Stretching and Shrinking Check up 2

 

So far in the first third, we are learning about stretching and shrinking shapes. This is our stretching and shrinking check up #2.

 

On the first page, the question was, “Which figures are similar? How do you know?” I thought that Z and T were similar and Y and W were similar.

I thought that Z and T were similar because T is half of Z and Z is two times the amount of T. This makes the scale factor from Z to T 2, and the scale factor from T to Z 1/2.

I thought that Y and W were similar because W times 1/2 or .5 equals Y, and Y times 2 equals W. The scale factor is the same as Z and T. The scale factor from Y to W is 2 and the scale factor from W to Y is 1/2.

 

The first question on the second page is, “Draw a figure similar to the rectangle but not congruent. Why is it similar?” I drew the rectangle which is labeled 1, on the second picture. The shape I drew is similar to the rectangle in the picture because it is half of the size of the original rectangle. Now the side lengths are 1.5 by 2, instead of 3 by 4.

The second question is, “Draw a rectangle NOT similar to the given rectangle. Why is it similar?” I drew the rectangle which is labeled 2. The rectangle that I drew is not similar to the given rectangle because the side lengths do not match up at all. The side lengths are 5 by 3 and the original side lengths are 3 by 4.

The third question is, “Draw a figure similar to the triangle but not congruent. Why is it similar?” I drew a triangle labeled on the sheet, number 4. This triangle is similar to the original triangle because it has a scale factor of 2. The reasoning behind this is that if you multiply the sides of the original triangle by 2, you get the lengths of the larger triangle. Now the lengths of the larger  triangle are 12 by 12 by 8.

The fourth question is, “Draw a triangle NOT similar to the given triangle. Why isn’t it similar?” I drew the triangle that is labeled 4. The triangle that I drew is not similar to the given triangle because the lengths do not match up. It is also a totally different shape than the given triangle and the proportions of the triangle I drew are all different. The lengths are now 3.1 by 3 by 2, this does not match up with the larger triangle. The lengths of the given triangle are 6 by 4 by 6.