geometry
example of integers
-2 -1 0 1 2
show reasoning behind answer: is the conditional statement true or false? if 121 is a prime number, then 10 is a multiple of 3
121 is not a prime number so the hypothesis is false 10 is not a multiple of 3 so the conclusion is false the statement is true
opposite rays
2 rays with common an endpoint that forms a straight line
if 2 angles are supplementary and congruent, what is their measurement
90 degrees
set up an equation and simplify for the following problem: find the measure of complement of measure of angle K= 6x+12
90-(6x+12) 90-6x-12 78-6x
T/F a pair vertical angles form a pair of linear
False; to form a linear pair, vertical angles must share a common side
find H and C: a triangle with congruent angles and sides is an equilateral triangle
H: a triangle has congruent angles and congruent sides C: the triangle is an equilateral
midpoint formula
M(x1+x2/2, y1+y2/2)
bisector
a point that deivides a segment into 2 equal segments
rational
a real number that can be written as a fraction. rational numbers can be formed into p/q where p and q are integers and q is not 0
create a counterexample for the following: if a quadrilateral has 4 angles measuring 90, then it is a square
a rectangle is a quadrilateral with 4 90 degree angle measures that is not a square
if a ray divides an angle into 2 complementary angles, what is the original angle
a right angle
counter example
a specific example that shows a statement of conjecture is false
conjecture
a statement you believe is true based on inductive reasoning
if a ray divides an angle into 2 supplementary angles, the original angle is
a straight line
find two points on the y-axis that are a distance of 5 units form (4,2)
add 5 units both ways to the yaxis while keeping the x the same\ 2+5=7 (4,7) 2-5=-3 (4,-3)
integers are
all sets of negative and positive WHOLE numbers including 0
vertical angles
are two non-adjacent angles with one common vertex; formed by intersecting lines
postulate or
axiom is a statement accepted as true without proof
transformation
change in the position size or shape of a figure
in a venn diagram, the bigger circle is the ____ represented with___ and the subcircle is the ___ represented with
conclusion/q/hypothesis/p
related conditions (name them)
conditional converse inverse contrapositive
what kind of statement can be written in "if p then q" form
conditional statement
in a ___ statement, q is the
conditional/conclusion
in a ___ statement, p is the
conditional/hypothesis
a conditional statement is equivalent to ____
contrapositive
distance formula
d= square root of (x2-x1)^2 +(y2-y1)^2
in hs, students must take history before geometry. peter is going to geometry, so he must have taken history. deductive or inductive?
deductive
biologist disprove a previously believed myth. deductive or inductive reasoning?
deductive because the conclusion of something being a myth is based on logical reasoning from scientific research
angle bisector
divides an angle into 2 congruent angles
through any 2 points there is
exactly one line
through any 3 noncollinear points there is
exactly one plane containing them
deductive reasoning is more associated with
facts
the sides of vertical angles
form a pair of opposite rays
real numbers
found in an number line, includes rational and irrational
write the following into a conditional statement: the midpoint M of a segment bisects the segment
if M is a midpoint of a segment, then M bisects the segment
conditional
if p then q
law of syllogism
if p then q and if q then r are true, then "if p then r" is a true statement
law of detachment
if p then q is a true statement and p is true, then q is true
angle addition postulate
if point S is the interior of angle PQR, then the measure of PQR is equal to the measure of PQS plus the measure of SQR
converse
if q then p
inverse
if ~p then ~q
contrapositive
if ~q then ~p
observing something to check if it is a myth. deductive or inductive reasoning?
inductive because the conclusion of something being a myth is based on a pattern of OBSERVATION
-5/1 integer/noninteger:
integer
integer/noninteger: 3
integer
if 2 planes intersect they
intersect at exactly one line
if angle is acute, its complement has to be ___ than its supplement because
less; an angles supplement is always greater than its complement
finding coordinates of an endpoint
let the unknown endpoint be (x,y) find x coor of unknown x coor of midpoint = x coor of known endpoint+x/2 same for y coor
the inverse of a conditional statement is ______ to
logically equivalent / converse
to figure out what plane is in front
look to where edges over lap. the plane with the dashed edge is behind the other one
write a negation to the following: M is the midpoint of line Ab
m is not the midpoint of the line ab
4/9 integer/noninteger:
non
96.4 integer/noninteger:
non
~ symbol means
not
if m is an even number, then m is an integer. if m is an integer, then m is a rational number. 18.113 is a rational number. conclusion: 18.113 is an even number. VALID?
not valid.
preimage
original shape; shape before the transformation
linear pair
pair of adjacent angles whose non common side are opposite rays. linear piar form 180 degree angles when added
y=x line is the same as
parent function of a linear function
circumference of circle
pi * d
area of a circle
pi*radius squared
collinear
points on the same line
coplanar
points on the same plane
deductive reasoning is used to___/ it is the process of using __ to draw conclusions from
prove that a conjecture is true/ logic / facts, definitions
all integers are
rational
why is -18.54repeating a ___
rational number/ because it is a repeating decimal
every whole number is a ____ because it can be ___// example
rational number/ written as a fraction/300= 300/1
why are the square roots of 25 and 4 ___
rational/because they're perfect squares
inductive reasoning
reasoning that a rule or statement is trie because specific cases are true
a flip/___, each point is ___ from the
reflecion/the same distance /line of reflecion
in a turn/, each point is ___ from___ referred as
rotation/the same distance/the center of rotation/P
logically equivalent statement have
same truth value
interior angle
set of all points between the sides of an angle
if the measure of angle a is less then 90, then the measure of angle a is acute. if the measure of angle a is acute, then it is not a right angle. conjecture: if measure of angle a is less then 90, then the angle is not a right angle. VALID?
since q is the conclusion of the first conditional and the hypothesis of the second conditional you can conclude that "if p then r". the conjecture is valid
distance between two points is
the absolute value of difference of coordinates AB= the absolute value of b-a or a-b
if a question where to ask "find the measure of the angle" instead of "find the measure of its complement/supplement...
the answer would stop when you find the x (don't subtract it from its anything
tell whether the following conjecture is valid/what type of law proves it. if you are tardy 3 times, then you have to go to detention. jeane is in detention. conjecture: jeane was tardy three times
the conjecture matches the conclusion of a true statement but this does not mean the hypothesis is true. jeane could be in detention for another reason. the conjecture is not valid by law of detachment
image
the figure after the transformation
tell whether the following conjecture is valid/what type of law proves it. if 2 segments are congruent, then they have the same lenght. line ab is congruent to line xy. conjecture: ab=xy
the given statement line ab is congruent to line xy matches the H of a true conditional. by law of detachment, ab=xy. the conjecture is valid
if a number is divisible by 4(x), then it is divisible by 2(y). if a number is even(z) then it is divisible by 2 conjecture: if a number is divisible by 4, then it is even. VALID?
the law of syllogism cannot be used to draw conclusion since y is the conclusion of BOTH conditional statements. even tho the conjecture "if x then z"is true, the logic used to draw the conclusion is NOT valid.
if line JK bisects angle LJM then
the measure of angle LJK is congruent to the measure of angle KJM
if two points lie on a plane
then the line containing those 2 points also lies on the plane
If two congruent angles form a linear pair
they are right angles
If two angles form a linear pair
they are supplementary.
if two lines intersect
they intersect at exactly one point
in a slide/, all points in a figure ____
translation/move in the same direction and distance
inductive is more associated with
trends generalizing estimating
adjacent angles
two angles in the same plane with common vertex and common side but no common interior points
what kind of angles are congurent
vertical
if the hypothesis of a conditional statement is false, no matter
whether the conclusion is true or false, the entire statement will be considered true
set up the equation for the following problem: an angle measures 3 degrees less than twice the measure of its complement. find the measure of its complement.
x=measure of its complement x= 2(90-x)-3 when you find x, subtract it by 90 90-59-31