Benoit Geometry (Conditionals to Properties of Equality)
Stuff from my notes. I usually record Mr. Beniot's exact words, so this is probably pretty accurate. Not promising anything, though. I made up most of the postulate names because he never gives us any. ._.
Terms
undefined, object
copy deck
- Contrapositive
- Negate the Converse
- Postulate of a Line
- A line contains at least two points
- Division Property of Equality
- if a=b then a÷c=b÷c
- Postulate of Three Points
- Through ay three noncolinear points there exists exactly one point
- Multiplication Property of Equality
- if a=b then ac=bc
- Postulate of Two Points
- Through any two points there exists exactly one line
- Inverse
- Negate the Conditional
- Transitive Property
- if a=b and b=c then a=c
- <-->
- Implies both ways
- Step One of Inductive Reasoning
- Look for a Pattern
- Perpendicular Lines
- Two lines are perpendicular if they form a right angel
- Step One of Deductive Reasoning
- Use Postulates
- Step Two of Inductive Reasoning
- Make a Conjecture
- Reflexive Property
- if a=b then b=a
- Conditional Statements
- "if... then" statement
- Biconditional Statement
- "if and only if"
- Postulate of Intesecting Planes
- If two planes intersect then their intersection is exactly one line
- Segment Addition Postulate
- If B lies between A and C then AB + BC = AC
- -->
- Implies
- Postulate of Points on a Plane
- If two points lie on a plane then the line containing them lies in the plane
- Step Two of Deductive Reasoning
- Look at Laws
- Substitution Property
- if a=b then a or b may be substituted for eachother
- Step Three of Deductive Reasoning
- Look at Defined Terms
- Addition Property of Equality
- If a=b then a+c=b+c
- Negation (not exact)
- Yes turns to No, No turns to Yes (eg.
- Distributive Property
- a(b+c)=ab+ac
- Converse Statement
- A statement where the hypothesis and conclusion of the conditional are switched
- Postulate of Intersecting Lines
- If two lines intersect then their intersection is exactly one point
- Subtraction Property of Equality
- if a=b then a−c=b−c
- ~ (sorta looks like the symbol? )
- Negates
- Postulate of a Plane
- A plane consists of at least three noncolinear points