a quick citation note*

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dveloping and expanding concepts

we can develop and expand on concepts that we have learned already by using algebra and new conditional statements.

parallel lines and planes

lines within a coordenate plane

you can describe lines within a coordinate plane with line segments.

The Fundamentals of geometry

we describe our world geometrically using planes, angles, lines, segments, points and rays. here are there definitions.

Euclidean gometry and its reationship to paralell lines

Our definition of parallel lines greatly effects our understanding of euclidean geometry. Euclidean geometry allows us to define things using certain postulates and others as theorems. this allows us to better identify lines intersecting parallel lines.

formal logic

formal logic intersects with geometry in more ways than we would think. when making a proof in mathematics, formal logic and common knowledge are your two greatest tools. the idea that P->Q if Q-P is the best example of formal logic. this type of logic intersects with geometry in a big way.

Congruent Triangles

When you say triangles are congruent, you are saying that all 6 pairs of corresponding angles and sides are congruent.  here is an example:

inductive and deductive reasoning

Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.

Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. 

These types of reasoning are appropriate when making and verifying conjectures. A conjecture is a statement that has not been proven true but also has not been proven false. Inductive reasoning helps us make conjectures. Deductive reasoning helps us verify conjectures

defining triangles!

when defining triangles there are a couple main types. here are some examples

Proofs

Proofs!!!!!

A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. proofs are important for finding a justifiable way to prove your argument

there are several was that we can develop and present effective arguments and proofs. 
  The most common type of proofs are table proofs. table proof are the most straightforward way to explain your process. here is an example.













another example of a proof is a paragraph proof. paragraph proofs give the same information as a table proof but in a paragraph instead of a chart. here is an example

the third type of proof is the flowchart proof. the flowchart proof still provides an effective argument but puts the information into a flowchart. here is an example