Math 7 geometry 01 undefined terms rev 2
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This document provides an introduction to basic geometry concepts. It defines geometry as the branch of mathematics concerned with measuring and relating properties of shapes. It discusses key undefined terms like points, lines, and planes. It also covers related concepts such as collinear and coplanar points, as well as subsets of lines like segments and rays. The document explains how lines and planes intersect, with two lines intersecting at a single point, two planes intersecting in a single line, and a plane and line intersecting at a single point.
Math 7 geometry 01 undefined terms rev 2
- 2. A Mathematics 7 Lecture The Basics of Geometry
- 3. QUESTION! What words come to mind when you hear the word GEOMETRY? The Basics of Geometry for High School
- 4. Geometry
- 5. Geometry Geometry comes from the Greek words geo (earth) and metron (measure), so geometry literally means “earth measure” Geometry is the branch of mathematics that defines and relates the basic properties and measurements of shapes
- 6. Geometry The ancient Egyptians, Chinese, Babylonians, Romans, and Greeks used geometry for surveying, navigation, astronomy, and other practical occupations. The Greeks sought to systematize the geometric facts they knew by establishing logical reasons for them and relationships among them.
- 7. The systematizing of geometric facts and principles culminated in the geometry text Elements, written in approximately 325 B.C. by Euclid. This most remarkable text has been in use for over 2000 years. This recognizes Euclid as the Father of Geometry. Euclid Father of Geometry Geometry
- 8. Geometry in Art and Nature Geometry
- 9. • What are the undefined terms in geometry? • What concepts present the foundations of geometry? • Can you sketch the intersection of lines and planes? QUESTIONS! The Basics of Geometry for High School
- 10. THE UNDEFINED TERMS IN GEOMETRY The Basics of Geometry for High School
- 11. The terms points, lines, and planes are the foundations of geometry, but point, line, and plane are all what we call undefined terms. How can that be? Any definition we could give them would depend on the definition of some other mathematical idea that these three terms help define. In other words, the definition would be circular! Undefined Terms? The Basics of Geometry for High School
- 12. The Three Undefined Terms The Basics of Geometry for High School
- 13. • Has no dimension • Indicates location • Usually represented by a small dot A A point is represented with a capital letter. The above is called point A. The Basics of Geometry for High School Point
- 14. • Extends in one dimension. • Represented with a straight line with two arrowheads to indicate that the line extends without end in two directions. Line The Basics of Geometry for High School
- 15. Naming a Line l A B Line The Basics of Geometry for High School 1. Using a small letter (e.g. l or m) 2. Using two points on the line The given line can be named as AB (line AB) l (line l) Note that the letters can be interchanged, so we have BA
- 16. • Extends in two dimensions. • Represented by a slanted 4 sided figure, but you must imagine it extends without end, even though the representation has edges. Plane The Basics of Geometry for High School
- 17. A plane can be named using a capital letter or three points on the plane A B C M This is plane M or plane ABC Plane The Basics of Geometry for High School
- 18. Undefined Terms: A Summary Undefined Term Represen- tation Naming Other Information Point Dot • • P Read: point P Has no length, width or thickness; occupies no space Line Straight mark with two arrow heads Two capital letters with a double arrowhead above them or a lower case letter Has infinite length but no width and thickness; is straight Plane Slanted four- sided figure Single capital letter Read: Plane M Has infinite length and width but no thickness; is a flat surface M The Basics of Geometry for High School
- 19. Determine the undefined term suggested by each of the following. 1. the tip of a pencil 2. the top of the teacher’s table 3. telephone wires 4. the wall of your classroom 5. the surface of the page of your book Check your understanding point plane line plane plane
- 20. Determine the undefined term suggested by each of the following. 6. the ruler’s edge 7. the tip of a needle 8. a corner of a piece of paper 9. the floor of your bedroom 10. the string on a guitar Check your understanding line point point plane line
- 21. ADDITIONAL CONCEPTS RELATED TO THE UNDEFINED TERMS The Basics of Geometry for High School
- 22. • Collinear points are points that lie on the same line. l C A B Points A, B and C are collinear. The Basics of Geometry for High School Collinear and Coplanar Points • Coplanar points are points that lie on the same plane. A B C Points A, B and C are coplanar.
- 23. Examples COLLINEAR POINTS - B, A, L, K - S, M, K - Q, M, ? - T, ? , D S M Q B D H T K LA Collinear and Coplanar Points The Basics of Geometry for High School D or B A or S
- 24. NONCOLLINEAR POINTS - B, A, M, K - D, M, K - Q, M, ? - T, ? , D S M Q B D H T K LA Examples Collinear and Coplanar Points The Basics of Geometry for High School Any point except B and D Any point except A and S
- 25. Examples COPLANAR POINTS - G, E, O - F, L, I - O, E, ? - A, ? , C Collinear and Coplanar Points The Basics of Geometry for High School G or B F, L, or I
- 26. Examples NONCOPLANAR POINTS - F, A, G - G, O, A, L - O, E, ? - A, ? , C Collinear and Coplanar Points The Basics of Geometry for High School Any point except G or B Any point except F, L, or I
- 27. 1. 2 points that are collinear. 2. 3 points that are coplanar. 3. 2 points that are noncollinear. M G D F B Check your understandingGiven the figure shown, name the following: 4. 3 points that are noncoplanar.
- 28. A B D What happens if you cut the line shown below at points B and C? What figures will you form? C The Basics of Geometry for High School Subsets of a Line
- 29. A B DCA B C DB C RAY RAYSEGMENT The Basics of Geometry for High School Subsets of a Line
- 30. B A LINE SEGMENT (or segment) is a set of points consisting of two points on a line, and all the points on the line between the two points C LINE SEGMENT The Basics of Geometry for High School Subsets of a Line The two fixed points at the end of a line segment are called ENDPOINTS.
- 31. A line segment is named by its endpoints. The points can be interchanged in the name B C This is line segment BC or CB In symbols: BC or CB The Basics of Geometry for High School Subsets of a Line
- 32. A RAY is the part of the line which consists of a fixed point called the ENDPOINT and the set of all points on one side of the endpoint. The endpoint is the starting point and the arrow determine the direction of the ray. A B RAY The Basics of Geometry for High School Subsets of a Line
- 33. A ray BA but not ray AB DB C In naming a ray, the endpoint always comes first, followed by the second point. ray CD but not ray DC BA CD The Basics of Geometry for High School Subsets of a Line
- 34. Not all symbols are created equal! Symbol alert! BAAB is the same as AB BAis the same as BUT… A B A B The Basics of Geometry for High School Subsets of a Line The ray is different!
- 35. AB is NOT the same as BA A B AB A B BA Initial point 1st Notice that the initial point is listed first in the symbol. Also note that the symbolic ray always has the arrowhead on the right regardless of the direction of the ray. Symbol alert! The Basics of Geometry for High School Subsets of a Line
- 36. then and are opposite rays. If C is between A and B, Opposite Rays CA A BC CB C is the common initial point for the rays. The Basics of Geometry for High School Subsets of a Line
- 37. • Two or more geometric figures intersect if they have one or more points in common. • The intersection of the figures is the set of points the figure has in common How do 2 lines intersect? How do 2 planes intersect? What about a line and a plane? The Basics of Geometry for High School Intersection of Lines and Planes
- 38. To think about the questions on the last slide let’s look at the following… B A ETwo lines intersect at a point, like here at point A. F Line BF is the intersection of the planes G and H. G H Point E is the intersection of plane H and line EC D C The Basics of Geometry for High School Intersection of Lines and Planes
- 39. If two lines intersect, then they intersect in exactly one (one and only one) point. The point exists (there is at least one point) and is unique (no more than one point exists). The Basics of Geometry for High School Intersection of Lines and Planes A
- 40. If two planes intersect, then their intersection is a unique line. The Basics of Geometry for High School Intersection of Lines and Planes
- 41. A plane and a line not on the plane intersect at a unique point. The Basics of Geometry for High School Intersection of Lines and Planes E
- 42. Summing it up! The Basics of Geometry for High School
- 43. The Basics of Geometry 2: Introduction to Postulates and Theorems What’s Next? The Basics of Geometry for High School