## Task 4 – Point of Similarity

**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 **Task 2** and **Task 3** hold?

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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**Task 5 >>**