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Euclid's five postulates can be stated as follows
- It is possible to draw a straight line segment joining any two points.
- It is possible to indefinitely extend any straight line segment continuously in a straight line.
- Given any straight line segment, it is possible to draw a circle having the segment as a radius and one endpoint as its center.
- All right angles are equal to each other or congruent
- Through a given point not on a given straight line, only one line can be drawn parallel to a given line.
Intro to Euclidian Geometry
Introduction to Euclidian Geometry
Points and Lines and other Geometry from the point of view of Houston Texas
the collision of subatomic particles in CERN’s Large Hadron Collider is used to clarify the definition of a point, and the city of Houston, arranged on a grid of parallels and perpendiculars, illustrates why lines are preferred over curves as a way to organize a community. The video also suggests the Parthenon as a good example of how geometric elements—in this case, points, planes, and lines—are employed in architecture. Points in space, collinear and coplanar points, parallel and perpendicular lines, line segments, angles, and planes are all covered. Part of the series Geometry Applications. (4~ minutes)
Postulates are assumptions that we accept without proof. Theorems are statements proven with postulates, definitions, and other properties.
Units, perimeter, and circumference and Area
When it comes to measuring flat shapes, geometry generously provides a formula for every occasion. This program begins with an overview of how to convert English and metric units of measurement. Next, finding the perimeter of polygons is illustrated, after which a tour of Circleville provides a snapshot summary of circumference and pi. Finally, the Area Congruence and Area Addition Postulates are revealed, along with formulas for the area of squares, rectangles, parallelograms, triangles, trapezoids, and circles. (20 minutes)