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, and their corresponding sides are parallel. The three lines connecting the corresponding vertices intersect point as shown above. In Task 4, , 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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