The first set of triangles (top) has SAS similarity because they have the same angle 46° and see that
[tex]\frac{OH}{UG}=\frac{IH}{GY}\Rightarrow\frac{12}{7}=\frac{24}{14}[/tex]
Therefore we have SAS similarity.
Now the second pair of triangles has SSS similarity, because
[tex]\frac{SE}{KW}=\frac{TE}{WA}=\frac{SY}{AK}\Rightarrow\frac{12}{4}=\frac{18}{6}=\frac{9}{3}=3[/tex]
The third pair of triangles has no similarity, it's a right triangle and we know that
[tex]\begin{gathered} 10^2=8^2+a^2\Rightarrow a=6 \\ 20^2=10^2+b^2\operatorname{\Rightarrow}b=\sqrt{300} \end{gathered}[/tex]
Plus
[tex]\frac{20}{10}\ne\frac{\sqrt{300}}{8}[/tex]
Therefore there's no similarity
Now the fourth and last pair of triangles has AA similarity. If we know the value of two angles we can find the value of the last angle, then to probe AA similarity we just need to know two angles, if they are equal, it's similar.
As we can see both triangles have 36° and 47° as internal angles, then it's AA similar
Final answers:1 . SAS similarity
2. SSS similarity
3. none
4. AA similarity
