Question

***WILL MEDAL***

Answer 1

zepdrix was nice enough to get this far and I am very thankful for that I need help getting the rest of it.

Answer 2

your first statement should be a separate line
whats given is "K is the midpoint of JL"
the first statement is the definition of a midpoint

Answer 3

you can use the base angle theorem to prove that angle L is congruent with angle M

and the definition of an isosceles triangle is a triangle that has two congruent sides and two congruent angles

Answer 4

So it should be like this

Answer 5

or so ive read

Answer 6

that should be your 3rd statement

the first couple statements should always be whats given

Answer 7

and the given statement should be exactly what is written

Answer 8

Im confused....Could you draw it out for me please?

Answer 9

Oh ok

Answer 10

using the given information, you immediately recognized that LK=KJ
and your reasoning was the definitino of the midpoint

Answer 11

so that would be your 3rd statement/reasoning

Answer 12

now before you continue, we see that the main point of the proof is determining that triangle KLM is an isosceles triangle

Answer 13

So i would puth the letters under statements and put the def. of a midpoint under reasons

Answer 14

Sorry If this is taking long I never learned this in school

Answer 15

so we need to look up what the definition of an isosceles triangle
from what ive read, its a triangle with 2 congruent angles and 2 congruent sides

so your last step would be using the definition in order to prove an isosceles triangle

Answer 16

now, we only know that we have 2 congruent sides, but we dont know if we have 2 congruent angles, so we need to see if there are any theorems of postulates that will allow us to prove that 2 angles are congruent

Answer 17

Im sorry are we still on 3

Answer 18

3, you already assumed statement LK=KJ, reasoning was the definition of a midpoint

Answer 19

Oh ok sorry

Answer 20

we just went over the final step, maybe step 7, proving that the triangle is an isosceles triangle based on the definition

Answer 21

in order to determine what additional information is required in order to prove its an isosceles triangle

Answer 22

so our step 4 would be trying to prove angle L = angle M

Answer 23

Would it definition equality?

Answer 24

no

Answer 25

2 column proofs are a bit stupid, but the overall reasoning of it, is essentially trying to slow down the thoughts into a systematic steps

Answer 26

intuitively we know that the 2 angles are equal to each other, but there's no mathematical proof in thinking so

Answer 27

http://www.mathwarehouse.com/geometry/congruent_triangles/isosceles-triangle-theorems-proofs.php

Answer 28

look through the proofs on that website,

you will notice that the base angle theorem will fit what you're looking for,

basically you have 2 congruent sides, and you use that information to prove that you have 2 congruent angles

Answer 29

So the reason for number4 would be given?

Answer 30

"BASE ANGLE THEOREM"

given only implies the information the problem states

Answer 31

oh it seems we skipped a step

Answer 32

the actual step 4

Answer 33

Oh I thought we working on it...

Answer 34

step inbetween what we're working on

Answer 35

we know that KJ=LK and the KJ=KM

we dont know LK=KM
so our actual 4th step would be proving LK=KM

Answer 36

So the statement for number 4 would be angle L ≅ angle M

Answer 37

nope, thats step 5 now

Answer 38

And the reason would be base angle theorm

Answer 39

theorem*

Answer 40

yes, since we're using LK=KM to get angle K=angle M

Answer 41

but we cant assume LK=KM, so we need to determine the reasoning for that

Answer 42

So thats for five...

Answer 43

base angle theorem is statement/reason 5

Answer 44

Ok

Answer 45

LK=KM is statement 4 but we dont know the reasoning for it yet

Answer 46

there is actually 2 reasons we can use for LK=KM

Answer 47

Would it be substitution prop. or linear pair angles are supplementary

Answer 48

substitution works fine

the other one would be the transitive property of equality

linear pair angles are supplementary does not make sense, since that only proves that 2 angles will equal 180 degrees

Answer 49

transitive property of equality
A=B & B=C thus A=C

Answer 50

Oh ok

Answer 51

soooo, 6 step proof

Answer 52

quick review,
first 2 step are given
3. using the definion of midpoint
4. using substitution or transitive property
5. proving base angles are congruent
6 using the definition of an isosceles triangle to proove the triangle is isosceles

Answer 53

So how would I right the 5 and 6 on the chart?

Answer 54

And 4

Answer 55

the statement or the reasoning?

Answer 56

both I got lost on how to right them out