Y. Davis Geometry Notes Chapter 1

3 undefined terms in geometry Point Line Plane

Collinear Anything that lies on the same line

Coplanar Anything that lies in the same plane.

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)

Definitions Using known terms to describe unknown terms.

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

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

Betweenness of points Between any 2 points lies another point.

Congruent segments Segments with the same measure (length).

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

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

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

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

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

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.

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

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.

Degree Units used for measuring angles.

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)

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

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

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

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

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

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

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

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.

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.

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

Equilateral All sides congruent

Equiangular All angles congruent

Regular Both equilateral and equiangular

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

Circumference Distance around a circle

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

Polyhedron A solid that is completely enclosed by polygons.

Face The polygons of a polyhedron

Edges Where the faces of a polyhedron intersect

Vertex Where 3 or more edges of a polyhedron intersect.

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.

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

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

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