2-5; 2-6
Time Frame Period 1 Dates: Sept.4 Oct.26 Big Idea/Topic Essential Standards NS1.1 Estimate, round, and manipulate very large and very small numbers. Materials Envision Topic 1 1-1; 1-2; 1-3; 1-4 Envision