Question

How would you justify that triangle PQR is similar to triangle STU.

Answer 1

Ok, so

We want to justify the fact that triangle PQR is similar to triangle STU.

First, let me draw the situation here below:

If you notice, both angles of each triangle are equal. We can also see that the sides of triangles PQR and STU should have a ratio.

This is:

`(QR)/(TU)=(PR)/(SU)`

If we replace:

`\begin{gathered} (2)/(1)=(3)/(1.5) \\ 2=2 \end{gathered}`

With this, we can affirm that there's a dilation scale factor of 2. This means that the bigger figure is two times bigger than the smaler one. Therefore, the triangles PQR and STU are similar.

Both triangles are similar because their corresponding angles are congruent and the corresponding sides are in proportion.