Evaluate the third angle measure of each triangle.
Are the triangles similar? No.
Practice makes perfect
We are given two angle measures of each triangle and asked to determine if they are similar.
Let's evaluate the third angle measure of each triangle. To do this, we will use the fact that in a triangle the sum of the measures of angles is 180^(∘). We will start with ∠ QRS.
∠ QRS+ 47^(∘)+ 68^(∘)=180^(∘)
∠ QRS+115^(∘)=180^(∘)
∠ QRS = 65^(∘)
Now, we will do the same with ∠ TUV.
∠ TUV+ 47^(∘)+ 59^(∘)=180^(∘)
∠ TUV+106^(∘)=180^(∘)
∠ TUV= 74^(∘)
Let's add these information to our diagram.
As we can see these triangles have only one congruent angle. Therefore, they are not similar because to prove the similarity we need to have at least two congruent angles.
