Shown below are ∆STU and ∆MNO.

1.) Are the two triangles similar? Why?[br][br]2.) What is the ratio of the lengths of their corresponding sides?[br][br]3.) Use the Line tool to connect the corresponding vertices of the two triangles. Did your observations in Tasks 2 and 3 hold?  [br][br]4.) Make a conjecture about the lines connecting the corresponding vertices of similar triangles. [br][br][br] [br][br][br]

If two triangles are similar and their corresponding sides are parallel, then the line connecting their corresponding vertices will intersect at a  point. This point is called the [b]center of similarity[/b] or [b]point of similarity[/b].

In Task 3, ∆ABC ~ ∆A'B'C' and their corresponding sides are parallel. The three lines connecting the corresponding vertices intersect point P as shown above.  In Task 4, ∆STU ~ ∆MNO, but their corresponding sides are not parallel, so the three lines connecting their corresponding vertices do not intersect at a point.[br][br][br]