Key vocabulary for Basics of Geometry, Logic, and Reasoning.
The undefined terms that are the building blocks of geometry.
Point: A location with no dimension. A
Line: A one-dimensional path extending forever.
Plane: A two-dimensional flat surface extending forever.
Parts of a line with defined endpoints.
Line Segment: Part of a line with two endpoints. Notation: $\overline{AB}$
Ray: Part of a line with one endpoint. Notation: $\vec{AB}$
A logical statement with a hypothesis and a conclusion, often in "if-then" form.
If p (hypothesis), then q (conclusion).
$p \rightarrow q$
Formed by switching the hypothesis and conclusion of a conditional statement.
If q, then p.
$q \rightarrow p$
Formed by negating both the hypothesis and conclusion of a conditional statement.
If not p, then not q.
$\sim p \rightarrow \sim q$
Formed by switching AND negating the hypothesis and conclusion.
If not q, then not p.
$\sim q \rightarrow \sim p$
Making a conclusion based on observing a pattern.
Example: Seeing the sequence 2, 4, 6, 8,... and concluding the next number is 10.
Using facts, definitions, and logic to reach a conclusion.
Example: All squares are rectangles. ABCD is a square. Therefore, ABCD is a rectangle.
A specific example that proves a statement is false.
Statement: "All birds can fly."
Counterexample: A penguin.
Relationships between two lines.
Parallel Lines ($\|$): Coplanar lines that never intersect. They have the same slope.
Perpendicular Lines ($\perp$): Lines that intersect at a 90° angle. Their slopes are negative reciprocals.