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.

### Pause and Reflect

If 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?

Interactive popup. Assistance may be required.

The area ratios would still be the square of the ratios of the lengths of the corresponding sides for similar quadrilaterals. ### Practice

Use the similar triangles shown below to answer questions 1 and 2. 1. If the perimeter of ΔABC is 17 units, what is the perimeter of ΔDEF?

Interactive popup. Assistance may be required.

How do you determine the perimeter of a triangle? Interactive popup. Assistance may be required.

Perimeters of similar figures have the same ratios as the lengths of their corresponding sides.

AB over DE AB DE = AB over DE PABC) PDEF)

3.3 over 4.95 3.3 4.95 = 17 over x 17 x

x = 25.5 2. What is the ratio of the area of ΔDEF to the area of ΔABC?

Interactive popup. Assistance may be required.

What is the ratio of the lengths of the corresponding sides? Interactive popup. Assistance may be required.  