geometry lesson 2-5
reflexive property (property of congruence)
<ab congruent to <ab <a congruent to <a
reflexive property
A=A equals itself
multiplication property
If A = B, then A*C = B*C
transitive property
If A=B and B=C, then A=C
division property
If a = b and c 0, then a/c = b/c.
substitution property
If a = b, then a can be substituted for b in any equation or expression
subtraction property
If a=b, then a-c=b-c
bioconditional
a single true statement that combines a true conditional and a true converse statement joins the two parts with (iff) if and only if example- two angle are only supplementary (iff) the sum of the measures of the 2 angles is 180
converse
exchange the hypothesis and the conclusion regular conditional sentence- if the measure is 15 then angle m is acute Changed version -if angle m is acute then angle m = 15 if q then p q-----> p
transitive property ( property of congruence)
if <a is congruent to <b and <b is congruent to <c then <a is congruent to ,c
additional property
if a=b , then a+c=b+c
symmetric property (property of =)
if a=b, then b=a
no conclusion
if angela plays hockey(p) then she can ice skate( q), Anglea can ice skate( q) no conclusion
symmetric property ( property of congruence)
if line ab is congruent to line cd then cd is congruent to line ab
law of syllogism
if the conclusion of one true conditional is the hypothesis of the other true conditional statement you can state a conclusion from the two statements P----> q, q---r, p---->r example- if it is July (p) , then you are on summer vacation(q), if you are on summer vacation (q), then you work at the smoothie shop(r) final version- if its july, then you work at a smoothie shop
law of detachment
if the hypothesis of a true conditional is true, then the conclusion is true example- if you go to the pool(p), then you wear sunblock.(q) Francis went to the pool(p) final version- francis wear sunblock
conditional
is a if -then statement p---> q
counterexample
is an example that is used to disprove a statement if I play a sport, then I play soccer final- softball is a sport
hypothesis
is the part of p following the if p------> q
conclusion
is the part q following then
inverse
negate both the hypothesis and the conclusion of the conditional regular conditional-if the measure is 15 then angle m is acute changed version- if angle m is not 15 then angle m is not acute not p -----> not q
contrapositive
negate both the hypothesis and the conclusion of the converse converse sentence- if angle m is not 15 then angle m is not acute changed- if angle a is not acute then angle m isn't 15 not q----> not p if not q then not p
distributive property
use multiplication to distribute a to each term of the sum or the difference within the parenthesis (combine like terms)
conditional (statement)
use the given hypothesis and conclusion regular conditional-if the measure is 15 then angle m is acute example- if the measure is 15 then the angle m is acute P-----> q if p then q