Lesson 7

Similar Polygons

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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 \(DEF\)?

A:

\(41^\circ\)

B:

\(82^\circ\)

C:

\(123^\circ\)

D:

\(164^\circ\)

Solution

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Problem 2

Draw two polygons that are similar but could be mistaken for not being similar. Explain why they are similar.

Solution

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Problem 3

Draw two polygons that are not similar but could be mistaken for being similar. Explain why they are not similar.

Solution

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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.

Solution

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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.

Solution

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(From Unit 2, Lesson 3.)

Problem 6

  1. Draw a horizontal line segment \(AB\).

  2. Rotate segment \(AB\) \(90^\circ\) counterclockwise around point \(A\). Label any new points.
  3. Rotate segment \(AB\) \(90^\circ\) clockwise around point \(B\). Label any new points.
  4. Describe a transformation on segment \(AB\) you could use to finish building a square.

Solution

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(From Unit 1, Lesson 8.)