8. Plane Geometry

数学英语



周维祺

Geometry

The branch of mathematics concerned with the properties and relations of various spaces and spatial objects

Axioms

An unconditioanlly accepted statement for subsequent arguments or inferences

Euclid's Postulates

  • A straight line segment can be drawn joining any two points

  • Any straight line segment can be extended indefinitely in a straight line

  • Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center

  • All right angles are congruent

  • If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then these two lines must intersect on that side if extended far enough

Basic Terms

  • Points

  • Line/Ray/Line Segment

  • Angle

  • Curve

Right Triangles

Two Legs of a Right Triangle

Pythagorean Theorem

Equilateral and Isosceles Triangles

Regular and Irregular Polygons

Conic Sections

Ruler and Compasss Constructions

Summary

  • Axioms and Postulates

  • Basic Terms

  • Polygons

  • Circles and curves

  • Ruler and compass constructions