Where should Sam and Marla Wilson look for a new apartment that is equidistant from their jobs?

Size: px
Start display at page:

Download "Where should Sam and Marla Wilson look for a new apartment that is equidistant from their jobs?"

Transcription

1 Where should Sam and Marla Wilson look for a new apartment that is equidistant from their jobs? anywhere on B street 1

2 12.6 Locus: A Set of Points In the warm up, you described the possible locations based on a certain condition. A locus is a set of points, all of which meet a stated condition. Loci is the plural of locus. 2

3 What is a sketch and description for each locus of points in a plane? The points 1 cm from a given point C C The locus is a circle with center C and radius 1 cm. 3

4 What is a sketch and description for each locus of points in a plane? The points 1 cm from AB A B The locus is a pair of parallel segments, each 1 cm from AB, and two semicircles with centers at A and B. 4

5 What is a sketch and description for each locus of points in a plane? The points 1 cm from AB A B The locus is a pair of parallel lines, each 1 cm from AB 5

6 You can use locus descriptions for geometric terms. The locus of points in the interior of an angle that are equidistant from the sides of the angle is an angle bisector. In a plane, the locus of points that are equidistant from a segment's endpoints is the perpendicular bisector of the segment. 6

7 Sometimes a locus is described by two conditions. You can draw the locus by first drawing the points that satisfy each condition. Then find their intersection. 7

8 What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from intersecting lines k and m The points 5 cm from the point where k and m intersect k m points A, B, C and D 8

9 What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from two points X and Y The points 2 cm from the midpoint of XY X Y points A and B 9

10 What is the locus of points in space that are c units from a point D? D The locus is a sphere with center at point D and radius c. 10

11 What is the locus of points in space that are 3 cm from a line l? l The locus is an endless cylinder with radius 3 cm and centerline l. 11

12 What is the locus in a plane of the points that are equidistant from two parallel lines? The locus is the line to and equidistance from the given lines midway between them. 12

13 What is the locus in a space of the points that are equidistant from two parallel planes? The locus is a plane to and equidistance from the given planes midway between them. 13

14 What is a sketch and description for each locus of points in a plane? Points 4 cm from a point X X The locus is a circle with center c and radius 4 cm. 14

15 What is a sketch and description for each locus of points in a plane? Points 2 in. from UV U V The locus is a pair of segments, each segment 2 in. from UV, and two semicircles with radius 2 in. and centers U and V. 15

16 What is a sketch and description for each locus of points in a plane? Points 3 mm from LM L M The locus is a pair of lines, each 3 mm from LM. 16

17 What is a sketch and description for each locus of points in a plane? Points 1 in. from a circle with radius 3 in. The locus is a two circles concentric with the original circle; the smaller circle has radius 2 in. and the larger circle has radius 4 in. 17

18 What is a sketch and description for each locus of points in a plane? Points 1 cm from the endpoints of CD C D The loci are circles with a radius of 1 cm centered at C and D. 18

19 What is a sketch and description for each locus of points in a plane? Points 2 cm from a given point P P The locus is a circle with center P and radius 2 cm. 19

20 What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from the endpoints of segment MN The points less than or equal to 2 cm from the midpoint of segment MN M N The locus is a segment of the perpendicular bisector of MN with a length of 2 cm on each side of MN. 20

21 Describe the locus (or loci) of points in space that are 5 cm from plane P. P two parallel planes in space that are 5 cm from the original plane 21

22 Describe the locus of points in space that are 3 in. from point Q. Q a sphere in space with a radius of 3 in. and center Q. 22

1. Reasoning If the question for part (b) asked for the locus of points in a plane 1 cm from < AB >, how would the sketch change?

1. Reasoning If the question for part (b) asked for the locus of points in a plane 1 cm from < AB >, how would the sketch change? 12-6 Locus: Set of Points ommon ore State Standards G-GMD..4... Identify three-dimensional objects generated by rotations of two-dimensional objects. MP 1, MP 3, MP 4, MP 6 Objective To draw and describe

More information

Chapter 11: Constructions and Loci

Chapter 11: Constructions and Loci Chapter 11: Section 11.1a Constructing a Triangle given 3 sides (sss) Leave enough room above the line to complete the shape. Do not rub out your construction lines. They show your method. 1 Section 11.1b

More information

Mathematics Revision Guides Loci Page 1 of 10 Author: Mark Kudlowski M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier LOCI

Mathematics Revision Guides Loci Page 1 of 10 Author: Mark Kudlowski M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier LOCI Mathematics Revision Guides Loci Page 1 of 10 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier LOCI Version: 2.1 Date: 28-10-2014 Mathematics Revision Guides Loci Page 2 of 10

More information

Circles Assignment Answer the following questions.

Circles Assignment Answer the following questions. Answer the following questions. 1. Define constructions. 2. What are the basic tools that are used to draw geometric constructions? 3. What is the use of constructions? 4. What is Compass? 5. What is Straight

More information

Locus Locus. Remarks

Locus Locus. Remarks 4 4. The locus of a point is the path traced out by the point moving under given geometrical condition (or conditions). lternatively, the locus is the set of all those points which satisfy the given geometrical

More information

Constructing Perpendicular and Parallel Lines. Adapted from Walch Education

Constructing Perpendicular and Parallel Lines. Adapted from Walch Education Constructing Perpendicular and Adapted from Walch Education Perpendicular Lines and Bisectors Perpendicular lines are two lines that intersect at a right angle (90 ). A perpendicular line can be constructed

More information

Name No. Geometry 9-3 1) Complete the table: Name No. Geometry 9-1 1) Name a secant. Name a diameter. Name a tangent. Name No. Geometry 9-2 1) Find JK

Name No. Geometry 9-3 1) Complete the table: Name No. Geometry 9-1 1) Name a secant. Name a diameter. Name a tangent. Name No. Geometry 9-2 1) Find JK Geometry 9-1 1) Name a secant 1) Complete the table: Name a diameter Name a tangent Geometry 9-2 1) Find JK 2) Find the measure of 1 Geometry 9-2 2) 3) At 2:00 the hands of a clock form an angle of 2)

More information

(1) Page 482 #1 20. (2) Page 488 #1 14. (3) Page # (4) Page 495 #1 10. (5) Page #12 30,

(1) Page 482 #1 20. (2) Page 488 #1 14. (3) Page # (4) Page 495 #1 10. (5) Page #12 30, Geometry/Trigonometry Unit 8: Circles Notes Name: Date: Period: # (1) Page 482 #1 20 (2) Page 488 #1 14 (3) Page 488 489 #15 26 (4) Page 495 #1 10 (5) Page 495 496 #12 30, 37 39 (6) Page 502 #1 7 (7) Page

More information

GCSE Mathematics (Non-calculator Paper)

GCSE Mathematics (Non-calculator Paper) Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature GCSE Mathematics (Non-calculator Paper) Practice Paper Style Questions Topic: Loci & Constructions

More information

6.1 Warm Up The diagram includes a pair of congruent triangles. Use the congruent triangles to find the value of x in the diagram.

6.1 Warm Up The diagram includes a pair of congruent triangles. Use the congruent triangles to find the value of x in the diagram. 6.1 Warm Up The diagram includes a pair of congruent triangles. Use the congruent triangles to find the value of x in the diagram. 1. 2. Write a proof. 3. Given: P is the midpoint of MN and TQ. Prove:

More information

GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)

GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance

More information

Name: Date: Period: Chapter 15: Locus Topic 9: Compound Loci Word Problems

Name: Date: Period: Chapter 15: Locus Topic 9: Compound Loci Word Problems Chapter 15: Locus Topic 9: Compound Loci Word Problems Compound Loci: Recall: A compound locus is a problem that involved two or more locus conditions occurring at the same time. To Find Points that Satisfy

More information

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify

More information

Tangents to Circles. The distance across the circle, through its center, is the diameter of the circle. The diameter is twice the radius.

Tangents to Circles. The distance across the circle, through its center, is the diameter of the circle. The diameter is twice the radius. ircles Tangents to ircles circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. circle with center P is called circle P. The distance from

More information

Stretch lesson: Constructions

Stretch lesson: Constructions 29 Stretch lesson: onstructions Stretch objectives efore you start this chapter, mark how confident you feel about each of the statements below: I can construct the perpendicular bisector of a given line.

More information

You MUST know the big 3 formulas!

You MUST know the big 3 formulas! Name 3-13 Review Geometry Period Date Unit 3 Lines and angles 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

More information

b. Describe how a horizontal translation changes the coordinates of the endpoints.

b. Describe how a horizontal translation changes the coordinates of the endpoints. Pre-Test Name Date. Determine the distance between the points (5, 2) and (2, 6). 2. Mari draws line segment AB on a coordinate plane. The coordinates of A are (, 5). The coordinates of B are (23, 2). She

More information

Sec Geometry - Constructions

Sec Geometry - Constructions Sec 2.2 - Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have

More information

0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0)

0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0) 0810ge 1 In the diagram below, ABC! XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements

More information

Geometry SOL G.4 Constructions Name Date Block. Constructions

Geometry SOL G.4 Constructions Name Date Block. Constructions Geometry SOL G.4 Constructions Mrs. Grieser Name Date Block Constructions Grab your compass and straight edge - it s time to learn about constructions!! On the following pages you will find instructions

More information

Math 3 Geogebra Discovery - Equidistance Decemeber 5, 2014

Math 3 Geogebra Discovery - Equidistance Decemeber 5, 2014 Math 3 Geogebra Discovery - Equidistance Decemeber 5, 2014 Today you and your partner are going to explore two theorems: The Equidistance Theorem and the Perpendicular Bisector Characterization Theorem.

More information

Pre-Test. Name Date. 1. Can skew lines be coplanar? Explain.

Pre-Test. Name Date. 1. Can skew lines be coplanar? Explain. Pre-Test Name Date 1. Can skew lines be coplanar? Explain. 2. Point D is at the center of a circle. Points A, B, and C are on the same arc of the circle. What can you say about the lengths of AD, BD, and

More information

Geometry. 6.1 Perpendicular and Angle Bisectors.

Geometry. 6.1 Perpendicular and Angle Bisectors. Geometry 6.1 Perpendicular and Angle Bisectors mbhaub@mpsaz.org 6.1 Essential Question What conjectures can you make about a point on the perpendicular bisector of a segment and a point on the bisector

More information

If you haven t already done so, please collect a Do Now from the tray on the supply table and sit in your assigned seat and complete it in silence.

If you haven t already done so, please collect a Do Now from the tray on the supply table and sit in your assigned seat and complete it in silence. If you haven t already done so, please collect a Do Now from the tray on the supply table and sit in your assigned seat and complete it in silence. Thank you. M9-12.G.CO.1 SWBAT know precise definitions

More information

9-1: Circle Basics GEOMETRY UNIT 9. And. 9-2: Tangent Properties

9-1: Circle Basics GEOMETRY UNIT 9. And. 9-2: Tangent Properties 9-1: Circle Basics GEOMETRY UNIT 9 And 9-2: Tangent Properties CIRCLES Content Objective: Students will be able to solve for missing lengths in circles. Language Objective: Students will be able to identify

More information

12 Constructions and Loci

12 Constructions and Loci MEP Y9 Practice ook 12 onstructions and Loci 12.1 Recap: ngles and Scale Drawing The concepts in this unit rely heavily on knowledge acquired previously, particularly for angles and scale drawings, so

More information

UNIT 1 GEOMETRY. (revision from 1 st ESO) Unit 8 in our books

UNIT 1 GEOMETRY. (revision from 1 st ESO) Unit 8 in our books UNIT 1 GEOMETRY (revision from 1 st ESO) Unit 8 in our books WHAT'S GEOMETRY? Geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. In geometry, one explores

More information

Materials: Computer lab or set of calculators equipped with Cabri Geometry II and lab worksheet.

Materials: Computer lab or set of calculators equipped with Cabri Geometry II and lab worksheet. Constructing Perpendiculars Lesson Summary: Students will complete the basic compass and straight edge constructions commonly taught in first year high school Geometry. Key Words: perpendicular, compass,

More information

9.1 and 9.2 Introduction to Circles

9.1 and 9.2 Introduction to Circles Date: Secondary Math 2 Vocabulary 9.1 and 9.2 Introduction to Circles Define the following terms and identify them on the circle: Circle: The set of all points in a plane that are equidistant from a given

More information

The 7* Basic Constructions Guided Notes

The 7* Basic Constructions Guided Notes Name: The 7* asic Constructions Guided Notes Included: 1. Given an segment, construct a 2 nd segment congruent to the original. (ctually not included!) 2. Given an angle, construct a 2 nd angle congruent

More information

(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions.

(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. Seventh Grade Mathematics Assessments page 1 (Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. A. TLW use tools to draw squares, rectangles, triangles and

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction Prerequisite Skills This lesson requires the use of the following skills: using a compass understanding the geometry terms line, segment, ray, and angle Introduction Two basic instruments used in geometry

More information

1. Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. Begin with line segment XY.

1. Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. Begin with line segment XY. 1. onstruct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. egin with line segment. 2. lace the compass at point. djust the compass radius so that it is more

More information

CONSTRUCTION #1: Segment Copy

CONSTRUCTION #1: Segment Copy CONSTRUCTION #1: Segment Copy Objective: Given a line segment, construct a line segment congruent to the given one. Procedure: After doing this Your work should look like this Start with a line segment

More information

Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1

Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1 Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 3: Constructing Polygons Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 3: Constructing Polygons Instruction rerequisite Skills This lesson requires the use of the following skills: using a compass copying and bisecting line segments constructing perpendicular lines constructing circles of a given radius Introduction

More information

Using inductive reasoning and conjectures Student Activity Sheet 2; use with Exploring The language of geometry

Using inductive reasoning and conjectures Student Activity Sheet 2; use with Exploring The language of geometry 1. REINFORCE Find a geometric representation for the following sequence of numbers. 3, 4, 5, 6, 7, 2. What are the three undefined terms in geometry? 3. Write a description of a point. How are points labeled?

More information

STRAND H: Angle Geometry

STRAND H: Angle Geometry Mathematics SKE, Strand H UNIT H3 onstructions and Loci: Text STRND H: ngle Geometry H3 onstructions and Loci Text ontents Section H3.1 Drawing and Symmetry H3.2 onstructing Triangles and ther Shapes H3.3

More information

Angles formed by Transversals

Angles formed by Transversals Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel

More information

2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)

2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2) Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down

More information

Pre-Calc. Slide 1 / 160. Slide 2 / 160. Slide 3 / 160. Conics Table of Contents. Review of Midpoint and Distance Formulas

Pre-Calc. Slide 1 / 160. Slide 2 / 160. Slide 3 / 160. Conics Table of Contents. Review of Midpoint and Distance Formulas Slide 1 / 160 Pre-Calc Slide 2 / 160 Conics 2015-03-24 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 160 Review of Midpoint and Distance Formulas Intro to Conic Sections

More information

UNIT 14 Loci and NC: Shape, Space and Measures Transformations 3b, 3c, 3d and 3e

UNIT 14 Loci and NC: Shape, Space and Measures Transformations 3b, 3c, 3d and 3e UNIT 14 Loci and NC: Shape, Space and Measures Transformations 3b, 3c, 3d and 3e TOPICS (Text and Practice Books) St Ac Ex Sp 14.1 Drawing and Symmetry - - - 14.2 Scale Drawings - - 14.3 Constructing Triangles

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB # AC. The measure of!b is 40. 1) a! b 2) a! c 3) b! c 4) d! e What is the measure of!a? 1) 40 2) 50 3) 70

More information

Topic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements)

Topic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements) Topic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements) 1. Duplicating (copying) a segment 2. Duplicating (copying) an angle 3. Constructing the bisector of a segment (bisecting a segment)

More information

1-2 Measuring and Constructing Segments. Holt Geometry

1-2 Measuring and Constructing Segments. Holt Geometry 1-2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance bisect length segment bisector

More information

Constructions. Learning Intention: By If you use 1 litre of orange, you will use 4 litres of water (1:4).

Constructions. Learning Intention: By If you use 1 litre of orange, you will use 4 litres of water (1:4). Constructions Scales Scales are important in everyday life. We use scales to draw maps, to construct building plans, in housing, street construction... It is impossible to draw building plans with the

More information

Constructions. Unit 9 Lesson 7

Constructions. Unit 9 Lesson 7 Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS

More information

4 The Cartesian Coordinate System- Pictures of Equations

4 The Cartesian Coordinate System- Pictures of Equations The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the Pythagorean

More information

Semester A Review Answers. 1. point, line, and plane. 2. one. 3. three. 4. one or No, since AB BC AC 11. AC a. EG FH.

Semester A Review Answers. 1. point, line, and plane. 2. one. 3. three. 4. one or No, since AB BC AC 11. AC a. EG FH. 1. point, line, and plane 2. one 3. three 4. one 5. 18 or 8 6. b 23, c 30 7. No, since C C 8. 8 9. x 20 10. C 470 11. C 12 12. x 10 13. x 25 14. x 25 15. a. EG FH b. EG 43 16. m 2 55 o 17. x 30 18. m 1

More information

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Graph ellipses centered at the origin. Write equations of ellipses in standard

More information

Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points.

Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points. Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the given

More information

Objective: Use a compass and straight edge to construct congruent segments and angles.

Objective: Use a compass and straight edge to construct congruent segments and angles. CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Introduction to Constructions Constructions: The drawing of various shapes using only a pair of compasses

More information

S. Stirling Page 1 of 14

S. Stirling Page 1 of 14 3.1 Duplicating Segments and ngles [and riangles] hese notes replace pages 144 146 in the book. You can read these pages for extra clarifications. Instructions for making geometric figures: You can sketch

More information

2. What distance from the transmitter must the phone be within when Katie draws the locus of points in the range of the transmitter?

2. What distance from the transmitter must the phone be within when Katie draws the locus of points in the range of the transmitter? Worksheet 1: Programme Questions 1. What is the plural of locus? 2. What distance from the transmitter must the phone be within when Katie draws the locus of points in the range of the transmitter? 3.

More information

Objective: Use a compass and straight edge to construct congruent segments and angles.

Objective: Use a compass and straight edge to construct congruent segments and angles. CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1 Introduction to Constructions Constructions: The drawing of various shapes

More information

Pre Calc. Conics.

Pre Calc. Conics. 1 Pre Calc Conics 2015 03 24 www.njctl.org 2 Table of Contents click on the topic to go to that section Review of Midpoint and Distance Formulas Intro to Conic Sections Parabolas Circles Ellipses Hyperbolas

More information

ONE. angles which I already know

ONE. angles which I already know Name Geometry Period ONE Ticket In Date Ticket In the Door! After watching the assigned video and learning how to construct a perpendicular line through a point, you will perform this construction below

More information

7th Grade Drawing Geometric Figures

7th Grade Drawing Geometric Figures Slide 1 / 53 Slide 2 / 53 7th Grade Drawing Geometric Figures 2015-11-23 www.njctl.org Slide 3 / 53 Topics Table of Contents Determining if a Triangle is Possible Click on a topic to go to that section

More information

22.1 Locus From Common Conditions

22.1 Locus From Common Conditions .5 of 52 Locus From ommon onditions 22.1 Locus From ommon onditions Example 1 1. In the figure, EG is a square with sides of 2 cm. iagonals E and G intersect at K.,, F and H are the midpoints of, E, EG

More information

Elementary Geometric Drawings Angles. Angle Bisector. Perpendicular Bisector

Elementary Geometric Drawings Angles. Angle Bisector. Perpendicular Bisector Lessons and Activities GEOMETRY Elementary Geometric Drawings Angles Angle Bisector Perpendicular Bisector 1 Lessons and Activities POLYGONS are PLANE SHAPES (figures) with at least 3 STRAIGHT sides and

More information

Pre-Calc Conics

Pre-Calc Conics Slide 1 / 160 Slide 2 / 160 Pre-Calc Conics 2015-03-24 www.njctl.org Slide 3 / 160 Table of Contents click on the topic to go to that section Review of Midpoint and Distance Formulas Intro to Conic Sections

More information

Geometric Constructions

Geometric Constructions Geometric onstructions (1) opying a segment (a) Using your compass, place the pointer at Point and extend it until reaches Point. Your compass now has the measure of. (b) Place your pointer at, and then

More information

Geometry - Midterm Exam Review - Chapters 1, 2

Geometry - Midterm Exam Review - Chapters 1, 2 Geometry - Midterm Exam Review - Chapters 1, 2 1. Name three points in the diagram that are not collinear. 2. Describe what the notation stands for. Illustrate with a sketch. 3. Draw four points, A, B,

More information

Challenges from Ancient Greece

Challenges from Ancient Greece Challenges from ncient Greece Mathematical goals Make formal geometric constructions with a variety of tools and methods. Use congruent triangles to justify geometric constructions. Common Core State Standards

More information

4. Draw the development of the lateral surface of the part P of the cylinder whose front view is shown in figure 4. All dimensions are in cm.

4. Draw the development of the lateral surface of the part P of the cylinder whose front view is shown in figure 4. All dimensions are in cm. Code No: Z0122 / R07 Set No. 1 I B.Tech - Regular Examinations, June 2009 ENGINEERING GRAPHICS ( Common to Civil Engineering, Mechanical Engineering, Chemical Engineering, Bio-Medical Engineering, Mechatronics,

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

Find the coordinates of the midpoint of a segment having the given endpoints.

Find the coordinates of the midpoint of a segment having the given endpoints. G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to

More information

Geometer s Skethchpad 8th Grade Guide to Learning Geometry

Geometer s Skethchpad 8th Grade Guide to Learning Geometry Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

More information

Math 1330 Section 8.2 Ellipses

Math 1330 Section 8.2 Ellipses Math 1330 Section 8.2 Ellipses To form a conic section, we ll take this double cone and slice it with a plane. When we do this, we ll get one of several different results. 1 Part 1 - The Circle Definition:

More information

Revision Topic 6: Loci and Constructions

Revision Topic 6: Loci and Constructions Revision Topic 6: Loci and onstructions onstructions isecting an angle N.. To bisect an angle means to cut it in half. (1) Use your compasses to mark points and which are the same distance from the point

More information

Project Maths Geometry Notes

Project Maths Geometry Notes The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam

More information

This early Greek study was largely concerned with the geometric properties of conics.

This early Greek study was largely concerned with the geometric properties of conics. 4.3. Conics Objectives Recognize the four basic conics: circle, ellipse, parabola, and hyperbola. Recognize, graph, and write equations of parabolas (vertex at origin). Recognize, graph, and write equations

More information

Tangents and Chords Off On a Tangent

Tangents and Chords Off On a Tangent Tangents and Chords SUGGESTED LERNING STRTEGIES: Group Presentation, Think/Pair/Share, Quickwrite, Interactive Word Wall, Vocabulary Organizer, Create Representations, Quickwrite CTIVITY 4.1 circle is

More information

Geometric Constructions

Geometric Constructions Geometry Name: Part 1: What are Geometric Constructions? Geometric Constructions Go to http://www.mathopenref.com/constructions.html. Answer the following questions. 1. What is a construction? 2. What

More information

Unit 6 Guided Notes. Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle.

Unit 6 Guided Notes. Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle. Unit 6 Guided Notes Geometry Name: Period: Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle. Materials: This paper, compass, ruler

More information

The Magic Circle Basic Lesson. Developed by The Alexandria Seaport Foundation

The Magic Circle Basic Lesson. Developed by The Alexandria Seaport Foundation The Magic Circle Basic Lesson Developed by The Alexandria Seaport Foundation The Tools Needed Compass Straightedge Pencil Paper (not graph paper, 8.5 x 11 is fine) Your Brain (the most important tool!)

More information

3. Given the similarity transformation shown below; identify the composition:

3. Given the similarity transformation shown below; identify the composition: Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the

More information

Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0

Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume

More information

Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics

Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would

More information

(Length and Area Ratio s)

(Length and Area Ratio s) (Length and Area Ratio s) Standard Televisions are measured by the length of the diagonal. Most manufactures included the TV frame as part of the measurement (when measuring CRT (cathode ray tube) screens).

More information

Student Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Form: 501

Student Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Form: 501 Student Name: Teacher: Date: District: Rowan Assessment: 9_12 T and I IC61 - Drafting I Test 1 Description: Test 4 A (Diagrams) Form: 501 Please use the following figure for this question. 1. In the GEOMETRIC

More information

9.3 Properties of Chords

9.3 Properties of Chords 9.3. Properties of Chords www.ck12.org 9.3 Properties of Chords Learning Objectives Find the lengths of chords in a circle. Discover properties of chords and arcs. Review Queue 1. Draw a chord in a circle.

More information

Copyrighted Material. Copyrighted Material. Copyrighted. Copyrighted. Material

Copyrighted Material. Copyrighted Material. Copyrighted. Copyrighted. Material Engineering Graphics ORTHOGRAPHIC PROJECTION People who work with drawings develop the ability to look at lines on paper or on a computer screen and "see" the shapes of the objects the lines represent.

More information

Chapter 5: Relationships Within Triangles

Chapter 5: Relationships Within Triangles Name: Hour: Chapter 5: Relationships Within Triangles GeoGebra Exploration and Extension Project Mr. Kroll 2013-14 GeoGebra Introduction Activity In this tutorial, you will get used to the basics of GeoGebra.

More information

CHAPTER 10 PROPERTIES OF CIRCLES

CHAPTER 10 PROPERTIES OF CIRCLES HT 0 OTIS OF ILS In this chapter we address ig IS: ) Using properties of segments that intersect circles ) pplying angle relationships in circles 3) Using circles in the coordinate plane Section: ssential

More information

1999 Mathcounts National Sprint Round Solutions

1999 Mathcounts National Sprint Round Solutions 999 Mathcounts National Sprint Round Solutions. Solution: 5. A -digit number is divisible by if the sum of its digits is divisible by. The first digit cannot be 0, so we have the following four groups

More information

Extra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d)

Extra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d) Master 8.24 Extra Practice 1 Lesson 8.1: Parallel Lines 1. Which line segments are parallel? How do you know? a) b) c) d) 2. Look at the diagram below. Find as many pairs of parallel line segments as you

More information

Period: Date Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections

Period: Date Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections : Common 3-Dimensional Shapes and Their Cross- Sections Learning Target: I can understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice. Warm

More information

Pre-Calc. Midpoint and Distance Formula. Slide 1 / 160 Slide 2 / 160. Slide 4 / 160. Slide 3 / 160. Slide 5 / 160. Slide 6 / 160.

Pre-Calc. Midpoint and Distance Formula. Slide 1 / 160 Slide 2 / 160. Slide 4 / 160. Slide 3 / 160. Slide 5 / 160. Slide 6 / 160. Slide 1 / 160 Slide 2 / 160 Pre-alc onics 2015-03-24 www.njctl.org Slide 3 / 160 Slide 4 / 160 Table of ontents click on the topic to go to that section Review of Midpoint and istance Formulas Intro to

More information

1 st Subject: 2D Geometric Shape Construction and Division

1 st Subject: 2D Geometric Shape Construction and Division Joint Beginning and Intermediate Engineering Graphics 2 nd Week 1st Meeting Lecture Notes Instructor: Edward N. Locke Topic: Geometric Construction 1 st Subject: 2D Geometric Shape Construction and Division

More information

Module 1H: Creating an Ellipse-Based Cylindrical Sheet-metal Lateral Piece

Module 1H: Creating an Ellipse-Based Cylindrical Sheet-metal Lateral Piece Inventor (10) Module 1H: 1H- 1 Module 1H: Creating an Ellipse-Based Cylindrical Sheet-metal Lateral Piece In this Module, we will learn how to create an ellipse-based cylindrical sheetmetal lateral piece

More information

FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.

FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true. FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth

More information

Parallel and Perpendicular Lines on the Coordinate Plane

Parallel and Perpendicular Lines on the Coordinate Plane Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the

More information

If the sum of two numbers is 4 and their difference is 2, what is their product?

If the sum of two numbers is 4 and their difference is 2, what is their product? 1. If the sum of two numbers is 4 and their difference is 2, what is their product? 2. miles Mary and Ann live at opposite ends of the same road. They plan to leave home at the same time and ride their

More information

Geometry 1 FINAL REVIEW 2011

Geometry 1 FINAL REVIEW 2011 Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram.

More information

b. Draw a line and a circle that intersect at exactly one point. When this happens, the line is called a tangent.

b. Draw a line and a circle that intersect at exactly one point. When this happens, the line is called a tangent. 6-1. Circles can be folded to create many different shapes. Today, you will work with a circle and use properties of other shapes to develop a three-dimensional shape. Be sure to have reasons for each

More information

3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up

3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up 3.1 Start Thinking Sketch two perpendicular lines that intersect at point. Plot one point on each line that is not. all these points and. onnect and to make. What type of figure do points,, and make? ould

More information

RAKESH JALLA B.Tech. (ME), M.Tech. (CAD/CAM) Assistant Professor, Department Of Mechanical Engineering, CMR Institute of Technology. CONICS Curves Definition: It is defined as the locus of point P moving

More information

NCERT Solutions for Practical Geometry

NCERT Solutions for Practical Geometry 1 NCERT Solutions for Practical Geometry Exercise 14.1 Question 1: Draw a circle of radius 3.2 cm Step 1 Open the compasses for the required radius of 3.2 cm. Step 2 Mark a point with a sharp pencil where

More information

Constructing Angle Bisectors and Parallel Lines

Constructing Angle Bisectors and Parallel Lines Name: Date: Period: Constructing Angle Bisectors and Parallel Lines TASK A: 1) Complete the following steps below. a. Draw a circle centered on point P. b. Mark any two points on the circle that are not

More information