geooo quiz 2
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Conjecture
Unproven statement that is based on observations

Inductive reasoning
use it when you find a patteren in specific cases and then write a conjucture for the general case

counterexample
a specific case for which the conjecture is false

conditional statement
LOGICAL STATEMENT THAT HAS TWO PARTS, A HYPOTHESIS AND A CONCLUSION

if then form
The "if " part containts the hypothesis and the then part contains the conclusion

Converse
 If < A is obtuse then M< A =99
 where you switch the two
 exchange the hypothesis and conclusion

Inverse
 Nagate both the Hypothesis and the conclusion
 if m not equal to 99 theh <a is not obtuse
 make both negitive in the same order

contrapositive
 You first write the converse and then negate bothe the hypothesis and the conclusion
 if <a ia not obtuse then M< A is not 99
 you switch them and make both negitive.

Perpendicular lines
Two lines that intersect to from a right angle

equivalent statements
When two statements are both true or both false.

Biconditional statement
A statement that contains the phrase "if and only if"

definition: If two lines intersect to form a right angle, then they are perpendicular lines
converse:
Biconditional:
 converse: if two lines are perpendicular, then they intersct to form a right angle
 Biconditional: Two lines are perpendicular if and only if they intersect to from a right angle

Deductive reasoning
uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

Law of detachment
If the hypothesis of a true conditional statement is true, then the conclusion is also true.

Law of syllogism
 If Hypothesis p, then conclusion q
 If Hypothesis q, then conclusion r.
 If hypotesis q then conclusion r.
if the top two are true then the bottom is also true

Postulates or axioms
rules that are accepted without proofs.

Theorems
rules that are proved

A Line perpendicular to a plane
If and only if the line intercects the plane in a point and is perpendicular to every line in the plane that interscts it at theat point.

Addition property
if a=b then a+c=b+c

subtraction propertey
if a=b then ac= bc

multiplication property
if a=b then ac=bc

division propertey
if a=b and c is not equal to 0 the a/c=b/c

subsitution property
if a=b then a can be subsituted for b in any equation or expression

proof
logical argument that shows a statement is true

two column proof
has numbered statment and corresponding reason that show an argument in a logical orger

theorem
statement that can be proven

congreence of segments
reflexive:
Symmetric:
Transitive:
 reflexive: for an seg. ab, ab is congrent to Ab
 Symmetric: If seg AB is cong to CD then CD is cong to AB
 Transitive: If seg AB is cong to CD and CD is cong to EF then seg AB is con to EF

Right angle congruence theorem
all right angels are congrent

Congruent supplement theorem
 if two angle are supplementary to the same angle then they are congrent
 If <4 and <5 are complemtrarty and <6 and <5 are complemtry then <4 is congrent to <6`

Linear pair Postulate
 If two angles for a liner pair, then they are supplementery
 <1 and <2 form a linear pair, so <1 and <2 are supplementary and M<1 + M<2 = 180

Vertical angles congruence theorem
vertical angles are congruent