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Stuff you need to know to pass Matt's test
Terms
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- polyhedron
- bounded by polygons, exist in space, and is 3 dimensional
- exterior angle theorem
- an exterior angle of a triangle is greater than either remote interior angle
- indirect proof
- assume the opposite then prove by contradiction
- postulate one
- 2 point determine a line
- obtuse
- iff more than 90 but less than 180
- deductive reasoning
- uses logic to draw conclusion from statements already acccepted as true
- line segment
- part of a line bounded by 2 endpoints...can be measured
- vertical angle theorem
- vertical angles are equal
- plane
- space
- betweeness of points theorem
- if A-B-C, then AB+BC = AC
- addition theorem of inequality
- if a>b and c>d, then a+c > b+d
- ASA postulate
- if 2 angles and the included side of one triangle are equal to two angles and the included side of another triandle, the triangles are congruent
- division property
- if a>b and c>o, then a/c >b/c
- deductive system
- a logical system of constructing proofs using definitions, postulates and theorems
- subtraction property
- if a>b, then a-c> b-c
- betweeness of rays theorem
- if OA-OB-OC, then AOB+BOC = AOC
- conditional statement
- P-->Q statements..if rain, then wet.
- addition property
- if a>b, then a+c > b+c
- theorem 13
- if 2 sides of a triangles are unequal then angles opposite them are unequal in the same order
- exterior angle
- a angle that forms a linear pair with an angle of the trianle
- area
- number of units squares equal in measure to it's surface
- identity
- a+0=a do something to make it itself
- point
- refers to a location on a plane
- corollary to congruent
- 2 triangles congruent to a 3rd triangle are congruent to eachother
- SAS postulate
- if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent
- betweeness of points
- A-B-C iff ab>c
- iff
- if and only if
- inductive reasoning
- drawing conclusions through a limited set of observations
- SSS theorem
- if three sides of one triangle are equal to the three sides of another, the triangles are congruent
- theorem
- a statement that is proved by reasoning deductively
- whole greater than part theorem
- if a>0, b>0, and a+b=c, then c>a and c>b
- parallel
- lie on the same plane but never intersect
- division property
- if a = b and c is not zero, then a/c = b/c
- transitive property
- if a>b and b>c, then a>c
- triangle inequality theorem
- the sum of any 2 sides of a triangle is greater than the third side
- non collinear
- can never be on the same line
- collinear
- on the same line
- addition property
- if a=b, then a+c = b+c
- commutative
- (A+B = B+A) you can switch adding order
- substitution property
- if a = b, then a can be used for b in any expression
- corollary
- can be easily proved from a postulate or another theorem
- 3 possibilities property
- either a>b, a
- multiplication property
- if a>b and c>0, then ac > bc
- polygon
- a connected set of at least 3 line segments in the same plane such that each segment intersects exactly 2 others
- ray
- a line that extends from a point and goes on forever in one direction
- converse
- reversing the conditional statement
- inverse
- a+(-a)=0 the what you started with the opposite
- reflexive property
- a=a...any # is equal to itself
- ruler postulate
- i can use my ruler to measure stuff
- multiplication property
- if a=b, then ac = bc
- theorem 10
- if 2 angles of a triangle are equal the sides opposite them are equal
- conclusion
- Q or the then part
- postulate
- assumed to be true without proof
- postulate 2
- 3 noncollinear points determine a plane
- associative
- (a+b)+c=a+(b+c) you can move brackets around
- coplanar
- points on the same plane
- theorem 9
- if 2 sides of a triangle are equal the angles opposite them are equal
- subtraction property
- if a=b, then a-c = b-c
- perimeter
- sum of all the sides
- hypothesis
- P or the if part
- congruent
- if a shape is congruent there is a correspondence between their vertics and all sides are equal and correspond
- line
- straight, endless arrangement of points going on in both directions
- triangle angle sum
- sum of all angles equals 180
- angle
- a pair of rays with the same endpoint
- concurrent
- lines that contain the same point
- theorem 14
- if 2 anles of a triangle are unequal, the sides opposite them are unequal in the same order