If two polygons are similar, then their ____________________ and ___________________.
Look at the figure below. Quadrilateral ABCD~Quadrilateral EFGH. State anything that you can about the angles and sides.
When we are looking at similar figures, we can also look at the perimeters and the areas. If we know the scale factor of a set of similar figures, then the perimeters of the figures have the same scale factor. The ratio of the areas is the scale factor squared.
Example:
1. What is the scale factor of ABCD to EFGH?
2. What is the ratio of the perimeters of ABCD to EFGH?
3. What is the ratio of the areas of ABCD to EFGH?
4. If CD = 50, what is GH?
5. If HE = 20, what is DA?
6. If AB = 60, what is FE?
7. Check to see if the ratio of the sides is the same as the perimeters.
8. Could you also check the areas? Explain.
Investigation (Assignment
5):
Your task is to investigate if the same relationship exists with 3 dimensional solids. To look at this, CLICK HERE
and click on the example. The example will guide you through some applications of this concept with prisms. Come up with a conjecture about the perimeters and areas of solid figures.