Math test chapter 2

a logical statement that has two parts: a hypothesis, p and a conclusion, q

if an animal is a monkey, then it has a tail; p: an animal is a money; q: it has a tail; if p, then q

the opposite of the original statement

an animal is not a monkey; not p

switch the hypothesis and the conclusion

if an animal has a tail, then it is a monkey; if q, then p

negate both the hypothesis and the conclusion

if an animal is not a monkey, then it has no tail; if not p, then not q

switch and the negate both the hypothesis and the conclusion

if an animal has no tail, then it is not a monkey; if not q, then not p

two statements that are both true or false

if a figure is a triangle, then it is a polygon

a statement that contains the phrase “if and only if”; can only be written if both the conditional and converse statements are always true

a figure is a triangle if and only if it is a polygon; p if and only if q

if two lines intersect to form a right angle; their slopes are negative reciprocals

an unproven statement based on an observation; an educated guess based on data and examples; is false if there is a counter example

prime numbers are odd, proof: 1, 3, 5, 7, 11, 13 are odd

a specific case for which the conjecture is false

2 is prime and an even number

the process of finding a pattern in specific places and then writing a conjecture for the general case

most softball players become coaches, sue is a softball player, so she’ll become a coach

uses facts, definitions, properties, and the laws of logic (detachment and syllogism) to form a logical argument

all dogs have ears; golden retrievers are dogs, therefore they have ears

if the hypothesis of true conditional statement is true, then the conclcusion is true

Mary goes to the movies every friday and saturday night, today is a friday; Mary goes to the movies; if pq is true, and p is true, then q is true

if the statements: hypothesis p, then conclusion q and if hypothesis q, then conclusion r are true then this statement is true: if hypothesis p, then conclusion r; if p = q and q=r, then p=r

if Jane taks chemistry this year, then Ella will be Janes lab partner, if Ella is Jane’s lab partner, then Jane will get an A is chemistry; if Jane takes chemistry this year, she will get an A in chemistry

through any two points, there, exists exactly one line; if two points, then one line

a line contains at least two points; if line, then two or more points

if two lines intersect, then their intersection is one point

through any three non collinear points that exists exactly one plane; if three non collinear points, then one plane

a plain contains at least three non collinear points; if one plane, then three non collinear points

if two points lie in a plane, then the line containing them lies in the plane

if two planes intersect, then their intersection is a line

if a = b, then a + c = b +c

if a = b, the a-c = b-c

if a=b, then ac=bc

if a=b and c≠0, then a/c=b

for any real numbers a, b, and c; a(b+c)=ab+ac

for any real numbers a, b, and x; ax+bx=(a+b)x

if a=b, then b=a

for any real number a: a=a

if a=b and b=c, then a=c

if a=b, then a could be substituted for b in any expression

a logical statement that uses deductive reasoning to show that a statement is true

given information OR the result of applying properties, definitions, or known facts

responses for each corresponding statement

for any segment AB, AB=AB

if AB is congruent to CD, then Cd is congruent to AB

if AB is congruent to CD, and CD is congruent to EF, then AB is congruent to EF

For any angle A, measure A is congruent to measure A

if angle A is congruent to angle B, then angle B is congruent to angle A

if angle A is congruent to angle B, and Angle B is congruent to angle C, then angle A is congruent to angle C

all right angles are congruent, one right angle is 90*

two angles that add up to 180*, do not have to be adjacent or share a vertex

if two angles are supplementary to the same angle (or to congruent angles), then they are congruent

two angles that add up to 90*, do not have to be adjacent or share a vertex

if two angles are complementary to the same angle (or two congruent angles), then they are congruent

if two angles form a linear pair, then they are supplementary

vertical angles are congruent