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.

Test your understanding of basic geometry concepts, including points, lines, planes, angles, shapes, and transformations. Review properties of triangles, quadrilaterals, and circles, and apply theorems and formulas to solve problems.