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