Question

Please can someone help will fan and medal!!
Define inductive reasoning and explain its purpose in mathematics.
Define deductive reasoning and explain its purpose in mathematics.

Answer 1

@jim_thompson5910

Answer 2

It's hard for me personally to define inductive reasoning, so I figured I'd search the web. It's sometimes best not to reinvent the wheel (so to speak)

http://changingminds.org/disciplines/argument/types_reasoning/induction.htm

that page states "Inductive reasoning, or induction, is reasoning from a specific case or cases and deriving a general rule. It draws inferences from observations in order to make generalizations."

so basically you look at a few (or a lot) of sample points drawn from a population and you try to make a general rule for all of the items in the population

Answer 3

one example of inductive reasoning:

Rock #1 is hard
Rock #2 is hard
Rock #3 is hard

so...all rocks must be hard

notice how this type of reasoning doesn't always work. Some rocks are actually soft so the conclusion isn't true in this case, but in other cases, inductive reasoning works.

Answer 4

ok great thank you do you mind helping me with another question?

Answer 5

do the same for deductive reasoning

Answer 6

yeah sure, what is it

Answer 7

ok

Answer 8

2. Which of the following pairs of angles are always congruent? If they are not always congruent, what is their
relationship? Assume that parts a) through d) are formed by two parallel lines intersected by a transversal.

a) corresponding angles
b) alternate interior angles
c) alternate exterior angles
d) same side interior angles
e) vertical angles
f) linear pair

Answer 9

@jim_thompson5910 sorry i took so long

Answer 10

which two angles are corresponding angles?

Answer 11

1 and 5 do you want all of the angles

Answer 12

how about one more pair

Answer 13

ok 3 and 7

Answer 14

good

Answer 15

it turns out that any two corresponding angles are congruent if the lines are parallel

Answer 16

how about alternate interior angles? are they always congruent? also name me 2 pairs of alternate interior angles

Answer 17

3/6 and 4/5 yes they are always congruent

Answer 18

nailed all 3 parts

Answer 19

same question for alternate exterior angles

Answer 20

thanks 2/7 and 1/8

Answer 21

very good, you're a natural at this stuff

Answer 22

are alternate exterior angles always congruent?

Answer 23

yes

Answer 24

correct

Answer 25

well assuming you have those 2 parallel lines of course

Answer 26

are same side interior angles always congruent?

Answer 27

no

Answer 28

arent they supplementary

Answer 29

yes that is correct, they add to 180 degrees

Answer 30

so that is the relationship between them

what is one pair of same side interior angles?

Answer 31

3 and 5

Answer 32

good

Answer 33

are vertical angles always congruent?

name 1 pair of vertical angles

Answer 34

yes they are 1 and 4

Answer 35

correct

Answer 36

and finally, are a linear pair of angles always congruent?

Answer 37

no arent they supplementary too?

Answer 38

very good, they also add to 180

they are adjacent angles that are supplementary

Answer 39

what is one pair of angles that are also a linear pair?

Answer 40

8 and 7
@jim_thompson5910

Answer 41

you are correct

Answer 42

so it seems like you know all this stuff, which is good

Answer 43

so is that it then i completed the question (with your help of course :)) ?
@jim_thompson5910

Answer 44

That is correct. Everything is all done.

Answer 45

ok thank you so much