Question

are these triangles similar? yes no

Explanation:

Step1: Recall angle - sum property of triangles

The sum of interior angles of a triangle is 180°. For \(\triangle STU\), we can find the third - angle measure. Let the third angle be \(x\). Then \(x = 180-(55 + 94)=180 - 149 = 31^{\circ}\). For \(\triangle KIJ\), let the third - angle be \(y\). Then \(y=180-(55 + 91)=180 - 146 = 34^{\circ}\).

Step2: Check AA (angle - angle) similarity criterion

Two triangles are similar if two pairs of corresponding angles are equal. In \(\triangle STU\) and \(\triangle KIJ\), one pair of angles is \(55^{\circ}=55^{\circ}\), but the other non - equal angles (\(94^{\circ}
eq91^{\circ}\) and \(31^{\circ}
eq34^{\circ}\)) are not equal. So, the triangles do not satisfy the AA similarity criterion.

Answer:

no