Question

are these triangles similar?
triangle vut with angle at u: 100°, angle at t: 31°.
triangle efd with angle at d: 100°, angle at e: 31°.
options: yes, no

Explanation:

Step1: Find angle in first triangle

In triangle \( VUT \), we know two angles: \( \angle U = 100^\circ \) and \( \angle T = 31^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle V=180^\circ - 100^\circ - 31^\circ = 49^\circ \).

Step2: Find angle in second triangle

In triangle \( EDF \), we know two angles: \( \angle D = 100^\circ \) and \( \angle E = 31^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle F = 180^\circ - 100^\circ - 31^\circ = 49^\circ \).

Step3: Check angle - angle similarity

Triangle \( VUT \) has angles \( 100^\circ \), \( 31^\circ \), \( 49^\circ \) and triangle \( EDF \) has angles \( 100^\circ \), \( 31^\circ \), \( 49^\circ \). 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 have two pairs of equal angles (\( 100^\circ \) and \( 31^\circ \) are common), so they are similar.

Answer:

yes