Similar figures property

yma16

Junior Member
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Jan 10, 2018
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Is there a theorem about any two similar plane figures as the following,

The ratio of sizes of the two similar figures is equal to the square of the ratio of their circumferences.

For example, consider two squares of sizes 1 and 4. Their circumferences are 4 and 8. 1/4=(4/8)^2
 
Is there a theorem about any two similar plane figures as the following,

The ratio of sizes of the two similar figures is equal to the square of the ratio of their circumferences.

For example, consider two squares of sizes 1 and 4. Their circumferences are 4 and 8. 1/4=(4/8)^2

"ratio of sizes" is not well-defined.

It is ALWAYS thus (in Euclidean Geometry):

Ratio of any Linear Measure (Side, Circumference, Diagonal): A:B
Ratio of Area: A^2:B^2
Ratio of Volume: A^3:B^3
 
I do not need to use ratio. Let me change it.

Assume there two similar figures in a plane,
The
size of one figure divided by the size of another is equal to the square of the circumference of the first figure divided by the square of the circumference of the second figure.
 
Assume there two similar figures in a plane,
The
size of one figure divided by the size of another is equal to the square of the circumference of the first figure divided by the square of the circumference of the second figure.
"Circumference" usually restricts discussion to circles. Are you here using "circumference" to mean "perimeter", being the length around the outside of the shape?

By "size", do you mean "area"?

By the way, dividing the values is essentially the same thing as forming the ratios, so the earlier response stands. ;)
 
You are right. Thank you.

I am not good at the terms. My kid asked me about two similar triangles and I told her it should be the true for any two similar shapes.
 
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