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