Question

whether the two triangles are similar.
6

Explanation:

Step1: Calculate angle in triangle FED

In triangle \( FED \), we know two angles: \( \angle F = 31^\circ \) and \( \angle E = 104^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle D = 180^\circ - 31^\circ - 104^\circ = 45^\circ \).

Step2: Calculate angle in triangle ABC

In triangle \( ABC \), we know two angles: \( \angle A = 45^\circ \) and \( \angle B = 104^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle C = 180^\circ - 45^\circ - 104^\circ = 31^\circ \).

Step3: Check angle correspondence

Now, let's list the angles of each triangle:

• Triangle \( FED \): \( \angle F = 31^\circ \), \( \angle E = 104^\circ \), \( \angle D = 45^\circ \)
• Triangle \( ABC \): \( \angle A = 45^\circ \), \( \angle B = 104^\circ \), \( \angle C = 31^\circ \)

We can see that the angles are equal when we match them as \( \angle F = \angle C = 31^\circ \), \( \angle E = \angle B = 104^\circ \), \( \angle D = \angle A = 45^\circ \). By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), the two triangles are similar.

Answer:

The two triangles are similar.