Can someone help me with these problems? I'm not sure how to do them and I have to turn it in tomorrow.

- anonymous

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- anonymous

sure what problems

- sleepyjess

Hello! I'm definitely willing to try! What's the first question? ^_^

- AlexandervonHumboldt2

what are your questions?

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## More answers

- anonymous

##### 2 Attachments

- anonymous

i cant really read the first one

- sleepyjess

Question, on the first question, reason #2, how do you know it's the definition of midpoint? Point C hasn't been mentioned as the midpoint of line BD

- RAM231

perpendicular is the opposite of parallel. so if parallel is like a parallelogram, and its like a train track. what would perpendicular mean?

- sleepyjess

I feel like

- anonymous

@sleepyjess I don't know what i'm doing, I tried looking for examples online and i guessed.

- anonymous

ans easy way to remember perpendicular is: imagine a big lowercase t

- sleepyjess

Okay, normally all of the "Given"s will be in the first couple of slots

- anonymous

or cross

- anonymous

In the second picture, would the Statement #2 be AC BD for definition of perpendicular?

- sleepyjess

We already used AC perpendicular to BD, perpendicular means there will be right angles somewhere. Where do you think there would be right angles knowing that AC is perpendicular to BD?

- anonymous

angle c?

- anonymous

or would it be angle 1 and angle 2

- RAM231

with perpendicular lines, @sleepyjess they don't always have to have right angles in them. just a thought

- sleepyjess

Perpendicular means that there will be right angles

- RAM231

not how I learned it in school and I am in 11th grade geometry

- RAM231

and my twin is in AP pre calculous

- sleepyjess

I took precal in 10th grade,
A line is perpendicular to another if it meets or crosses it at right angles (90°). Perpendicular means "at right angles". A line meeting another at a right angle, or 90° is said to be perpendicular to it.
http://www.mathopenref.com/perpendicular.html

- RAM231

|dw:1449806960244:dw| these can be perpendicular lines, and they don't cross at 90 degrees.....

- sleepyjess

Those are not perpendicular lines

- RAM231

im not going to fight. But being in a house full of smart mathletes that compete in competitions and win... I know what they are....

- anonymous

what is the isosceles triangle theorem?

- sleepyjess

Sorry about that jcr, would you like to continue with the problems?

- anonymous

yes please

- sleepyjess

This is what I found about it:
Isosceles Triangle Theorems. The Base Angles Theorem. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of the Base Angles Theorem.
http://www.mathwarehouse.com/geometry/congruent_triangles/isosceles-triangle-theorems-proofs.php

- sleepyjess

I've actually never heard of that...

- sleepyjess

Are we doing #50 right now?

- anonymous

yes, #50

- sleepyjess

Okay, we're looking for 2 angles that are 90 degrees, on line BD

- anonymous

angle 1 and angle 2

- sleepyjess

Yes! So for the statement on #2, it will be <1 \(\cong\) <2

- anonymous

Okay. for 3. would it be reflexive?

- sleepyjess

Now we have to figure out something that will make triangle ABD isosceles...

- anonymous

Sides AB and AD are congruent. Would that be part of it? because isosceles has two = sides

- sleepyjess

I feel like the statement is going to be AB \(\cong\) AD, but I'm not sure of the reason

- anonymous

Okay, so what about #5? Im not sure on that one

- sleepyjess

I honestly am just going around in circles with this....

- anonymous

|dw:1449808300747:dw|
This is what I have for markings on the picture

- sleepyjess

Why can't we just prove that ABC \(\cong\) ADC now...

- anonymous

I'm not sure. Can we go look at the other one?

- sleepyjess

@myininaya , can you help?

- jigglypuff314

I can help with your number 49 :)

- jigglypuff314

Let's look at your step 2 in your problem 49
if \(AB\) is parallel to \(DE\)
then that means that \(AE\) and \(BD\) are "traversals" right?

- anonymous

Yes

- jigglypuff314

so what would that make your comparisons between your
Angle 1 and Angle 2
or
Angle 3 and Angle 4
?
(what can those pairs be classified as?) :)

- myininaya

By the way just so no one is confused about a earlier debate on this thread... Two lines are perpendicular if at their crossing the 4 angles formed there are 90 degrees...
|dw:1449809081389:dw|
sorry to interrupt

- anonymous

alternate exterior??

- jigglypuff314

ooo
really close!
but since they are Inside the triangles
and between the two parallel lines
it would be "alternate interior"
does that make sense? :)

- anonymous

Yes

- jigglypuff314

great!
so that would be your step two :)

- anonymous

So for step 3 am I correct on the vertical angles?

- jigglypuff314

#49
step 3 is perfect :)
then onto step 4
it is the second to last step
so perhaps we should try proving that the Triangles are congruent
what Congruency Postulate do you think we can use to prove that the Triangles are congruent?

- anonymous

Is it called Angle Angle?

- jigglypuff314

hmm close!
remember that we were given that there's a side that's congruent too? :)
AB = DE

- anonymous

Angle Side Angle?

- jigglypuff314

even closer!! but not quite
http://prntscr.com/9csnyj

- anonymous

Side Angle Angle?

- jigglypuff314

Yes!
there you go :)

- jigglypuff314

Would you have an idea on what the last reason might be? :)

- anonymous

Would it be cpctc? I remember hearing it but im not sure if thats it

- jigglypuff314

^^ that is exactly it! :D

- anonymous

I was wondering if you could help me on one more thing? Its different from this

- jigglypuff314

of course I can try :)

- anonymous

When you are given a midpoint and one endpoint, how do you find the other endpoint?

- jigglypuff314

This is the formula you are familiar with right? :)|dw:1449810288429:dw|

- anonymous

Yes

- jigglypuff314

so if the Midpoint coordinate is \( (x, y) \)
that would mean that
\(\huge x = \frac{x_1 + x_2}{2}\)
and
\(\huge y = \frac{y_1 + y_2}{2}\)
does that make sense so far? :)

- anonymous

So if i had the midpoints (-2,9) then I would plug those into the big x and y??

- jigglypuff314

exactly :)
if you had the Midpoint = (-2, 9)
\(x = -2\)
\(y = 9\)
and one of the end points \((x_1, y_1)\)

- anonymous

So can i do one and show you? so i can make sure im doing it right?

- jigglypuff314

sure：）

- anonymous

So midpoint (4,8) and endpoint ( 5,3)

- jigglypuff314

ok
what do you think you should do next? :)

- anonymous

to find x would i do 4= to 5+4/2

- jigglypuff314

not quite :)
I think it would be more like
\( \large 4 = \huge \frac{5 + x_2}{2}\)
and you would be looking for \(x_2\)

- anonymous

Okay so for Y,
8= 3+x/2

- jigglypuff314

8 = 3+y/2
yes :)

- anonymous

do you need to get y by itself?

- jigglypuff314

indeed, that would be the y coordinate of your missing end point :)

- anonymous

subtract y from both sides?

- jigglypuff314

you might want to try multiplying both sides by 2 first :)

- anonymous

y=5.3?

- jigglypuff314

\[8 = \frac{3+y}{2} \rightarrow 16 = 3 + y\]

- anonymous

divide by 3 on both sides

- jigglypuff314

huh why?
don't we start with
3 + y
8 = --------
2
which becomes
16 = 3 + y

- anonymous

is that the answer?

- jigglypuff314

not yet
16 = 3 + y
-3 -3 try subtracting 3 from both sides to get y alone
-------------------
__ = y

- anonymous

13=y

- jigglypuff314

perfect :)
then the x value would be
solve for x from
5 + x
4 = --------
2

- anonymous

3=x

- jigglypuff314

there you go
you have now found your missing endpoint :)

- anonymous

Thank you so much for your help! Sorry it took me so long.

- jigglypuff314

I'm glad I could help ^_^
and don't worry about it, everyone learns at their own pace :)

- bubblegum.

@RAM231 Can you please tell me what does perpendicular means :)

- anonymous

|dw:1449840002906:dw|

- sleepyjess

@bubblegum. , perpendicular means "at right angles". A line meeting another at a right angle, or 90° is said to be perpendicular to it.
credit: http://www.mathopenref.com/perpendicular.html

- RAM231

@bubblegum. Perpendicular means lines are crossing. It doesn't have to be at a 90 degree angle. its like a 4 way street. they are perpendicular because they cross each other. This can also be perpendicular. |dw:1449864072050:dw|
Because they are passing through the y axis. I just got the answer from my math teacher as well.

- sleepyjess

I have now given you multiple resources to show that perpendicular means lines crossing at a 90 degree angle. Whether you choose to believe the truth or not is up to you.

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