Geometry Basics

Geometry

Points, Lines, and Planes

• A point is a location in space, represented by a set of coordinates (x, y, z).
• A line is a set of points that extend infinitely in two directions.
• A plane is a flat surface that extends infinitely in all directions.

Angles and Measurements

• An angle is formed by two rays sharing a common endpoint (vertex).
• Angles can be measured in degrees, with 360° in a full circle.
• Right angles are 90°, acute angles are less than 90°, and obtuse angles are greater than 90°.

Properties of Shapes

• Congruent shapes have the same size and shape.
• Similar shapes have the same shape but different sizes.
• Regular polygons have all sides and angles equal.

Types of Shapes

• Triangles: 3-sided polygons with interior angles totaling 180°.
  • Equilateral: all sides equal.
  • Isosceles: two sides equal.
  • Scalene: all sides different.
• Quadrilaterals: 4-sided polygons.
  • Rectangles: all angles are right angles.
  • Squares: all sides equal and all angles are right angles.
• Circles: sets of points equidistant from a central point (center).

Theorems and Formulas

• Pythagorean Theorem: a^2 + b^2 = c^2 (for right triangles).
• Area of a triangle: (base * height) / 2.
• Circumference of a circle: 2 * π * radius.

Transformations

• Translations: moving a shape by a fixed distance in a specific direction.
• Rotations: rotating a shape around a fixed point by a fixed angle.
• Reflections: reflecting a shape over a line or point.