Answer:
To prove that △PRT ∼ △QRS, we need to show that the corresponding angles of the two triangles are equal and that the corresponding sides are proportional.
We can use the given information that Q lies on line PR and S lies on line RT to show that the triangles are similar.
The condition that proves △PRT ∼ △QRS is:
Angle-angle-angle (AAA) similarity condition: If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent, and the triangles are similar.
In this case, we can see that:
∠PRT and ∠QRS are corresponding angles (both are opposite to segment RS)
∠PTR and ∠QSR are corresponding angles (both are opposite to segment QS)
Therefore, we have two pairs of corresponding congruent angles, and by the AAA similarity condition, we can conclude that △PRT ∼ △QRS.
Explanation: