Lesson 7
Reasoning about Similarity with Transformations
Problem 1
Sketch a figure that is similar to this figure. Label side and angle measures.
Solution
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Problem 2
Write 2 different sequences of transformations that would show that triangles \(ABC\) and \(AED\) are similar. The length of \(AC\) is 6 units.
\(AC=6\)
Solution
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Problem 3
What is the definition of similarity?
Solution
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(From Unit 3, Lesson 6.)Problem 4
Select all figures which are similar to Parallelogram \(P\).
Parallelogram \(P\)
Figure \(A\)
Figure \(B\)
Figure \(C\)
Figure \(D\)
Figure \(E\)
Figure \(A\)
Figure \(B\)
Figure \(C\)
Figure \(D\)
Figure \(E\)
Solution
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Problem 5
Find a sequence of rigid transformations and dilations that takes square \(ABCD\) to square \(EFGH\).
Translate by the directed line segment \(AE\), which will take \(B\) to a point \(B’\). Then rotate with center \(E\) by angle \(B’EF\). Finally, dilate with center \(E\) by scale factor \(\frac{5}{2}\).
Translate by the directed line segment \(AE\), which will take \(B\) to a point \(B’\). Then rotate with center \(E\) by angle \(B’EF\). Finally, dilate with center \(E\) by scale factor \(\frac{2}{5}\).
Dilate using center \(E\) by scale factor \(\frac25\).
Dilate using center \(E\) by scale factor \(\frac52\).
Solution
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(From Unit 3, Lesson 6.)Problem 6
Triangle \(DEF\) is formed by connecting the midpoints of the sides of triangle \(ABC\). What is the perimeter of triangle \(ABC\)?
Solution
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(From Unit 3, Lesson 5.)Problem 7
Select the quadrilateral for which the diagonal is a line of symmetry.
parallelogram
square
trapezoid
isosceles trapezoid
Solution
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(From Unit 2, Lesson 14.)Problem 8
Triangles \(FAD\) and \(DCE\) are each translations of triangle \( ABC\)
Explain why angle \(CAD\) has the same measure as angle \(ACB\).
Solution
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(From Unit 1, Lesson 21.)