Geometry Basics: Points, Lines, Planes, and Angles

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

• An angle is formed by two rays sharing a common endpoint, called the vertex.
• Angles can be classified as:
  • Acute: less than 90°
  • Right: exactly 90°
  • Obtuse: greater than 90° but less than 180°
  • Straight: exactly 180°
  • Reflex: greater than 180° but less than 360°

Properties of Shapes

• Congruent figures have the same size and shape.
• Similar figures have the same shape but not necessarily the same size.
• Symmetry occurs when a shape can be divided into two identical parts.
• Perimeter is the distance around a shape.
• Area is the amount of space inside a shape.

Types of Shapes

• Triangles:
  • Equilateral: all sides are equal
  • Isosceles: two sides are equal
  • Scalene: no sides are equal
• Quadrilaterals:
  • Rectangle: all angles are right angles
  • Square: all sides are equal and all angles are right angles
  • Rhombus: all sides are equal, but not all angles are right angles
• Polygons:
  • Regular: all sides and angles are equal
  • Irregular: not all sides and angles are equal
• Circles:
  • Center: the 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

Geometry

Points, Lines, and Planes

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

Angles

• An angle is formed by two rays sharing a common endpoint called the vertex.
• Angles can be classified as:
  • Acute: less than 90°
  • Right: exactly 90°
  • Obtuse: greater than 90° but less than 180°
  • Straight: exactly 180°
  • Reflex: greater than 180° but less than 360°

Properties of Shapes

• Congruent figures have the same size and shape.
• Similar figures have the same shape but not necessarily the same size.
• Symmetry occurs when a shape can be divided into two identical parts.
• Perimeter is the distance around a shape.
• Area is the amount of space inside a shape.

Types of Shapes

Triangles

• Equilateral triangles have all sides equal.
• Isosceles triangles have two sides equal.
• Scalene triangles have no sides equal.

Quadrilaterals

• Rectangles have all angles as right angles.
• Squares have all sides equal and all angles as right angles.
• Rhombi have all sides equal, but not all angles as right angles.

Polygons

• Regular polygons have all sides and angles equal.
• Irregular polygons do not have all sides and angles equal.

Circles

• The center of a circle is the point equidistant from all points on the circle.
• The radius of a circle is the distance from the center to any point on the circle.
• The circumference of a circle is the distance around the circle.