Geometric Figures
Concepts
Simple Closed Surface
Boundary edges that encloses a region called interior
A surface without holes
Nets
Models of polyhedrons that depict the pattern of figures.
Curved Surface
Spheres, hemispheres, cones, prisms.
Plane
The flat surface that is infinite in all directions,
Theorem
Euler's Formula
The numbers V of vertices , F of faces and E of edges of a polyhedron are related by formula V+F= E+2
Jordan curve
A simple closed plane curve partitions the plane into three disjoints subsets: the curve itself, the interior of the curve , and the exterior angles.
Total turn
The total turn made when traversing any closed curve is an integer multiple of 360*
Sums of the angle measure in convex polygon
Sum of the measures of the exterior angles of convex polygon is 360* the sum is (n-2) 180*
Definitions
Half space
The two regions that are separated by plane
Skew Lines
Two lines that do not belong to a common plane
Sphere
the set of points in space at a constant distance from a single point called center
Solid
a space figure that is the union of all points on a simple closed surface and all points in its interior.
pyramid
a closed surface given by a polygon and point not in plane of a polygon called its apex
Prism
consists of two congruent polygons in parallel planes together with the lateral faces joining at the bases.
Tetrahedron
Is a three dimensional shape with four faces
Pentahedron
Is a three dimensional shape with five faces
Hexadedron
Is a Three dimensional shape with six faces
Property
If two parallel lines are cut by a transversal, then their corresponding angles have the same measure.
IF two lines in the plane are cut by a transversal and some pair of their corresponding angles has the same measure, then the lines are parallel.