Unproven statement that is based on observations
use it when you find a patteren in specific cases and then write a conjucture for the general case
a specific case for which the conjecture is false
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
- If < A is obtuse then M< A =99
- where you switch the two
- exchange the hypothesis and conclusion
- 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
- 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.
Two lines that intersect to from a right angle
When two statements are both true or both false.
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: 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
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.
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.
if a=b then a+c=b+c
if a=b then a-c= b-c
if a=b then ac=bc
if a=b and c is not equal to 0 the a/c=b/c
if a=b then a can be subsituted for b in any equation or expression
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
statement that can be proven
congreence of segments
- 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