Question

given (\triangle stu) with (overline{st}paralleloverline{xy}). prove (\frac{sx}{xu}=\frac{ty}{yu}). complete the steps of the proof. angle (stu) is congruent to angle (xyu). triangle (stu) is congruent to triangle (xyu). triangle (stu) is similar to triangle (xyu).

Explanation:

Step1: Recall AA similarity theorem

AA (Angle - Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Step2: Check angles

We know that \(\angle1\cong\angle2\) and \(\angle3\cong\angle4\) (from steps 2 - 4). So, by AA similarity theorem, triangle \(STU\) and triangle \(XYU\) have two pairs of congruent angles.

Step3: Apply the theorem

Since two pairs of angles are congruent, by AA similarity theorem, \(\triangle STU\sim\triangle XYU\) (triangle \(STU\) is similar to triangle \(XYU\)) which is the statement for step 5.

Answer:

triangle \(STU\) is similar to triangle \(XYU\)