# Lesson 7

Reasoning about Similarity with Transformations

### Problem 1

Sketch a figure that is similar to this figure. Label side and angle measures.

### Solution

For access, consult one of our IM Certified Partners.

### 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.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

What is the definition of similarity?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 6.)### Problem 4

Select **all** figures which are similar to Parallelogram \(P\).

Figure \(A\)

Figure \(B\)

Figure \(C\)

Figure \(D\)

Figure \(E\)

### Solution

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 21.)