Geometric proof
A drawing shows a fact for one figure. What would it take to know it for every figure of that kind?
Where you are 18 inside
What this area is about
A geometric proof argues from the Given, through definitions and results already accepted, to the Prove, with a reason on every line. Once proved, a theorem holds for every figure that meets its hypothesis, and can itself be cited.
How these fit together
Ways of knowing. Inductive reasoning proposes a pattern from examples; deductive reasoning makes the conclusion follow.
The machinery. Given, prove and the diagram sets a proof up. A theorem and its converse and properties of congruence supply kinds of reasons, and justifying each step puts one on every line. Auxiliary lines may be added, each with a reason.
First theorems. Angle pairs, proving lines parallel, alternate interior angles and the triangle angle sum.
Forms. Indirect proof shows something never happens; choosing a format compares two-column, paragraph, flowchart and coordinate proofs.
Proof families. Congruent triangles, parallelograms, rigid motions and dilations, similarity and circles.
A path through it
The two kinds of reasoning, then Given and Prove, converses, properties of congruence, justifying each step and auxiliary lines. Next angle pairs, parallel lines, alternate interior angles and the angle sum, then indirect proof and formats. Last congruent triangles, parallelograms, transformational proofs, similarity and circles.
This area leads to justifying a construction, which proves that a compass and straightedge figure is exactly what it claims to be.