Question

Prove that the two circles shown below are similar.

Answer 1

Something about dilation? I don't know how to prove it though

Answer 2

@mathstudent55 @mathslover @mertsj

Answer 3

what does it mean for something to be similar?

Answer 4

similar shape / size

Answer 5

so, are all squares similar?

Answer 6

yes

Answer 7

are all 30-60-90 right triangles similar?

Answer 8

same with circles

Answer 9

are all 360 degree circles similar?

Answer 10

yup, same idea

Answer 11

yes and yes

Answer 12

they are all the same shape. The scale is the only difference

Answer 13

so you have to figure out the scale for the circles. find the radius?

Answer 14

well I mean, as a general rule, all cricles are similar, so you are sort of done there

Answer 15

radius of circle x is 6 and radius of circle y is 3.

Answer 16

Yea i just wasn't sure on how to prove it

Answer 17

just show every circle is similar, no matter the radii and you're done

Answer 18

so go by def. os my choice. What is the specific def. of similar?

Answer 19

I'll look real quick.

Answer 20

has the same shape, but not necessarily the same size

Answer 21

is what it says in glossary

Answer 22

ok, so you could do a simple pf. of by def. because all _______ are ________ with the exact same shape, just different _________. Every ______ is _________.

Answer 23

it's really simple

Answer 24

no need to do anything else in my opinion, and it actuallymakes your life easier in the future

Answer 25

that's all i thought you needed to do but schools are weird and want you to prove everything.

Answer 26

another interp:
"Let’s use the definition of Similarity given in the standards:

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

We’ll start by showing any two circles are the same. Take any two circles, and slap some Cartesian Coordinates on them, such that the first is at the origin. Translate the second circle to the origin, then dilate it until the radii match. Thus the pair of circles is similar.

If any two circles are similar, then all circles are similar by transitivity of similarity. QED"
- http://commoncoretools.me/forums/topic/prove-that-all-circles-are-similar/

Answer 27

but basically, geometry proofs can be pretty straight forward. If you don't mind me asking, what level are you?

Answer 28

54

Answer 29

huh?

Answer 30

i mean in school not here haha

Answer 31

10th going into 11th

Answer 32

behind as far as my math schedule because I retook algebra

Answer 33

wow, they have you guys doing proofs now?

Answer 34

that is shocking to me

Answer 35

but make sure you're a real pro at algebra before you take alg. II or trig

Answer 36

you'll need to be

Answer 37

Got a B and C in 8th grade. Retook and got an A and an A in 9th :). I'm not one to usually blame teachers as far as school but my math teacher in 8th grade was horrible

Answer 38

, they let you retake it 3 times? that's weird

Answer 39

and teachers make or break it. trust me on that

Answer 40

Only took the class 2 times, 8th and 9th. Finishing up geometry for 10th now

Answer 41

oh, still odd, but ok. And actually, where I went to HS that was normal.

Answer 42

Some people I know are already taking pre-calc. Wish I was that good at math. thanks for the help

Answer 43

Do yourself one favor, never say you are bad at math. If you do, you will be. Instead say you just haven't had enough practice. :)