[[Special Right Triangles]] # Preface This page begins by focusing on [[Euclidean Geometry]], most pre-college learners will only experience this kind of geometry. It is named after Euclid, who assembled an [[axiomatic]] approach to explaining and producing truths about geometry. While his original approach is now seen as partially flawed, or at the very least incomplete, it was sufficient to begin applying geometry to many problems, especially for the ages it endured. The knowledge geometry promises relies on the learner's trust in the definitions and axioms. Some "definitions" are primitive in the sense that they can only be understood in their relation to other primitives. The axioms expand on these relations to state agreed upon truths that will be necessary for proving more complex statements. Rather than present a block of definitions now, they will be linked to as mentioned. Once in college and beyond, it is normal to question the clarity of definitions, the integrity of the axioms, and the possibilities that might be ignored by blindly accepting these. Hopefully after writing a few more courses, I will still have the energy to explore [[Non-Euclidean Geometry]] # Enough to Get Started A [[Figure]] is an object with boundaries that distinguish an interior, and therefor an exterior. The figure with no interior, is called the [[Point|point]] All things in geometry are made up of [[Point| points]]. They are hard to define or describe since they don't really have any qualities or quantities. A [[Point|point]] itself is meaningless, and really only starts to have meaning when there are other [[Point|points]] nearby to relate with it. Luckily, whether they are visibly represented or not, there are points everywhere in all directions. Since there are a lot of them, we like to give them names, usually capital letters. Naming one point $A$ and a different point $B$, one interpretation of relating $A$ and $B$ would be to connect or link them together. An ordered [[Set]] of points that connect $A$ and $B$ is called a [[‡ Curve]]. Unlike its name suggests, a [[‡ Curve]] does not need to be "curvy". Also, because they are made up of [[Point|points]], [[‡ Curve|curves]] can be components of "larger" curves, and they can be broken down into "smaller" curves. Allowing for more wiggle room (dimension) allows for more [[‡ Curve|curves]] to be drawn connecting $A$ and $B$. Of all curves connecting two points $A$ and $B$, the one with the least wiggle room is [[Line, Line-Segment, Ray|line-segment]] $\overline{AB}$. The interior of line-segment like $\overline{AB}$ contains more points such as a point like $C$. Just like $C$ can be between $A$ and $B$, another point $D$ can exist so that $B$ is in the interior of $\overline{AD}$. If this process is repeated, the segment is extended, and if done so infinitely, the resulting figure is a [[Line, Line-Segment, Ray|ray]] $\overrightarrow{AB}$, or equivalently $\overrightarrow{AC}$ or $\overrightarrow{AD}$. [[Line, Line-Segment, Ray]] [[Plane]] [[ Geometric Constructions]] [[Circle]] [[radius]] [[Diameter]] [[Chord]] [[Secant line]] [[Tangent line]] [[circumference]] [[Arc]] [[angle]] [[Length of an arc]] [[area of a circle]] [[Sector of a circle]] [[Area of a sector of a circle]] [[† Every Chord's Perpendicular Bisector is a Diameter]] [[Central angle of a Circle]] [[Inscribed angle of a Circle]] [[† Congruent central angles intercept congruent arcs]] [[Intersecting Chords, Secants, and Tangents theorem]] [[Power of a point with respect to a circle]]