Lesson 12
Similar Polygons
Let’s look at sides and angles of similar polygons.
Problem 1
Triangle \(DEF\) is a dilation of triangle \(ABC\) with scale factor 2. In triangle \(ABC\), the largest angle measures \(82^\circ\). What is the largest angle measure in triangle \(DEF\)?
\(41^\circ\)
\(82^\circ\)
\(123^\circ\)
\(164^\circ\)
Problem 2
Draw two polygons that are similar but could be mistaken for not being similar. Explain why they are similar.
Problem 3
Draw two polygons that are not similar but could be mistaken for being similar. Explain why they are not similar.
Problem 4
These two triangles are similar. Find side lengths \(a\) and \(b\). Note: the two figures are not drawn to scale.
![Two triangles. First, sides 9, b, 21. Second, sides 3, 5, a.](https://cms-im.s3.amazonaws.com/tUD7wGhKgWG8h7Kz4ay8CPp2?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.09.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.09.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004305Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad66b185254d53ee9ea75630d0519b9e87f3b475b954eac8371c1093081740ad)
Problem 5
Jada claims that \(B’C’D’\) is a dilation of \(BCD\) using \(A\) as the center of dilation.
What are some ways you can convince Jada that her claim is not true?
![Point A, angle B C D and angle image B prime, C prime, D prime.](https://cms-im.s3.amazonaws.com/569PZmcpBEFFVkxjkULNhSxb?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.17.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.17.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004305Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=22aaf74542e2b74d1bfc7f05725d0ba2b133f36e673984a703b3c63ee10547a6)
Problem 6
-
Draw a horizontal line segment \(AB\).
- Rotate segment \(AB\) \(90^\circ\) counterclockwise around point \(A\). Label any new points.
- Rotate segment \(AB\) \(90^\circ\) clockwise around point \(B\). Label any new points.
- Describe a transformation on segment \(AB\) you could use to finish building a square.