Question

are these triangles similar?
triangle ghi with angle at g: 43°, angle at h: 107°.
triangle def with angle at d: 43°, angle at e: 96°.
options: yes, no

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle GHI \), if \( \angle G = 43^{\circ} \) and \( \angle H=107^{\circ} \), then \( \angle I=180^{\circ}-(43^{\circ} + 107^{\circ})=180^{\circ}-150^{\circ} = 30^{\circ} \)

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

For \( \triangle DEF \), if \( \angle D = 43^{\circ} \) and \( \angle E=96^{\circ} \), then \( \angle F=180^{\circ}-(43^{\circ}+96^{\circ})=180^{\circ}-139^{\circ}=41^{\circ} \)

Step3: Check for angle - angle similarity

Similar triangles must have all corresponding angles equal. The angles of \( \triangle GHI\) are \( 43^{\circ},107^{\circ},30^{\circ} \) and the angles of \( \triangle DEF\) are \( 43^{\circ},96^{\circ},41^{\circ} \). Since not all corresponding angles are equal.

Answer:

no