standard_description: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
problem_activity: In the following figure,
$${\overline{AE}}$$
and
$${\overline{BD}}$$
are segments.
[IMG]
a) Show that
$${{{{\triangle ABC}}}}$$
and
$${{{{\triangle CDE}}}}$$
are similar.
b) What is the scale factor of similarity transformation that takes
$${{{{\triangle ABC}}}}$$
to
$${{{{\triangle CDE}}}}$$
?
c) What is the value of the ratio of the area of
$${{{{\triangle ABC}}}}$$
to the area of
$${{{{\triangle CDE}}}}$$
? Explain how you know.
d) If the area of
$${{{{\triangle ABC}}}}$$
is
$${30\space \mathrm{cm^2}}$$
, what is the area of
$${{{{\triangle CDE}}}}$$
?


aligns: no