Geometry Basics

Points and Lines

• A point is a location in space, represented by a set of coordinates (x, y, z).
• A line is a set of points extending infinitely in two directions.
• Line segment: a part of a line with a fixed length.
• Ray: a line that extends from a point to infinity in one direction.

Angles and Measurement

• An angle is formed by two rays sharing a common endpoint.
• Angle measurement: degrees, radians, or revolutions.
• Types of angles:
  • Acute (less than 90°)
  • Right (exactly 90°)
  • Obtuse (greater than 90°)
  • Straight (exactly 180°)
  • Reflex (greater than 180°)

Properties of Shapes

• Properties of 2D shapes:
  • Sides: lines that make up the shape.
  • Vertices: corners of the shape.
  • Angles: formed by the sides.
• Properties of 3D shapes:
  • Faces: flat surfaces.
  • Edges: lines where faces meet.
  • Vertices: corners of the shape.

Types of Shapes

• 2D shapes:
  • Triangles: 3 sides, 3 vertices.
  • Quadrilaterals: 4 sides, 4 vertices.
  • Polygons: 5 or more sides, 5 or more vertices.
  • Circles: continuous curved shape.
• 3D shapes:
  • Pyramids: triangular base, sloping sides.
  • Prisms: rectangular base, flat sides.
  • Spheres: continuous curved surface.

Theorems and Postulates

• Theorems:
  • Pythagorean theorem: a^2 + b^2 = c^2 (right triangles).
  • Perimeter theorem: sum of side lengths is constant.
• Postulates:
  • Ruler postulate: points can be paired with real numbers.
  • Angle postulate: angles can be measured and compared.

Points and Lines

• A point is a location in space, represented by a set of coordinates (x, y, z).
• A line is a set of points extending infinitely in two directions.
• A line segment is a part of a line with a fixed length.
• A ray is a line that extends from a point to infinity in one direction.

Angles and Measurement

• An angle is formed by two rays sharing a common endpoint.
• Angles can be measured in degrees, radians, or revolutions.
• Types of angles include:
  • Acute angles, which are less than 90°.
  • Right angles, which are exactly 90°.
  • Obtuse angles, which are greater than 90°.
  • Straight angles, which are exactly 180°.
  • Reflex angles, which are greater than 180°.

Properties of Shapes

• 2D shapes have:
  • Sides, which are lines that make up the shape.
  • Vertices, which are corners of the shape.
  • Angles, which are formed by the sides.
• 3D shapes have:
  • Faces, which are flat surfaces.
  • Edges, which are lines where faces meet.
  • Vertices, which are corners of the shape.

Types of Shapes

• 2D shapes include:
  • Triangles, which have 3 sides and 3 vertices.
  • Quadrilaterals, which have 4 sides and 4 vertices.
  • Polygons, which have 5 or more sides and 5 or more vertices.
  • Circles, which are continuous curved shapes.
• 3D shapes include:
  • Pyramids, which have a triangular base and sloping sides.
  • Prisms, which have a rectangular base and flat sides.
  • Spheres, which have a continuous curved surface.

Theorems and Postulates

• Theorems include:
  • The Pythagorean theorem, which states that a^2 + b^2 = c^2 for right triangles.
  • The Perimeter theorem, which states that the sum of side lengths is constant.
• Postulates include:
  • The Ruler postulate, which states that points can be paired with real numbers.
  • The Angle postulate, which states that angles can be measured and compared.