Question

b. complete the statements below about similar figures:
in similar figures, the corresponding angles must be____
and the corresponding sides must grow____

1. select all true statements about internal ratios of similar figures.

a. the internal ratios are equivalent ratios
b. the internal ratios will always give the same quotient.
c. internal ratios are the same in figures that are similar.

Explanation:

Step1: Recall the properties of similar figures

Similar figures have equal corresponding angles and proportional corresponding sides.

Step2: Analyze each statement

• Statement a:

The internal ratios (ratios of corresponding sides) of similar figures are equivalent. For example, if we have two similar triangles \(\triangle ABC\) and \(\triangle DEF\) with \(AB/DE = BC/EF=AC/DF = k\) (the scale factor), so this statement is true.

• Statement b:

Take two similar rectangles. Let one rectangle have length \(l_1 = 4\) and width \(w_1=2\), and the other have length \(l_2 = 8\) and width \(w_2 = 4\). The ratio of length to width for the first rectangle is \(4/2=2\), and for the second rectangle is \(8/4 = 2\). But if we consider a non - uniform scaling (which is not allowed for similar figures in the strict sense, but if we assume some wrong internal ratios), if we have a figure and we scale one side by a factor \(k_1\) and another side by a factor \(k_2
eq k_1\), the figures will not be similar. In the case of similar figures (with the correct definition of similarity where all corresponding sides are scaled by the same factor), the internal ratios (ratios of corresponding sides) are equivalent. So the statement "The internal ratios will always give the same quotient" is not a correct way to describe similarity. The key is that the ratios of corresponding sides are equal (equivalent ratios), not just that some internal ratios give the same quotient in a non - corresponding sense. This statement is false.

• Statement c:

By the definition of similar figures, if two figures are similar, the ratios of their corresponding sides (internal ratios of corresponding sides) are equal. So this statement is true.

Answer:

A. The internal ratios are equivalent ratios
C. Internal ratios are the same in figures that are similar