If two polygons are SIMILAR, then the corresponding angles must be _____. If two polygons are SIMILAR, then the corresponding sides must be _____.

Question

1. If two polygons are SIMILAR, then the corresponding angles must be _____.
2. If two polygons are SIMILAR, then the corresponding sides must be _____.
3. The composition of two (or more) isometries is always ______
4. A rectangle has a length of 9 mm. A similar rectangle is drawn using a scale of 1:3. What is the length of the second rectangle?
5. A right triangle has a base of 5 ft and a height of 12 ft. A similar triangle has an area of 270 square feet. What are the dimensions of the similar triangle.

Answer 1

Here is the information you need to answer these questions:

There are 4 transformations you are studying. 3 of them, reflections (flip), rotations (turns), and translations (slides), result in a congruent image of the original figure. The image will be the same size and same shape as the original figure. When that happens, the transformation is called an Isometry, or RIGID transformation. A composition of isometries is when more than one isometry has occurred. A composition of isometries will also be an isometry.

The last of the 4 basic transformations you are studying is a dilation. A dilated figure will be the same shape but (probably) a different size of the original. A dilation is a NON-RIGID transformation. Figures that are the same shape but may be different sizes are called similar figures. The lengths will be in equal ratio. For example, if you multiply all lengths of a figure by 3, then the resulting figure will be similar. All the lengths will be 3x the original lengths. We call 3 the scale factor. However, the angles of similar figures won't change. This is because angles are turns between two sides and the actual turn won't change, just the sides that connect to make the angle will grow or shrink. So angles will remain congruent (or we say they are "preserved")

If you have a scale of 1:3 that means that the scale factor is 3 and all lengths will get multiplied by 3.

The last question is the most difficult because Area is not a length, but is the result of working with lengths. The first triangle will have area = 1/2 base * height= 1/2 *5 * 12 =30 square feet. The similar figure has an area of 270 square feet. 270/30=9. But remember, area is from TWO lengths, so the scale factor is actual the square root of 9, which is 3 (tricky!). So multiply the original lengths by 3.

Hope this makes sense. Good luck!