Question

given \\( \triangle s t u \\) with \\( s t \parallel x y \\)
prove \\( \frac { s x } { x u } = \frac { t y } { y u } \\)

complete the steps of the proof

Explanation:

Step1: Recall AA similarity theorem

Two triangles are similar if two pairs of corresponding angles are congruent.

Step2: Use the congruent angles

Since \(\angle1\cong\angle2\) and \(\angle3\cong\angle4\) (from previous steps), by the AA (Angle - Angle) similarity theorem, \(\triangle UXY\) and \(\triangle UST\) have two pairs of congruent angles.

Step3: State the similarity

So, \(\triangle UXY\sim\triangle UST\) (by AA similarity theorem) which is the statement for step 5.

Answer:

\(\triangle UXY\sim\triangle UST\)