Geometric Figures

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The Pythagorean Theorem

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Exploring Angles

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The Number System

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Euclidean Geometry

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Geometric Figures

Property

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.

If two parallel lines are cut by a transversal, then their corresponding angles have the same measure.

Definitions

Hexadedron

Is a Three dimensional shape with six faces

Pentahedron

Is a three dimensional shape with five faces

Tetrahedron

Is a three dimensional shape with four faces

Prism

consists of two congruent polygons in parallel planes together with the lateral faces joining at the bases.

pyramid

a closed surface given by a polygon and point not in plane of a polygon called its apex

Solid

a space figure that is the union of all points on a simple closed surface and all points in its interior.

Sphere

the set of points in space at a constant distance from a single point called center

Skew Lines

Two lines that do not belong to a common plane

Half space

The two regions that are separated by plane

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*

Theorem

Total turn

The total turn made when traversing any closed curve is an integer multiple of 360*

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.

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

Concepts

Plane

Curved Surface

Spheres, hemispheres, cones, prisms.

Nets

Models of polyhedrons that depict the pattern of figures.

Simple Closed Surface

A surface without holes

Boundary edges that encloses a region called interior