1. Y. Davis Geometry Notes
Chapter 1

2. 3 undefined terms in geometry
Point
Line
Plane

3. Collinear
Anything that lies on the same line

4. Coplanar
Anything that lies in the same plane.

5. Intersection
The set of points that two or more geometric figures have in common.
(The intersection of 2 lines is a point)
(The intersection of 2 planes is a line)

6. Definitions
Using known terms to describe unknown terms.

7. Space A boundless, 3-dimensional set of all points.
(Space can contain lines and planes)

8. Line segment (segment)
Part of a line that consist of 2 endpoints and all the points that lie between them.

9. Betweenness of points
Between any 2 points lies another point.

10. Congruent segments
Segments with the same measure (length).

11. Constructions
Creating geometric figures using tools (pencil, straight edge and compass)

12. Distance
The absolute value of the difference between the coordinates of 2 points.

13. Irrational number
A number that cannot be expressed as a terminating or repeating decimal

14. Midpoint
A point that is halfway between the endpoints of a segment.

15. Segment Bisector
Any line, segment or plane that intersects a segment at its midpoint.

16. Ray
Part of a line that consist of an initial point and all the point on the line that lie on the same side as a given point.

17. Opposite Rays
2 rays with the same initial point that extend in opposite directions.
(must be collinear)

18. Angle
Formed by 2 non-collinear rays with the same initial point that extend in different directions.
Rays form the sides of the angle.
Initial point is the vertex of the angle.
Interior—all points that lie between the sides
Exterior—all the points that do not lie between the sides.

19. Degree
Units used for measuring angles.

20. Classifications of Angles
Acute—measures less than 90 degrees
Right—measures exactly 90 degrees
Obtuse—measures more than 90 degrees and less than 180 degrees
Straight– measures exactly 180 degrees ( line or opposite rays)

21. Angle Bisector
A ray that divides an angle into 2 congruent angles.

22. Adjacent Angles
2 coplanar angles with a common vertex and common side, but no common interior points

23. Linear Pair
A pair of adjacent angles whose non-common sides form an opposite ray

24. Vertical Angles
2 non-adjacent angles whose sides form 2 pair of opposite rays

25. Complementary angles
2 angles whose measures have a sum of 90 degrees

26. Supplementary angles
2 angles whose measures have a sum of 180 degrees

27. Perpendicular
2 lines, segments, rays or planes that intersect to form a right angle

28. Polygon A many sided figure. A closed figure.
All sides are formed by segments.
Each side must intersect exactly 2 other sides.
Vertex of each angle is the vertex of the polygon.

29. Classifications of Polygons
Convex—no line that contains a side of the polygon contains points in the interior of the polygon.
Concave—A line that contains a side of the polygon does contain a point or points in the interior of the polygon.

30. Polygons are named by the # of sides
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
n-gon

31. Equilateral
All sides congruent

32. Equiangular
All angles congruent

33. Regular
Both equilateral and equiangular

34. Perimeter
The sum of the lengths of the sides of a polygon

35. Circumference
Distance around a circle

36. Area
The number of square units needed to cover a surface.

37. Polyhedron
A solid that is completely enclosed by polygons.

38. Face
The polygons of a polyhedron

39. Edges
Where the faces of a polyhedron intersect

40. Vertex
Where 3 or more edges of a polyhedron intersect.

41. Types of Solids
Prism—a polyhedron with 2 parallel congruent faces called bases (connected by parallelogram faces)
Pyramid—a polyhedron that has a polygonal base and 3 or more triangular faces that meet at a common vertex
Cylinder—a solid with congruent parallel circular bases connected by a curved surface
Cone—a solid with a circular base connected by a curved surface to a single vertex
Sphere—a set of points in space that are the same distance from a given point. (It has no faces, edges or vertices.

42. Regular polyhedron (5 Platonic solids)
A polyhedron where all faces are regular congruent polygons
Tetrahedron—4 regular triangular faces
Cube (Hexahedron)—6 square faces
Octahedron—8 regular triangular faces
Dodecahedron—12 regular pentagonal faces
Icosahedron—20 regular triangular faces

43. Surface Area
The sum of the area of each face of a solid figure

44. Volume
The number of cubic units enclosed in a solid figure.