Question

are these triangles similar?
f
g
56°
31°
h
w
25°
v
56°
u
yes
no

Explanation:

Step1: Calculate the third angle of triangle \(FGH\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle FGH\), let the third - angle be \(\angle F\). Then \(\angle F=180^{\circ}-(31^{\circ} + 56^{\circ})=180^{\circ}-87^{\circ}=93^{\circ}\)

Step2: Calculate the third angle of triangle \(WUV\)

For \(\triangle WUV\), let the third - angle be \(\angle V\). Then \(\angle V=180^{\circ}-(25^{\circ}+56^{\circ})=180^{\circ}-81^{\circ}=99^{\circ}\)

Step3: Check the similarity condition

Two triangles are similar if their corresponding angles are equal. The angles of \(\triangle FGH\) are \(31^{\circ},56^{\circ},93^{\circ}\) and the angles of \(\triangle WUV\) are \(25^{\circ},56^{\circ},99^{\circ}\). Since not all corresponding angles are equal.

Answer:

no