Question

question
determine if triangle stu and triangle vwx are or are not similar, and, if they are, state how you know. (note that figures are not
necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles ≹ similar.

Explanation:

Step1: Calculate the third angle of triangle STU

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(x\). Then \(x + 62^{\circ}+71^{\circ}=180^{\circ}\). So \(x=180^{\circ}-(62^{\circ} + 71^{\circ})=47^{\circ}\).

Step2: Calculate the third angle of triangle VWX

Let the third angle be \(y\). Then \(y+62^{\circ}+71^{\circ}=180^{\circ}\). So \(y = 180^{\circ}-(62^{\circ}+71^{\circ})=47^{\circ}\).

Step3: Check for similarity

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. In \(\triangle STU\) and \(\triangle VWX\), \(\angle S=\angle X = 62^{\circ}\), \(\angle T=\angle W=71^{\circ}\).

Answer:

The triangles \(STU\) and \(VWX\) are similar. By the AA (Angle - Angle) similarity criterion, since two pairs of corresponding angles (\(\angle S=\angle X = 62^{\circ}\) and \(\angle T=\angle W = 71^{\circ}\)) are equal, the triangles satisfy the condition for similarity.