Incorporate at least two module vocabulary words in your responses to parts ii and iii.
part ii: observation
what do you notice about the area of the polygons as the number of sides increase?
how does the area of the polygons compare to π?
if you were to continue to increase the number of sides on the polygon inscribed in the circle, what would you expect?
part iii: extend your thinking
using the results of your observation, how can you calculate the area of the circle if you know the circle’s circumference? show all work to support your thinking.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

the argument of alfred t. mahan, henry cabot lodge, and albert j. beveridge was the economically and mass production the the americans could not consume themselves. this led expansion to sell to other foreign nations for profits.

step-by-step explanation:

this is my explanation

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