Question

△DEF is similar to △STU. Write a proportion that
contains ST and SU.

Answer 1

Since triangles ΔDEF and ΔSTU are similar, their corresponding sides are proportional. This means that the ratio of any two sides in ΔDEF to their corresponding sides in ΔSTU will be the same. However, since the question specifically asks for a proportion containing ST and SU, let's focus on that.

First, recall that similar triangles have corresponding angles that are equal. To write a proportion that contains ST and SU, we need to figure out which sides in ΔDEF correspond to ST and SU in ΔSTU. Without additional information, we can't know for sure which sides these are. However, the problem is still solvable because it only asks for a proportion that includes ST and SU, not necessarily a particular one.

Let's denote the sides of ΔDEF as follows:

- DE corresponds to side ST in ΔSTU,
- EF corresponds to side TU in ΔSTU,
- FD corresponds to side SU in ΔSTU.

Now we can write a proportion using the corresponding sides that contain ST and SU:

DE / ST = FD / SU

This proportion shows the relationship between the sides DE and FD of ΔDEF and the sides ST and SU of ΔSTU, which maintains the equality of ratios that is characteristic of similar triangles.

Answer 2

The proportionality statement is
`(DE)/(ST)=(DF)/(SU)`

Explanation:

Given that ΔDEF is similar to ΔSTU.

We have to write the proportionality that contains the sides ST and SU.

As we know the statement of proportionality, for the two shapes to be similar, the sides must be in proportion i.e

`(DE)/(ST)=(EF)/(TU)=(DF)/(SU)`

we have to write the proportionality statement which contains ST and SU

`(DE)/(ST)=(DF)/(SU)`