MATH 341 FALL 2011 ASSIGNMENT 6 October 3, 2011
|
|
|
- Gavin Pope
- 5 years ago
- Views:
Transcription
1 MATH 341 FALL 2011 ASSIGNMENT 6 October 3, 2011 Open the document Getting Started with GeoGebra and follow the instructions either to download and install it on your computer or to run it as a Webstart application. You are going to be creating a triangle and the four triangle centers and it will be individualized to you. Start with your UKID number and taking the first six digits create three points in the first quadrant. If these three points are not distinct or are collinear, use more digits from your UKID, then from your driver s license number and finally from your SSN. By the time you have gone through those numbers, you should have three distinct, non-collinear points. Open GeoGebra. It should open up in the view similar to Figure 1, with the Algebra View on the left and the plane with a set of axes on the right. Choose the Move Graphics View button and move your plane so that it shows mostly the first quadrant in your window. You want to enter your three points into GeoGebra. Here A = (1,1), B= (9,1), and C = (7,5). To make sure you have your points, exactly, you will want to enter them into the Input window. These points were entered as (1,1), then (9,1) and (7,5). Note that in the Algebra View you have a listing of the points and their coordinates.
2 Next choose the Line between Two Points tool and choose Segment between Two Points and construct the segments AB, BC, and CA. You can now see that GeoGebra has indicated the lengths of your line segments in the Algebra View. QUESTION 1: Is your triangle isosceles? Is it an equilateral triangle? You can answer this question directly on the GeoGebra worksheet using Insert Text tool. Choose the tool, next to the last on the right, and choose Insert Text. Click on a spot in the Graphics View that will allow you to enter your answer to this question without having the answer get in the way of the diagram. An entry box will open up and you can type in 1. The triangle is. Now you want to find the centroid of your triangle. Choose the New Point tool and then choose Midpoint or Center within that menu. Then check on each of the three segments to find the midpoints of the three segments. These will most likely be labeled as D, E, and F. Now, construct your medians. 2
3 Now choose the second button (New Point tool) and choose the Intersect Two Objects. Click on two of the medians and you will get the Centroid and its coordinates. Hide your medians by clicking on the radio buttons next to the labels for your medial segments. QUESTION 2: Using the information from class, compute the centroid of your triangle? Do you get the same answer as GeoGebra? (If not, check that your points are correct and not just approximates.) Next, we want to find the Incenter of the triangle. This means we need the Angle Bisectors from the Perpendicular Line tool and then Angle Bisector. Using the same process as above, find the Incenter and its coordinates. Find the inradius of your triangle. 3
4 QUESTION 3: What are the coordinates of the incenter of your triangle? What is the inradius of your triangle. Next, find the Circumcenter of the triangle, the circumcircle and the equation of the circumcircle. For the circumcenter you need the perpendicular bisectors of the sides and you need to choose the Perpendicular Line tool and choose Perpendicular line. After finding the Circumcenter and hiding the perpendicular bisectors, choose the Circle with Center through Point tool and construct the circumcircle. You will see near the bottom of Algebra View an equation for the circle. For this triangle we get that the equation of the circle is ( x 5) y 2. 4 QUESTION 4: What are the coordinates of the circumcenter of your triangle? What is the equation of the circumcircle? What is the circumradius of your triangle? 4
5 Now find the Orthocenter of the triangle. For the orthocenter you need the altitudes. After finding the Orthocenter and hiding the altitudes, find the coordinates of the Orthocenter. Also, check that the slopes of the altitudes are the negative reciprocals of the slopes of the appropriate sides. QUESTION 5: What are the coordinates of the orthocenter of your triangle? What are the slopes of the lines that contain the sides of your triangle? What are the slopes of the lines of your altitudes? Now, construct the Euler segment of your triangle. What is the length of the Euler segment. QUESTION 6: What is the length of the Euler segment? What is the length of the segment from the circumcenter to the centroid? What is the length of the segment from the orthocenter to the centroid? Is their ratio correct in your triangle? QUESTION 7: What is the length of the segment from the circumcenter to the incenter? Is this consistent with the formula that we have for the distance from the circumcenter to the incenter? 5
6 Choose File Save As and name the file with LastnameFirstname.ggb. Upload the GeoGebra file to Blackboard. 6
SYSTEMS OF LINEAR EQUATIONS
SYSTEMS OF LINEAR EQUATIONS A system of linear equations is a set of two equations of lines. A solution of a system of linear equations is the set of ordered pairs that makes each equation true. That is
Visualizing Triangle Centers Using Geogebra
Visualizing Triangle Centers Using Geogebra Sanjay Gulati Shri Shankaracharya Vidyalaya, Hudco, Bhilai (Chhattisgarh) India http://mathematicsbhilai.blogspot.com/ sanjaybhil@gmail.com ABSTRACT. In this
Chapter 5: Relationships Within Triangles
Name: Hour: Chapter 5: Relationships Within Triangles GeoGebra Exploration and Extension Project Due by 11:59 P.M. on 12/22/15 Mr. Kroll 2015-16 GeoGebra Introduction Activity In this tutorial, you will
H.Geometry Chapter 3 Definition Sheet
Section 3.1 Measurement Tools Construction Tools Sketch Draw Construct Constructing the Duplicate of a Segment 1.) Start with a given segment. 2.) 3.) Constructing the Duplicate of an angle 1.) Start with
Example G1: Triangles with circumcenter on a median. Prove that if the circumcenter of a triangle lies on a median, the triangle either is isosceles
1 Example G1: Triangles with circumcenter on a median. Prove that if the circumcenter of a triangle lies on a median, the triangle either is isosceles or contains a right angle. D D 2 Solution to Example
Writing Equations of Lines and Midpoint
Writing Equations of Lines and Midpoint MGSE9 12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel
SOAR2001 GEOMETRY SUMMER 2001
SR2001 GEMETRY SUMMER 2001 1. Introduction to plane geometry This is the short version of the notes for one of the chapters. The proofs are omitted but some hints are given. Try not to use the hints first,
Semester Test Topic Review. Correct Version
Semester Test Topic Review Correct Version List of Questions Questions to answer: What does the perpendicular bisector theorem say? What is true about the slopes of parallel lines? What is true about the
Unit 1 Unit 1 A M. M.Sigley, Baker MS. Unit 1 Unit 1. 3 M.Sigley, Baker MS
A M S 1 2 G O E A B 3 4 LINE POINT Undefined No thickness Extends infinitely in two directions Designated with two points Named with two capital letters or Undefined No size Named with a capital letter
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
Lesson 27/28 Special Segments in Triangles
Lesson 27/28 Special Segments in Triangles ***This is different than on your notetaking guide*** PART 1 - VOCABULARY Perpendicular Angle Median Altitude Circumcenter Incenter Centroid Orthocenter A line
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: a b 1.
ASSIGNMENT ON STRAIGHT LINES LEVEL 1 (CBSE/NCERT/STATE BOARDS) 1 Find the angle between the lines joining the points (0, 0), (2, 3) and the points (2, 2), (3, 5). 2 What is the value of y so that the line
EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS
EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS Steps to Find the Median of a Triangle: -Find the midpoint of a segment using the midpoint formula. -Use the vertex and midpoint to find the
DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
Select the best answer. Bubble the corresponding choice on your scantron. Team 13. Geometry
Team Geometry . What is the sum of the interior angles of an equilateral triangle? a. 60 b. 90 c. 80 d. 60. The sine of angle A is. What is the cosine of angle A? 6 4 6 a. b. c.. A parallelogram has all
Unit 2 Triangles Part 1
Graded Learning Targets LT 2.1 I can Unit 2 Triangles Part 1 Supporting Learning Targets I can justify, using a formal proof, that the three angles in a triangle add up to 180. I can justify whether or
5.4 Medians and Altitudes in Triangles
5.4. Medians and Altitudes in Triangles www.ck12.org 5.4 Medians and Altitudes in Triangles Learning Objectives Define median and find their point of concurrency in a triangle. Apply medians to the coordinate
Segment Addition Postulate: If B is BETWEEN A and C, then AB + BC = AC. If AB + BC = AC, then B is BETWEEN A and C.
Ruler Postulate: The points on a line can be matched one to one with the REAL numbers. The REAL number that corresponds to a point is the COORDINATE of the point. The DISTANCE between points A and B, written
Centres of a Triangle. Teacher Notes
Introduction Centres of a Triangle Teacher Notes Centres of a Triangle The aim of this activity is to investigate some of the centres of a triangle and to discover the Euler Line. The activity enables
Name: Date: Period: Chapter 11: Coordinate Geometry Proofs Review Sheet
Name: Date: Period: Chapter 11: Coordinate Geometry Proofs Review Sheet Complete the entire review sheet (on here, or separate paper as indicated) h in on test day for 5 bonus points! Part 1 The Quadrilateral
5-2 Medians and Altitudes of Triangles. In, P is the centroid, PF = 6, and AD = 15. Find each measure. 1. PC ANSWER: 12 2.
In, P is the centroid, PF = 6, and AD = 15. Find each measure. In, UJ = 9, VJ = 3, and ZT = 18. Find each length. 1. PC 12 2. AP 10 3. INTERIOR DESIGN An interior designer is creating a custom coffee table
Geometry Rules. Triangles:
Triangles: Geometry Rules 1. Types of Triangles: By Sides: Scalene - no congruent sides Isosceles - 2 congruent sides Equilateral - 3 congruent sides By Angles: Acute - all acute angles Right - one right
Let s Get This Started!
Lesson. Skills Practice Name Date Let s Get This Started! Points, Lines, Planes, Rays, and Line Segments Vocabulary Write the term that best completes each statement.. A geometric figure created without
MATH 113 Section 8.2: Two-Dimensional Figures
MATH 113 Section 8.2: Two-Dimensional Figures Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Classifying Two-Dimensional Shapes 2 Polygons Triangles Quadrilaterals 3 Other
Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
: Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of
Chapter 7. Some triangle centers. 7.1 The Euler line Inferior and superior triangles
hapter 7 Some triangle centers 7.1 The Euler line 7.1.1 nferior and superior triangles G F E G D The inferior triangle of is the triangle DEF whose vertices are the midpoints of the sides,,. The two triangles
NEW YORK GEOMETRY TABLE OF CONTENTS
NEW YORK GEOMETRY TABLE OF CONTENTS CHAPTER 1 POINTS, LINES, & PLANES {G.G.21, G.G.27} TOPIC A: Concepts Relating to Points, Lines, and Planes PART 1: Basic Concepts and Definitions...1 PART 2: Concepts
Custom Tools and Customizing the Toolbar
Custom Tools and Customizing the Toolbar GeoGebra Workshop Handout 7 Judith and Markus Hohenwarter www.geogebra.org Table of Contents 1. The Theorem of Phythagoras 2 2. Creating Custom Tools 4 3. Saving
You MUST know the big 3 formulas!
Name: Geometry Pd. Unit 3 Lines & Angles Review Midterm Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation Writing the equation of a line given a graph. Graphing
Points of Concurrency on a Coordinate Graph
Points of Concurrency on a Coordinate Graph Name Block *Perpendicular bisectors: from the midpoint to the side opposite( ) 1. The vertices of ΔABC are A(1,6), B(5,4), C(5,-2). Find the coordinates of the
Shortcuts, Formulas & Tips
& present Shortcuts, Formulas & Tips For MBA, Banking, Civil Services & Other Entrance Examinations Vol. 3: Geometry Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles
1 Points and Distances
Ale Zorn 1 Points and Distances 1. Draw a number line, and plot and label these numbers: 0, 1, 6, 2 2. Plot the following points: (A) (3,1) (B) (2,5) (C) (-1,1) (D) (2,-4) (E) (-3,-3) (F) (0,4) (G) (-2,0)
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
Geometry (H) Worksheet: 1st Semester Review:True/False, Always/Sometimes/Never
1stSemesterReviewTrueFalse.nb 1 Geometry (H) Worksheet: 1st Semester Review:True/False, Always/Sometimes/Never Classify each statement as TRUE or FALSE. 1. Three given points are always coplanar. 2. A
MTH 362 Study Guide Exam 1 System of Euclidean Geometry 1. Describe the building blocks of Euclidean geometry. a. Point, line, and plane - undefined
MTH 362 Study Guide Exam 1 System of Euclidean Geometry 1. Describe the building blocks of Euclidean geometry. a. Point, line, and plane - undefined terms used to create definitions. Definitions are used
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median
Exterior Region Interior Region
Lesson 3: Copy and Bisect and Angle Lesson 4: Construct a Perpendicular Bisector Lesson 5: Points of Concurrencies Student Outcomes: ~Students learn how to bisect an angle as well as how to copy an angle
Question2: Which statement is true about the two triangles in the diagram?
Question1: The diagram shows three aid stations in a national park. Choose the values of x, y, and z that COULD represent the distances between the stations. (a) x = 7 miles, y = 8 miles, z = 18 miles
Solutions to the Test. Problem 1. 1) Who is the author of the first comprehensive text on geometry? When and where was it written?
Solutions to the Test Problem 1. 1) Who is the author of the first comprehensive text on geometry? When and where was it written? Answer: The first comprehensive text on geometry is called The Elements
Math Nation Section 7 Topics 3 8: Special Segments in a Triangle Notes
Math Nation Section 7 Topics 3 8: Special Segments in a Triangle Notes (7.1 7.4 Extension) Proportionality caused by a Parallel Segment Ex 1) Ex 2) Ex 3) How do we know that ΔABG ~ ΔACF ~ ΔADE? P a g e
Constructions with Compass and Straightedge - Part 2
Name: Constructions with Compass and Straightedge - Part 2 Original Text By Dr. Bradley Material Supplemented by Mrs.de Nobrega 4.8 Points of Concurrency in a Triangle Our last four constructions are our
G.CO.C.10: Centroid, Orthocenter, Incenter and Circumcenter
1 Which geometric principle is used in the construction shown below? 2 In the diagram below of ABC, CD is the bisector of BCA, AE is the bisector of CAB, and BG is drawn. 1) The intersection of the angle
CHAPTER - 10 STRAIGHT LINES Slope or gradient of a line is defined as m = tan, ( 90 ), where is angle which the line makes with positive direction of x-axis measured in anticlockwise direction, 0 < 180
CLASSICAL THEOREMS IN PLANE GEOMETRY. September 2007 BC 1 AC 1 CA 1 BA 1 = 1.
SSI THEORES I E GEOETRY ZVEZEI STKOV September 2007 ote: ll objects in this handout are planar - i.e. they lie in the usual plane. We say that several points are collinear if they lie on a line. Similarly,
TImath.com. Geometry. Special Segments in Triangles
Special Segments in Triangles ID: 8672 Time required 90 minutes Activity Overview In this activity, students explore medians, altitudes, angle bisectors, and perpendicular bisectors of triangles. They
Review Packet: Ch. 4 & 5 LT13 LT17
Review Packet: Ch. 4 & 5 LT13 LT17 Name: Pd. LT13: I can apply the Triangle Sum Theorem and Exterior angle Theorem to classify triangles and find the measure of their angles. 1. Find x and y. 2. Find x
Geometry 5-1 Bisector of Triangles- Live lesson
Geometry 5-1 Bisector of Triangles- Live lesson Draw a Line Segment Bisector: Draw an Angle Bisectors: Perpendicular Bisector A perpendicular bisector is a line, segment, or ray that is perpendicular to
0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 9 8 3 6 2 In the diagram below,. 4 Pentagon PQRST has parallel to. After a translation of, which line
Chapter 6.1 Medians. Geometry
Chapter 6.1 Medians Identify medians of triangles Find the midpoint of a line using a compass. A median is a segment that joins a vertex of the triangle and the midpoint of the opposite side. Median AD
If B is the If two angles are
If If B is between A and C, then 1 2 If P is in the interior of RST, then If B is the If two angles are midpoint of AC, vertical, then then 3 4 If angles are adjacent, then If angles are a linear pair,
GEOMETRY HONORS COORDINATE GEOMETRY PACKET
GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period 1 Day 1 - Directed Line Segments DO NOW Distance formula 1 2 1 2 2 2 D x x y y Midpoint formula x x, y y 2 2 M 1 2 1 2 Slope formula y y m x x 2 1
3. Radius of incenter, C. 4. The centroid is the point that corresponds to the center of gravity in a triangle. B
1. triangle that contains one side that has the same length as the diameter of its circumscribing circle must be a right triangle, which cannot be acute, obtuse, or equilateral. 2. 3. Radius of incenter,
a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
The Orthic-of-Intouch and Intouch-of-Orthic Triangles
Forum Geometricorum Volume 6 (006 171 177 FRUM GEM SSN 1534-1178 The rthic-of-ntouch and ntouch-of-rthic Triangles Sándor Kiss bstract arycentric coordinates are used to prove that the othic of intouch
GEOMETRY WITH GEOGEBRA
GEOMETRY WITH GEOGEBRA PART ONE: TRIANGLES Notations AB ( AB ) [ AB ] ] AB [ [ AB ) distance between the points A and B line through the points A and B segment between the two points A and B (A and B included)
Geometry - Concepts 9-12 Congruent Triangles and Special Segments
Geometry - Concepts 9-12 Congruent Triangles and Special Segments Concept 9 Parallel Lines and Triangles (Section 3.5) ANGLE Classifications Acute: Obtuse: Right: SIDE Classifications Scalene: Isosceles:
.(3, 2) Co-ordinate Geometry Co-ordinates. Every point has two co-ordinates. Plot the following points on the plane. A (4, 1) D (2, 5) G (6, 3)
Co-ordinate Geometry Co-ordinates Every point has two co-ordinates. (3, 2) x co-ordinate y co-ordinate Plot the following points on the plane..(3, 2) A (4, 1) D (2, 5) G (6, 3) B (3, 3) E ( 4, 4) H (6,
You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1
Name GRAPHICAL REPRESENTATION OF DATA: You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1 ) and (x, y ) is x1 x y1 y,.
Segments and Angles. Name Period. All constructions done today will be with Compass and Straight-Edge ONLY.
Segments and ngles Geometry 3.1 ll constructions done today will be with ompass and Straight-Edge ONLY. Duplicating a segment is easy. To duplicate the segment below: Draw a light, straight line. Set your
Definition / Postulates / Theorems Checklist
3 undefined terms: point, line, plane Definition / Postulates / Theorems Checklist Section Definition Postulate Theorem 1.2 Space Collinear Non-collinear Coplanar Non-coplanar Intersection 1.3 Segment
Term: Definition: Picture:
10R Unit 7 Triangle Relationships CW 7.8 HW: Finish this CW 7.8 Review for Test Answers: See Teacher s Website Theorem/Definition Study Sheet! Term: Definition: Picture: Exterior Angle Theorem: Triangle
1) If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
5.1 and 5.2 isectors in s l Theorems about perpendicular bisectors 1) If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. Given:
Geometry CP Pen Argyl Area High School 2018
Geometry emphasizes the development of logical thinking as it relates to geometric problems. Topics include using the correct language and notations of geometry, developing inductive and deductive reasoning,
Geometry Period Unit 2 Constructions Review
Name 2-7 Review Geometry Period Unit 2 Constructions Review Date 2-1 Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral
Acknowledgement: Scott, Foresman. Geometry. SIMILAR TRIANGLES. 1. Definition: A ratio represents the comparison of two quantities.
1 cknowledgement: Scott, Foresman. Geometry. SIMILR TRINGLS 1. efinition: ratio represents the comparison of two quantities. In figure, ratio of blue squares to white squares is 3 : 5 2. efinition: proportion
About Graphing Lines
About Graphing Lines TABLE OF CONTENTS About Graphing Lines... 1 What is a LINE SEGMENT?... 1 Ordered Pairs... 1 Cartesian Co-ordinate System... 1 Ordered Pairs... 2 Line Segments... 2 Slope of a Line
Constructions Quiz Review November 29, 2017
Using constructions to copy a segment 1. Mark an endpoint of the new segment 2. Set the point of the compass onto one of the endpoints of the initial line segment 3. djust the compass's width to the other
Geometry Midterm Review
Geometry Midterm Review **Look at Study Guide and old tests The Midterm covers: Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Parts of Chapter 6 Chapter 1 1.1 point: - has no dimension - represented
fall08ge Geometry Regents Exam Test Sampler fall08 4 The diagram below shows the construction of the perpendicular bisector of AB.
fall08ge 1 Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x 5, what is the value of x? 1) 8 4 The diagram below shows the construction of the perpendicular bisector of AB.
2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? Formula: Area of a Trapezoid. 3 Centroid. 4 Midsegment of a triangle
1 Formula: Area of a Trapezoid 2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? 3 Centroid 4 Midsegment of a triangle 5 Slope formula 6 Point Slope Form of Linear Equation *can
Chapter 2 Similarity and Congruence
Chapter 2 Similarity and Congruence Definitions Definition AB = CD if and only if AB = CD Remember, mab = AB. Definitions Definition AB = CD if and only if AB = CD Remember, mab = AB. Definition ABC =
Revision Problems for Examination 2 in Algebra 1
Centre for Mathematical Sciences Mathematics, Faculty of Science Revision Problems for Examination in Algebra. Let l be the line that passes through the point (5, 4, 4) and is at right angles to the plane
Midpoint of a Line Segment Pg. 78 # 1, 3, 4-6, 8, 18. Classifying Figures on a Cartesian Plane Quiz ( )
UNIT 2 ANALYTIC GEOMETRY Date Lesson TOPIC Homework Feb. 22 Feb. 23 Feb. 24 Feb. 27 Feb. 28 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.5 2.1-2.3 2.1-2.3 Mar. 1 2.6 2.4 Mar. 2 2.7 2.5 Mar. 3 2.8 2.6 Mar. 6 2.9 2.7 Mar.
Unit 4 Syllabus: Properties of Triangles & Quadrilaterals
` Date Period Unit 4 Syllabus: Properties of Triangles & Quadrilaterals Day Topic 1 Midsegments of Triangle and Bisectors in Triangles 2 Concurrent Lines, Medians and Altitudes, and Inequalities in Triangles
Geometry Period Unit 2 Constructions Review
Name 2-7 Review Geometry Period Unit 2 Constructions Review Date 2-1 Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral
GEOMETRY R Unit 4: More Transformations / Compositions. Day Classwork Homework Monday 10/16. Perpendicular Bisector Relationship to Transformations
GEOMETRY R Unit 4: More Transformations / Compositions Day Classwork Homework Monday 10/16 Perpendicular Bisector Relationship to Transformations HW 4.1 Tuesday 10/17 Construction of Parallel Lines Through
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
The Rectangular Coordinate System and Equations of Lines. College Algebra
The Rectangular Coordinate System and Equations of Lines College Algebra Cartesian Coordinate System A grid system based on a two-dimensional plane with perpendicular axes: horizontal axis is the x-axis
GeoGebra Workshop. Don Spickler Department of Mathematics and Computer Science Salisbury University
GeoGebra Workshop Don Spickler Department of Mathematics and Computer Science Salisbury University Contents Introduction... 3 What is GeoGebra?... 3 Get GeoGebra... 3 Workshop Sections... 3 Workshop Format...
1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R.
1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent to, ABC?
BISECTORS OF TRIANGLES
BISECTORS OF TRIANGLES To prove and apply the properties of perpendicular bisectors and angle bisectors KEY CONCET erpendicular bisector of a triangle line, segment or ray that is perpendicular to a side
14-9 Constructions Review. Geometry Period. Constructions Review
Name Geometry Period 14-9 Constructions Review Date Constructions Review Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties
Assignment List. Chapter 1 Essentials of Geometry. Chapter 2 Reasoning and Proof. Chapter 3 Parallel and Perpendicular Lines
Geometry Assignment List Chapter 1 Essentials of Geometry 1.1 Identify Points, Lines, and Planes 5 #1, 4-38 even, 44-58 even 27 1.2 Use Segments and Congruence 12 #4-36 even, 37-45 all 26 1.3 Use Midpoint
Suggested List of Mathematical Language. Geometry
Suggested List of Mathematical Language Geometry Problem Solving A additive property of equality algorithm apply constraints construct discover explore generalization inductive reasoning parameters reason
Name. 1) If Q is the vertex angle of isosceles PQR, and RA is a median, find m QR Q. 4 inches A. 2) Which side is the dot closest to?
enters of Triangles acket 1 Name 1) If Q is the vertex angle of isosceles QR, and R is a median, find m QR Q 4 inches R 2) Which side is the dot closest to? an you draw a point that is the same distance
Chapter 7 Coordinate Geometry
Chapter 7 Coordinate Geometry 1 Mark Questions 1. Where do these following points lie (0, 3), (0, 8), (0, 6), (0, 4) A. Given points (0, 3), (0, 8), (0, 6), (0, 4) The x coordinates of each point is zero.
First Quarter Second Quarter Third Quarter Fourth Quarter Unit 1: Geometry Basics
Document Definitions Geometry/Geometry Honors Pacing Guide Focus: Second Quarter First Quarter Second Quarter Third Quarter Fourth Quarter Unit 1: Geometry Basics 2.5 weeks/6 blocks Unit 2: Logic and Reasoning
VOCABULARY. Chapters 1, 2, 3, 4, 5, 9, and 8. WORD IMAGE DEFINITION An angle with measure between 0 and A triangle with three acute angles.
Acute VOCABULARY Chapters 1, 2, 3, 4, 5, 9, and 8 WORD IMAGE DEFINITION Acute angle An angle with measure between 0 and 90 56 60 70 50 A with three acute. Adjacent Alternate interior Altitude of a Angle
How to Construct a Perpendicular to a Line (Cont.)
Geometric Constructions How to Construct a Perpendicular to a Line (Cont.) Construct a perpendicular line to each side of this triangle. Find the intersection of the three perpendicular lines. This point
CHAPTER 2 REVIEW COORDINATE GEOMETRY MATH Warm-Up: See Solved Homework questions. 2.2 Cartesian coordinate system
CHAPTER 2 REVIEW COORDINATE GEOMETRY MATH6 2.1 Warm-Up: See Solved Homework questions 2.2 Cartesian coordinate system Coordinate axes: Two perpendicular lines that intersect at the origin O on each line.
Mathematics 10 Page 1 of 6 Geometric Activities
Mathematics 10 Page 1 of 6 Geometric ctivities ompass can be used to construct lengths, angles and many geometric figures. (eg. Line, cirvle, angle, triangle et s you are going through the activities,
VERIFYING PROPERTIES OF GEOMETRIC FIGURES. Ad is a median
UNIT NLYTI GEOMETRY VERIFYING PROPERTIES OF GEOMETRI FIGURES Parallelogram Rhombus Quadrilateral E H D F G = D and = D EF FG GH EH I L J Right Triangle Median of a Triangle K b a c d is a median D ltitude
Investigating Properties of Kites
Investigating Properties of Kites Definition: Kite a quadrilateral with two distinct pairs of consecutive equal sides (Figure 1). Construct and Investigate: 1. Determine three ways to construct a kite
GEOMETRY HONORS COORDINATE GEOMETRY PACKET
GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period Homework Lesson Assignment Day 1 - Slopes of Perpendicular WKSHT and Parallel Lines Day 2 - Writing an Equation of a Line HW- Honors TXTBK pages 615-617
Grade 9 Math Terminology
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
GeoGebra for Synthetic Geometry
ICT & MATHS Module 1 GeoGebra for Synthetic Geometry Published by The National Centre for Technology in Education in association with the Project Maths Development Team. Permission granted to reproduce
10-2 Circles. Warm Up Lesson Presentation Lesson Quiz. Holt Algebra2 2
10-2 Circles Warm Up Lesson Presentation Lesson Quiz Holt Algebra2 2 Warm Up Find the slope of the line that connects each pair of points. 1. (5, 7) and ( 1, 6) 1 6 2. (3, 4) and ( 4, 3) 1 Warm Up Find
Chapter 10 Similarity
Chapter 10 Similarity Def: The ratio of the number a to the number b is the number. A proportion is an equality between ratios. a, b, c, and d are called the first, second, third, and fourth terms. The
Get Ready. Solving Equations 1. Solve each equation. a) 4x + 3 = 11 b) 8y 5 = 6y + 7
Get Ready BLM... Solving Equations. Solve each equation. a) 4x + = 8y 5 = 6y + 7 c) z+ = z+ 5 d) d = 5 5 4. Write each equation in the form y = mx + b. a) x y + = 0 5x + y 7 = 0 c) x + 6y 8 = 0 d) 5 0
Name: Date: Period: Chapter 3 Constructions Review
Name: Date: Period: Chapter 3 Constructions Review Complete all questions. Questions 7-18 must be completed on looseleaf paper. Constructions & Definitions to know: Altitudes Orthocenter Centers to know: