Question

Anybody good at geometry here?

Answer 1

I can give it a go

Answer 2

This would be my question, I've been stuck on it all day.

Answer 3

Oh god yeah lol a little out of my reach. @Hero
I'd suggest you tag some more people. One of them may be able to assist you.
Good luck!

Answer 4

Well, because it is a perpendicualr bisector, what do you know?

Answer 5

Each point on the perpendicular bisector is the same distance from each of the endpoints of the original line segment. Angles 4 and 6 are both 90 degrees. Thats' about the extent of my knowledge with proofs.

Answer 6

The \(\angle 4 \cong \angle 6\) is superfluous if you think about the definition of perpendicular. Perpendicular means they meet at right angles... so ALL the angles are 90 degrees where they meet.

The equadiistant is good. That gives you some key information.

Answer 7

Now... if I said to play connect the dots, could you guess what my next step would be?

Answer 8

superfluous... I like that word. I feel like the definition of a perpendicular bisector with each point being the same distance it should answer the question. Im guessing the next step would be to make a triangle

Answer 9

Not one triangle... two. Two triangles that share one side, have "equadiistant" involved on a second side, and a known angle between them. So, know any Side, Angle, Side or SAS proofs?

Answer 10

Better triangleS? I dont really know any of those proofs, no.

Answer 11

Hmmm... know any rules about right triangles? Say the Pythagorean Theorem?

Answer 12

I do know the Pythagorean theorem :D

Answer 13

Good! So first, you need to prove you made right triangles! That is where perpendicular came in. Oce you have right triangles, then the Pythagorean Theorem applies.

Answer 14

Whoops I was trying to type and I messed something up there, let me retype that. I know that the perpendicular bisector has for 90 degree angles. For a triangle to be a right triangle it has to have a 90 degree angles as both of our triangles do so they are both right triangles. I know that the pythagorean theorem is a^2+b^2=c^2 where C is the side opposite of the right angle also known as the hypotenuses.

Answer 15

Yes, you are seeing it. Here, let me past in what I was working on:

If I call the intersection D (cause it is next up), then you can talk about \(\overline{AD}\) and \(\overline{BD}\) as the bisector parts. By the definition of bisect, \(\overline{AD}= \overline{BD}\). You already mentioned that.

So where does the Pythagorean Theorem come in? Well, lets see. Since these are right triangles:


\(\overline{AD}^2 + \overline{DC}^2 = \overline{AC}^2\)

AND:

\(\overline{BD}^2 + \overline{DC}^2 = \overline{BC}^2\)

So, if you can prove \(\overline{AD}= \overline{BD}\) (wait... that was given...) then you can prove that \(\overline{AC}= \overline{BC}\)

In a formal proof, you need to remember the part where you prove that they share the same side... yes, sound silly but that is part of doing proofs. EVERYTHING is proven, even the shared sides.

Answer 16

Alrighty so this is where that D is supposed to be I am guessing. I have never written a proof but I do actually understand what you are saying. Thanks for the help, I do have a few follow up questions but I am going to try and write out that paragraph and have it make hopefully(!) a bit of sense. Any pointers on what I should include in the paragraph, I'm certainly not going to ask you to write it out fully just like some main points. I know that the perpendicular bisector, 90 degree angles, right triangles, AD BD congruence AC BC congruence and the pythagorean theoream should all be main points but I am not sure if there should be a specific order or if I am missing any key points

Answer 17

First make D, and yes, that is it. Once you have D, use the definition of bisector to prove the small legs are the same. Then point out the long leg is shared and therefore the same. Then use the perpendicular to call it a right triangle. Then use the pythagorean to show that you would be using the same number for the short leg no matter what, therefore the hypotenuse would be the same. Then, just to be 100% clear, point out that the hypotenuse measure is the distance to C and since those are the same they are equadistant as requested.

Answer 18

I can't thank you enough for your help, I have no idea why teachers say openstudy is so bad. How long will you be around on here?

Answer 19

Now, you could say "It is perpendicuar therefore right" first. That order does not matter. But you must prove them right before you can use pythagoras. A proof is like that. You build up to a "big reveal." Everything in place and then, "Tada! All true so this is true!" OR: "Tada! I contradicted, so it can't be that!" which is called a proof by contradiction.

Answer 20

OpenStudy can be bad if you get a person that just wants answers r just wants to hand out answers. However, if you are adamant in wanting to learn you can find people to help you who are willing to teach.

Answer 21

I can see that viewpoint as well! This was the first question I have ever asked and I actually learned something for once.

Answer 22

Well, if you are lear in the question that you want to learn how and not just an answer, it can help. Then find a few people to tag that like helping. The ambassadors with an A before their name are good. So are a number of normal users.

Answer 23

So this is what I came up with. Would you personally add or subtract anything from it?

Answer 24

While it is not formal, it is what they asked for. You should be fine.