Triangles PQR and SQT are formed by the intersection of two transversals of parallel sides. Drag the points to adjust the triangles. Use this manipulative to see if you can find a way to prove that these triangles will always be similar... Use the questions below to help.

Questions[br][br]1. How are segments PR and TS related? They are parallel[br]2. If PR and ST were extended as lines, name two transversals of these lines. Transversals RT and PS[br]3. What type of angles are PQR and SQT? How are they related? They are vertical angles which means they are related because they are congruent.[br]4. Look at transversal PS and segments PR and ST only. How could you describe the relationship between angles RPQ and TSQ? They are corresponding angles which means they are congruent.[br]5. Look at transversal RT and PR and ST only. How could you describe the relationship between angles QRP and QTS? They are corresponding angles which means they are congruent.[br]6. List the congruent angle pairs in this diagram.[br]∠PQR and ∠ SQT[br]∠RPQ and ∠ TSQ [br]∠QRP and ∠ QTS[br][br]7. Complete the similarity statement: By the AA Similarity Theorem, ∆PQR ∼∆SQT[br]8. Based on this interactive, will two triangles created by the intersection of two transversals between parallel lines always be similar? Why or why not? Yes, since the lines on the outside are parallel, the transversals through them will always create two similar triangles.