Q: Are 2 squares with the same perimeter congruent?

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Yes.

no

No. Most squares probably are not congruent. Although they are similar.

Since the opposite sides are congruent: perimeter = 2(2) + 2(3) = 10

Yes because 2+2+2+2 = 8 cm

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Yes.

no

No. Most squares probably are not congruent. Although they are similar.

Squares and Rhombuses

Since the opposite sides are congruent: perimeter = 2(2) + 2(3) = 10

Every rectangle has. (That includes squares.)

No, because even through they have the same perimeter you must show how you can get 16 as the perimeter in two different ways.

Answer: Yes. A polygon can have the same perimeter length but smaller area than another polygon. Answer: For congruent or similar shapes, no. For different shapes, yes. Consider, for example, a rectangle 3 x 1, and another rectangle 2 x 2. They have different areas, but the same perimeter.

Yes, every square is congruent

no its an emphatic statement all squares can be cut in half to make 2 congruent isosceles right triangles is perhaps as general a statement as is possible

2 circles can be congruent. The have to have the same radius.

The easiest way to reason this is to consider how you could connect nine squares together while leaving the largest amount of perimeter exposed. In other words, what's the largest number of faces you can leave exposed on a set of squares that are all connected? The answer is that if you connect all of the squares in a line, then the two end squares will have three faces exposed and the other seven squares will have two faces exposed. That gives you 2 * 7 * 2cm + 3 * 2 * 2cm = 28cm + 12cm = 40cm. So the maximum perimeter you can get is 40cm. There are many other ways that you can arrange the squares to give you the same perimeter (eg. a plus sign, a zig-zag, and so on), but none that will give you more.