10.4. Side, Perimeter, and Area of Similar Figures.
Side, Perimeter, and Area Ratios of Similar Figures.
1. Check the "Side Ratio" box. Move point B around. What do you notice?
2. Are these polygons always similar? Explain.
3. Check the "Perimeter Ratio" box. Move point B around. What is the relationship between the ratio of sides and the ratio of perimeters?
4. Deselect the"Perimeter Ratio" box and check the "Area Ratio" Box. What is the relationship between the ratio of sides and the ratio of areas? HINT: Check the Square of Side ration box as well.
5. Complete the conjecture: If two pentagons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is _________.
6. Do you think this conjecture holds true for other polygons? Explain.