Task 4 – Point of Similarity
1.) Are the two triangles similar? Why?
2.) What is the ratio of the lengths of their corresponding sides?
4.) Make a conjecture about the lines connecting the corresponding vertices of similar triangles.
[toggle title=’Explanation’ title_font_size=’14px’]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, $latex \triangle ABC \sim \triangle A’B’C’$ and their corresponding sides are parallel. The three lines connecting the corresponding vertices intersect point $latex P$ as shown above. In Task 4, $latex \triangle STU \sim \triangle MNO$, but their corresponding sides are not parallel, so the three lines connecting their corresponding vertices do not intersect at a point.
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