Geometry Basics

Points

• A point is a location in space, represented by a set of coordinates (x, y, z)
• It has no size, only position

Lines

• A line is a set of points extending infinitely in two directions
• It can be defined by two points or a point and a slope
• Line properties:
  • Collinear points: points that lie on the same line
  • Intersecting lines: lines that share a common point
  • Parallel lines: lines that never intersect, always the same distance apart
  • Perpendicular lines: lines that intersect at a 90-degree angle

Angles

• An angle is formed by two rays sharing a common endpoint (vertex)
• Angle properties:
  • Acute angle: less than 90 degrees
  • Right angle: exactly 90 degrees
  • Obtuse angle: greater than 90 degrees but less than 180 degrees
  • Straight angle: exactly 180 degrees
  • Reflex angle: greater than 180 degrees but less than 360 degrees

Triangles

• A triangle is a polygon with three sides and three angles
• Triangle properties:
  • Equilateral triangle: all sides are equal
  • Isosceles triangle: two sides are equal
  • Scalene triangle: all sides are unequal
  • Right triangle: one right angle (90 degrees)
  • Oblique triangle: no right angles

Quadrilaterals

• A quadrilateral is a polygon with four sides and four angles
• Quadrilateral properties:
  • Rectangle: all angles are right angles, opposite sides are equal
  • Square: all sides are equal, all angles are right angles
  • Rhombus: all sides are equal, opposite sides are parallel
  • Trapezoid: two pairs of opposite sides, at least two sides are parallel

Circles

• A circle is a set of points equidistant from a central point (center)
• Circle properties:
  • Center: the fixed point equidistant from all points on the circle
  • Radius: the distance from the center to any point on the circle
  • Circumference: the distance around the circle
  • Diameter: the longest distance across the circle, passing through the center

Points

• A point is a location in space, represented by a set of coordinates (x, y, z) with no size, only position.

Lines

• A line is a set of points extending infinitely in two directions, definable by two points or a point and a slope.
• Collinear points lie on the same line.
• Intersecting lines share a common point.
• Parallel lines never intersect and are always the same distance apart.
• Perpendicular lines intersect at a 90-degree angle.

Angles

• An angle is formed by two rays sharing a common endpoint (vertex).
• Acute angles are less than 90 degrees.
• Right angles are exactly 90 degrees.
• Obtuse angles are greater than 90 degrees but less than 180 degrees.
• Straight angles are exactly 180 degrees.
• Reflex angles are greater than 180 degrees but less than 360 degrees.

Triangles

• A triangle is a polygon with three sides and three angles.
• Equilateral triangles have all sides equal.
• Isosceles triangles have two sides equal.
• Scalene triangles have all sides unequal.
• Right triangles have one right angle (90 degrees).
• Oblique triangles have no right angles.

Quadrilaterals

• A quadrilateral is a polygon with four sides and four angles.
• Rectangles have all angles as right angles, with opposite sides equal.
• Squares have all sides equal, with all angles as right angles.
• Rhombi have all sides equal, with opposite sides parallel.
• Trapezoids have two pairs of opposite sides, with at least two sides parallel.

Circles

• A circle is a set of points equidistant from a central point (center).
• The center is the fixed point equidistant from all points on the circle.
• Radius is the distance from the center to any point on the circle.
• Circumference is the distance around the circle.
• Diameter is the longest distance across the circle, passing through the center.