Question:
Triangle CBD has been dilated.
A. Determine the scale factor of the sides (small to large).
B. What is the ratio of the areas (small to large)?
C. Write a generalization about the ratio of the sides and the ratio of the areas of similar figures.
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part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

so

Let

z ----> the scale factor

The scale factor is equal to

substitute

simplify

Part B) What is the ratio of the areas (small to large)?

Area of the small triangle

Area of the large triangle

ratio of the areas (small to large)

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

need points to ask question

step-by-step explanation:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: