# Month: July 2018

## 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 >>**

## Task 3 – Connecting Vertices of Similar Triangles

**Questions **

1.) Are the two triangles similar? Why?

2.) Use the ** Line **tool to connect the corresponding vertices of the two triangles. What do you observe about the lines?

3.) Draw another triangle that is similar to $latex \triangle EFG$ and name it $latex \triangle HJI$. Connect their corresponding vertices. Did your observation in 2 also hold?