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1. Geometric Structure Basic Information

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3. Geometry is a way of thinking about and seeing the world. Geometry is evident in nature, art and culture. What geometric objects do you see in this picture? Introduction Instruction Examples Practice

4. Geometry is both ancient and modern. Geometry originated as a systematic study in the works of Euclid, through its synthesis with the work of Rene Descartes, to its present connections with computer and calculator technology. What geometric objects do you see in this picture? Introduction Instruction Examples Practice

5. The basic terms and postulates of geometry will be introduced as well as the tools needed to explore geometry. What geometric term are you familiar with? Introduction Instruction Examples Practice

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7. Three building blocks of geometry are points , lines and planes . They are considered building blocks because they are basic and undefined in terms of other figures. This is page 1 of 22 Page list Last Next Introduction Instruction Examples Practice

10. A line is named with two identified points on the line with a line symbol (double-headed arrows) placed over the letters; or by a single, lower case script letter. This is page 3 of 22 Page list Last Next Introduction Instruction Examples Practice

12. A plane is named with a script capital letter, Q. It may also be named using three points (not on the same line) that lie in the plane, such as G, F and E. This is page 5 of 22 Page list Last Next Introduction Instruction Examples Practice

14. Mathematicians accept undefined terms and definitions so that a consistent system may be built. The theorems of an axiomatic system rest on postulates and other theorems. This is page 16 of 22 Page list Last Next Introduction Instruction Examples Practice

15. As with all axiomatic systems, geometry is connected with logic. This logic is typically expressed with convincing argument or proof . This is page 17 of 22 Page list Last Next Introduction Instruction Examples Practice

18. Collinear points are points that lie on the same line. In the figure at the right, A, B and C are collinear. A, B and D are noncollinear. Any two points are collinear . This is page 6 of 22 Page list Last Next Introduction Instruction Examples Practice

19. Coplanar points are points that lie in the same plane. In the figure at the right, E, F, G, and H are coplanar. E, F, G, and J are noncoplanar. Any three points are coplanar. This is page 7 of 22 Page list Last Next Introduction Instruction Examples Practice

20. When geometric figures have one or more points in common, they are said to intersect . The set of points that they have in common is called their intersection. This is page 14 of 22 Page list Last Next Introduction Instruction Examples Practice

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31. With the foundational terms (point, line and plane) described, other geometric figures may be defined. This is page 8 of 22 Page list Last Next Introduction Instruction Examples Practice “ Let no one ignorant of geometry enter my door.” - Plato

34. Opposite rays are two collinear rays that share a common endpoint. and are opposite rays. This is page 10 of 22 Page list Last Next Introduction Instruction Examples Practice

35. The length or measure of a segment is the distance between its endpoints. e.g. the length of is PQ This is page 9 of 22 Page list Last Next Introduction Instruction Examples Practice

36. Segment with equal length are said to be congruent (  ). If AB = CD, then . This is page 9 of 22 Page list Last Next Introduction Instruction Examples Practice

37. B is between A and C iff they are collinear and AB + BC = AC. The midpoint of a segment is the point that divides the segment into two congruent segments. In the figure, DE = EF. This is page 9 of 22 Page list Last Next Introduction Instruction Examples Practice

38. A segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint. A perpendicular bisector intersects the segment at the midpoint and is perpendicular to it. This is page 9 of 22 Page list Last Next Introduction Instruction Examples Practice

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