anonymous
  • anonymous
The figure shows three right triangles. Triangles JKM, KLM, and JLK are similar.
Mathematics
chestercat
  • chestercat
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
Theorem: If two triangles are similar, the corresponding sides are in proportion.
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Using the given theorem, which two statements help to prove that if segment JL is x, then x2 = 100? A.Segment JL • segment JM = 64 Segment JL • segment LM = 48 B. Segment JL • segment JM = 48 Segment JL • segment LM = 36 C. Segment JL • segment JM = 64 Segment JL • segment LM = 36 D.Segment JL • segment JM = 36 Segment JL • segment LM = 64

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
anyone know how to do this?
anonymous
  • anonymous
do you know? @Calcmathlete
anonymous
  • anonymous
I know how to do the problem, but it's worded very strangely to me. It would make much more sense for x to be JK, KL, or KM. Give me a second, and I'll help you.
anonymous
  • anonymous
Ok. Have you done work with geometric means in these types of problems before?
anonymous
  • anonymous
no its actually a pretest so i havent done this before
anonymous
  • anonymous
but if x^2 is 100 then x must be 10
anonymous
  • anonymous
JL is 10 i mean
anonymous
  • anonymous
i thought it was x2 not x^2
anonymous
  • anonymous
Whenever you copy and paste, an exponent, it usually pastes it as x2 or something. @Venice-Gribbin
anonymous
  • anonymous
sorry hehe its x squared
anonymous
  • anonymous
i see.
anonymous
  • anonymous
Alright. Before we start, you may have noticed that you could've used Pythagorean Theorem to verify that JL = 10. Did you notice that?
anonymous
  • anonymous
yeah 36 plus 64=100
anonymous
  • anonymous
Ok. That's something that happens a lot in geometry. The key is that you need to use the given, which is the theorem they gave you. So, looking at similarity. The way the triangles are written are very significant. The order in which the letters appear tell you which sides are proportionate to what. So, if they were written as (JKM, KLM, and JLK) as you said, JL is proportionate to KL and JK. So, you could say that:\[\frac{JL}{KL}=\frac{JK}{KM}\]Are you following me so far?
anonymous
  • anonymous
yes so can we plug in their values into this proportion?
anonymous
  • anonymous
\[\frac{ 10 }{ 8 }=\frac{ 6 }{ ? }\]
anonymous
  • anonymous
If you have them, yes. Now, with this type of problem, you can only work with the values they gave you, even though it's obvious that JL does indeed equal 10. So, the only values you can actually plug in are JK and KL. The above proportion won't help you here. That was just for example. Hold on, and I'll help you get the right equation.
anonymous
  • anonymous
Lol @Gjallerhorn your name is perfect man
anonymous
  • anonymous
fellow destiny player?
anonymous
  • anonymous
Yeah I play it on xbox one. But before we continue this convo I want you to succeed in your math lol so ill wait till you get the answer
anonymous
  • anonymous
anyone who is familiar with Feizel crux's masterpiece knows their "Destiny..."
anonymous
  • anonymous
lolwut
anonymous
  • anonymous
I'll tell you how I got this specific proportion afterwards, but the one that will help you is\[\frac{JM}{JK}=\frac{JK}{JL}\]This can be simplified to \[JM\times JL=JK^2\]Now, plug in the values you have.
anonymous
  • anonymous
into the proportion or the equation under it?
anonymous
  • anonymous
The equation under it. I got the bottom equation by cross multiplying. The only values they gave you were JK and KL.
anonymous
  • anonymous
JMxJL=6^2 or 36?
anonymous
  • anonymous
Yes. That gives you the answer you need because none of the other answers have that as part of the answer. If you wanted to completely do the question, the other proportion you would use is:\[\frac{JL}{KL}=\frac{KL}{LM}\]which simplifies to \[JL\times LM=KL^2\]
anonymous
  • anonymous
ok lemme plug in
anonymous
  • anonymous
JLxLM=64 or 8^2
anonymous
  • anonymous
with those two values my answer would be D. correct?
anonymous
  • anonymous
Yes. That's correct. I'll write how I got those specific proportions in a second.
anonymous
  • anonymous
Now, the way I got those proportions is something called geometric means. A geometric mean between two numbers a and b is defined as \[Geometric ~Mean=\sqrt{ab}\]or you can also say \[ (Geometric~Mean)^2=a\times b\]Whenever you have a situation like this where you have the three similar right triangles with 2 of them within the bigger one, there are three relationships of "geometric means" that are extremely helpful (they are just similar triangles, so you can derive them later too). |dw:1436552274512:dw|
anonymous
  • anonymous
One of the geometric mean relationships is that BD is the geometric mean of AD and DC. In other words, \[\frac{AD}{BD}=\frac{BD}{DC}\]or\[AD\times DC=BD^2\]which is a geometric mean. The other two are that BC is the geometric mean of CD and AC and that AB is the geometric mean of AD and AC.
anonymous
  • anonymous
I remember it with the pneumonic "ALL".|dw:1436552524856:dw| That's the 'A' part of it.
anonymous
  • anonymous
These are the other two 'L' |dw:1436552558243:dw| |dw:1436552572987:dw| Sorry that the explanation is so long, just thought it'd be good if you knew where I got the information from.
anonymous
  • anonymous
wow thanks so much!!!!
anonymous
  • anonymous
No problem. If you need me to explain anything else, let me know.
anonymous
  • anonymous
Also, keep in mind that they need to be right triangles for these things to work because otherwise, they wouldn't be similar triangles.
anonymous
  • anonymous
im definitely fanning you.
anonymous
  • anonymous
thanks for the guidance and explanation!
anonymous
  • anonymous
No problem. I'm not online very often tbh, but when I am, I try to help as many people as possible.

Looking for something else?

Not the answer you are looking for? Search for more explanations.