In this section, you will investigate the relationship between ratios of the scale factor and areas of similar triangles. Below is the same geometric pattern found in Section 1.
Using the information in the figure, complete the table. Enter your answers as ratios in lowest terms using colons (e.g., 4:1 represents a ratio of 4 to 1). The box will turn red if your answer is incorrect. You will use the completed table to answer the conclusion questions that follow.
Interactive popup. Assistance may be required.
What patterns do you notice in the first numbers in the area ratios?Interactive popup. Assistance may be required.
The ratios of the areas are the squares of the ratios of the corresponding sides.Interactive popup. Assistance may be required.
What is 7^{2}?Interactive popup. Assistance may be required.
49:1Interactive popup. Assistance may be required.
What pattern do you observe in the ratios of the areas?Interactive popup. Assistance may be required.
n^{2}:1Interactive popup. Assistance may be required.
What is the inverse operation of squaring a number?Interactive popup. Assistance may be required.
15:1, since √225 = 15Interactive popup. Assistance may be required.
Apply your rule from the previous question to the ratio 2 over 3 2 3 :1.Interactive popup. Assistance may be required.
4 over 9 4 9 :1If you have similar quadrilaterals, how do you think the ratios of their areas would compare to the ratios of the lengths of the corresponding sides?
Use the similar triangles shown below to answer questions 1 and 2.
Interactive popup. Assistance may be required.
How do you determine the perimeter of a triangle?Interactive popup. Assistance may be required.
What is the ratio of the lengths of the corresponding sides?