Task 4 - Point of Similarity
Shown below are ∆STU and ∆MNO.
Questions
1.) Are the two triangles similar? Why?
2.) What is the ratio of the lengths of their corresponding sides?
3.) Use the Line tool to connect the corresponding vertices of the two triangles. Did your observations in Tasks 2 and 3 hold?
4.) Make a conjecture about the lines connecting the corresponding vertices of similar triangles.
Explanation
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 center of similarity or point of similarity.
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.