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Q: Are two rectangles with the same perimeter always congruent to each other?

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Not necessarily. Let's say that there is a circle with the area of 10. Now there is a star with the area of 10. They do not have the same perimeter, do they? That still applies with rectangles. There might be a very long skinny rectangle and a square next to each other with the same area, but that does not mean that they have the same perimeter. Now if the rectangles are congruent then yes.

that would be a prism

'B' and 'D'. The diagonals are equal to each other in rectangles and squares.

Congruent angles. are you cheating on your geometry homework?

Similar shapes need to have the same number of sides, the same angles and the ratio of the sides needs to be the same. Rectangles are not always similar to each other because they can have different dimensions, which would break the "same ratio" rule.

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Not necessarily. Let's say that there is a circle with the area of 10. Now there is a star with the area of 10. They do not have the same perimeter, do they? That still applies with rectangles. There might be a very long skinny rectangle and a square next to each other with the same area, but that does not mean that they have the same perimeter. Now if the rectangles are congruent then yes.

Only if they are congruent. One of them could be the a rotation of the other - eg 4m x 6m and 6m x 4m.

Yes. If two figures are congruent, then you literally can't tell one from the other.Anything that's true of one is also true of the other.

that would be a prism

Not normally but yes when they are congruent to each other.

Yes. Say there are two rectangles, both with perimeter of 20. One of the rectangles is a 2 by 8 rectangle. The area of this rectangle is 2 x 8 which is 16. The other rectangle is a 4 by 6 rectangle. It has an area of 4 x 6 which is 24.

It is a three dimensional shape whose faces are rectangles. There are three pairs of congruent parallel rectangles opposite each other. A smooth brick or box are good examples.

Yes, in similar triangles, the angles are always congruent, and the sides have the same proportions to each other.

"Congruent" means "same shape and size as the other one". So one thing all by itself is never congruent. It needs something else to be congruent with. An isosceles triangle is never congruent to a scalene triangle, sometimes congruent to any other kind of triangle, and always congruent to another isosceles triangle that's congruent to the first one.

Because Symmetry means that both sides of the line are congruent and each side is reflecting the other one

It is a skew prism. If the parallelograms are rectangles then it is a right prism.

Not always because its 4 sides can have different dimensions to other trapezoids

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