Congruence and Similarity
Identify Similar Polygons
If two Polygons are similar, then there corresponding angles are congruent and the measure of their corresponding sides are proportional.
In the example provided, you can see that these rectangles are in fact similar. First you check to see if all the corresponding angles are congruent. Corresponding mean that two polygons are identical in form. Since these are rectangles with all 90 degree angles, all the corresponding angles are congruent. Next you have to see if all the sides are proportional. Proportional means, corresponding in size or amount to something else. To set up a proportion for this figure, we take the height of the smaller rectangle and put it over the height of the larger rectangle. This will be 2/3. Next, you then you take the length of the smaller rectangle and put it over the height of the bigger rectangle. This will be 6/9, but you have to simplify it to make it become 2/3. Simplifying is to make (something) simpler or easier to do or understand. Since both the height and the length of the two rectangles are 2/3, the two rectangles are similar.
Lets try this example. Since both are rectangles with angles that equal 90 degrees there angles are congruent. Rectangle ABCD height over rectangle EFGH height is 2/4 which simplifies to 1/2. Rectangle ABCD length over rectangle EFGH length is 5/10 which simplifies to 1/2. Since the height and length of rectangles is one half, rectangle ABCD is similar to rectangle EFGH.( rectangle ABCD~rectangle EFGH).
Identifying Similarities by using Transfromations
Two figures are similar if the second can be obtained from the first by a sequence of transformations and dilation. First you figure out which transformations were used. Once you figure out which transformation was use, you map the shapes so it corresponds to each other. Next you write a ratio comparing thee lengths. If the lengths are proportional, the the shapes are similar.