Geometry Basics

Study Notes

Point: a location in space, represented by a set of coordinates (x, y, z)
Line: a set of points extending infinitely in two directions
- Can be defined by two points (e.g., line AB)
- Can be extended infinitely in both directions
Line Segment: a part of a line with a fixed length, with two endpoints
Plane: a flat surface that extends infinitely in all directions
- Can be defined by three points (e.g., plane ABC)

2D Shapes:
- Polygon: a closed shape with at least three sides (e.g., triangle, quadrilateral, hexagon)
- Circle: a set of points equidistant from a central point (called the center)
- Triangle: a polygon with three sides
- Quadrilateral: a polygon with four sides
3D Shapes:
- Prism: a shape with two identical faces and rectangular sides (e.g., cube, rectangular prism)
- Pyramid: a shape with a base and triangular sides that meet at the apex
- Sphere: a set of points equidistant from a central point (called the center)

Definition of a proof: a logical and systematic way to show that a statement is true
Basic proof techniques:
- Direct Proof: prove a statement by showing it is true for all cases
- Indirect Proof: prove a statement by showing that the opposite is false
- Proof by Contradiction: assume the opposite of a statement is true and show that it leads to a logical contradiction

Angle: formed by two rays sharing a common endpoint (called the vertex)
Types of Angles:
- Acute Angle: less than 90 degrees
- Right Angle: exactly 90 degrees
- Obtuse Angle: greater than 90 degrees
- Straight Angle: exactly 180 degrees
Measuring Angles:
- Degrees: a unit of measurement for angles (e.g., 30 degrees, 45 degrees)
- Protractor: a tool used to measure angles

Spatial Awareness: the ability to understand and visualize objects in space
Key Concepts:
- Visualization: the ability to create mental images of objects and shapes
- Orientation: the ability to understand the position and direction of objects in space
- Perspective: the ability to understand how objects appear from different angles and distances

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, and can be defined by two points.
A line segment is a part of a line with a fixed length, with two endpoints.
A plane is a flat surface that extends infinitely in all directions, and can be defined by three points.

Polygon: a closed shape with at least three sides, such as a triangle, quadrilateral, or hexagon.
Circle: a set of points equidistant from a central point (called the center).
Triangle: a polygon with three sides.
Quadrilateral: a polygon with four sides.
Prism: a 3D shape with two identical faces and rectangular sides, such as a cube or rectangular prism.
Pyramid: a 3D shape with a base and triangular sides that meet at the apex.
Sphere: a set of points equidistant from a central point (called the center).

Proof: a logical and systematic way to show that a statement is true.
Direct Proof: prove a statement by showing it is true for all cases.
Indirect Proof: prove a statement by showing that the opposite is false.
Proof by Contradiction: assume the opposite of a statement is true and show that it leads to a logical contradiction.

Spatial Awareness: the ability to understand and visualize objects in space.
Visualization: the ability to create mental images of objects and shapes.
Orientation: the ability to understand the position and direction of objects in space.
Perspective: the ability to understand how objects appear from different angles and distances.