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what is a postulate?
statements accepted without proof
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what are theorems?
proved statements
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what is the ruler postulate?
- the points on a line can be paired with the real numbers
- the distance between any two points is the absolute value of thier differences
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what is the segment addition postulate?
ab+bc = ac
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what is the angle addition postulate?
angle a + angle b = m angle b+ m angle a
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addition property
a=b c=d than a+c=b+d
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what is the subtraction property?
a= b and c=d, than a-c=b-d
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what is the multiplication property?
a=b, ca= cb
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division property
a=b, and c doesnt equal 0, a/c=b/c
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substitution property
a=b, than a or b can substitute each other
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symmetric property
a=b than b=a
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transitive property
a=b and b=c than a = c
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what is a converse?
- state ment: if p, than q
- converse: if q, than p
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what is biconditional?
- statement: if p, than q
- biconditional: p if and only if q
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you compliment a 90 year old. you dont a 180.
90=complimentary
180=supplimentry
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what is the sum of the measures of interior angles in a convex polygon and what is the exterior?
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what is deductive reasoning?
conclusions based on accepted statements
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what is inductive reasoning?
reasoning based on several observations
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what happens when two angles in a triangle are congruent?
the angles oppisite them are also congruent
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what is the hl thereom?
if the hypotonuse and one leg are congrent in a right triangle to corrosponding parts in another right triangle, the triangles are congruent
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wha is the aas thereom?
if two angles and a non included side of a triangle are congruent to corr. parts in another triangle, they are congruent
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what are the the methods of triangle congruency?
sss, sas, asa, hl, aas
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what are the four properties of parralelograms?
- opposite sides are parallel
- opposite sides are congruent
- opposite angles are congruent
- diagonals bisect each other
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what is the rule if three parallel lines cut of a transversal into congruent segments?
then they cut every transversal into congruent segments
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what is the rule about parrelelel lines in triangles?
if a line contains the midpoint of one side of a triangle, and is parralel to another side, it bisects the the third side
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what is a rule about a segment that joins the midpoints of two sides of a triangle?
it is parrellel to the the third and has a length equal to half the third
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what properties does the median of a trapazoid have?
it is parrallel to the bases and has a length equal to half the sum of the lengths of the bases
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what is the ratio of a to b?
a/b or a:b
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how to you begin an indirect proof
assume that what you want to prove is not true. if this temporary assumption leads to a contradiction of a known fact, than your temporary assumption must be false and what you with to prove true must be true.
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what is the shortest segment from a point to a line
a perpendicular segment
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what is sss triangle inequality theorem
if two sides of a triangle are congruent to two sides of another triangle but the the third side in the first is larger than the same in the second, the included angle of the two congruent sides of the first triangle is greater than that of the second
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what is the sas triangle inequality therem
if two triangles have two congruent sides but the included angle of the first is larger than the included angle of the second, than the third side of the first is larger than the second.
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what is the contropositive of if p, than q
if not q, than not p
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what is the inverse of if p, than q
if not p, than not q
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what is the triangle inequality theorem?
2 angles of a triangle added together are always greater than the third
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what is the sas trianglesimilarity theorem?
if two angles in two triangles are equal and the sides including those two angles are in porportion, then the triangles are similar.
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what is the sss triangle similarity theorem?
if every side in two triangles are in porportion, then then are similar
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what is aa triangle similiratiy thereom
if two triangles each have two equal angles, then they are similar
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 if de is parrellel to bc, than what must be true about the other two sides?
db/da = ec/ae
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what is the triangle proportoinality therom?
if a line parrellel to one side of a triangle interescts the other two sides, than it devides those sides proportionally.
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what happens if three parrellel lines intersect two transversals?
then they devide the transversals proportionally
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what is the triangle angle bisector theorem?
if a ray bisects an angle, than it devides the oppisite sides side proportionally to the two other sides.
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(a+b)/b=(c+d)/d if a/b=c/d
no answer
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what happens to opposite angles in an inscribed quadrilaterals?
they are supplementary
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what is the measure of an angle inscribed in a semicircle?
90 degrees
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what is the rule if two inscribed angles intercept the same arc?
they are congruent
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what is the distance formula?
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what is the equation of a circle?
(x - h)^2 + (y - k)^2 = r^2
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what is the midpoint formula?
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