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Q: The lengths of the 3 sides of a certain triangle are related as shown below where n is the length of the shortest side of the triangle. 0.5n 1.5n 2.5n Which of these name the lengths of the sides for?

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It only has two equal lengths out of however many sides like an isosceles triangle

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I'm pretty sure it refers to the fact that a triangle, when in two dimensions, can't collapse. That is, there's no way to change the actual shape of a triangle (other than rotating or moving it) without changing the lengths of the sides.http://i.imgur.com/pfd14.png (see related links below for a clickable link)Look at the image at the above link. Notice how when the square collapses into a parallelogram, the sides still stay the same lengths, but the angles change. That's not possible with a triangle-if the angles change, so do the lengths of the sides. Therefore, a triangle is rigid.(To help visualize this better, picture yourself holding a square frame with hinges at the corners, so it can be bent. It would be easy to bend it into a parallelogram. However, picture the same, only with a triangle. It can't be done.

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