Question

are these triangles similar?
(image of two triangles: triangle uvw with angles at u: 36°, at w: 93°; triangle hig with angles at i: 36°, at g: 92°. options: yes, no)

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle UVW \), if \( \angle U = 30^{\circ} \) and \( \angle W=63^{\circ} \), then \( \angle V=180^{\circ}-(30^{\circ} + 63^{\circ})=87^{\circ} \)

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

For \( \triangle HIG \), if \( \angle I = 30^{\circ} \) and \( \angle G=62^{\circ} \), then \( \angle H=180^{\circ}-(30^{\circ}+62^{\circ}) = 88^{\circ} \)

Step3: Check the AA (Angle - Angle) similarity criterion

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, only one pair of angles (\( \angle U=\angle I = 30^{\circ} \)) is equal. The other angles (\( \angle V = 87^{\circ}
eq\angle H=88^{\circ} \) and \( \angle W = 63^{\circ}
eq\angle G=62^{\circ} \)) are not equal.

Answer:

no