Essential Geometry Concepts: Formulas, Proofs, and Theorems
Fundamentals of Geometry
Undefined Terms and Basic Figures
- Point: Exact location in space with no size, written as a capital letter (e.g., A).
- Line: Straight path extending infinitely in both directions, no thickness, named with two points ($\overleftrightarrow{AB}$) or a lowercase script letter.
- Plane: Flat surface extending infinitely in all directions, named with a script capital letter or three non-collinear points.
- Collinear Points: Points that lie on the same line.
- Coplanar Points: Points that lie
Quality Management Calculations: EPMO, Control Charts, and Capability
Problem #6-1:
A bank has set a Standard that mortgage applications be processed within a certain number of days Of filing. If, out of a sample of 1000 Applications, 75 fail to meet this requirement, what is the epmo metric?
75 errors per Thousand is equivalent to 75000 epmo.
Problem #6-2:
Over the last year, 965 injections were administered at a clinic. Quality is measured by the proper amount of dosage as well as the Correct drug. In two instances, the Incorrect amount was given, and
Read MoreEssential Quality Tools for Process Improvement and Analysis
Quality Tools for Process Control
Quality tools are essential instruments used to control a process, identify faults, improve risk analysis systems, and drive continuous improvement.
Brainstorming
Brainstorming is a technique where a group encourages every member to participate and generate ideas, focusing on quantity over complexity. It is crucial that the group avoids criticizing ideas during the generation phase, as only some ideas will ultimately be valid.
Requirements for Effective Brainstorming
- The
Business Profitability: Revenue, Costs, and Break-Even Analysis
Understanding Business Profitability
Profit is the essential difference between a business’s revenue (sales) and its costs. When x units are produced and sold, this relationship can be expressed mathematically:
P(x) = R(x) - C(x)
Profit Calculation Fundamentals
Where:
- P(x): Represents the total profit derived from the sale of x units.
- R(x): Represents the total revenue generated from the sale of x units.
- C(x): Represents the total cost associated with the production and sale of x units.
Revenue Generation
Read MoreProjectile Motion Analysis: Kinematics and Real-World Applications
Kinematics: Projectile Motion and Relative Velocity
Aim and Background
Aim of Investigation
The aim of this investigation is to analyze projectile motion in two dimensions to understand how the horizontal and vertical components of velocity affect the trajectory, range, and time of flight of a projectile under constant acceleration due to gravity.
Background on Projectile Motion
Projectile motion describes the curved path an object follows when launched into the air, influenced only by gravity and initial
Read MoreGeometry Essentials: Theorems, Formulas, and Shapes
Geometric Foundations: Theorems and Postulates
Triangle Congruence and Similarity
Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of another triangle, and the sides including these angles are proportional (e.g., AB/DE = AC/DF), then the triangles are similar.
Properties of Geometric Shapes
Parallelogram Properties
- Opposite