Question

Is the triangles similar? If the triangles are similar then this is the statements that we have to use

Answer 1

When two triangles are similar, their corresponding angles are equal.

So, the first step to solve the exercise is to find the measure of the missing angle in each triangle.

We know that the sum of the interior angles of a triangle is 180. Then, we have:

• Measure of angle R

$\begin{gathered} 54\degree+68\degree+R=180\degree \\ 122\degree+R=180\degree \\ \text{ Subtract 122\degree from both sides} \\ 122\degree+R-122\degree=180\degree-122\degree \\ R=58\degree \end{gathered}$

• Measure of angle U

$\begin{gathered} 54\degree+67\degree+U=180\degree \\ 121\degree+U=180\degree \\ \text{ Subtract 121\degree from both sides} \\ 121\degree+U-121\degree=180\degree-121\degree \\ U=59\degree \end{gathered}$

As we can see, the corresponding angles of the triangles RST and UVW are not equal.

Therefore, the triangles are not similar.