# Lesson 7

Reasoning about Similarity with Transformations

### Problem 1

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

### 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.

### Problem 3

What is the definition of similarity?

### Solution

(From Unit 3, Lesson 6.)

### Problem 4

Select all figures which are similar to Parallelogram $$P$$.

A:

Figure $$A$$

B:

Figure $$B$$

C:

Figure $$C$$

D:

Figure $$D$$

E:

Figure $$E$$

### Problem 5

Find a sequence of rigid transformations and dilations that takes square $$ABCD$$ to square $$EFGH$$.

A:

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 $$\frac{5}{2}$$.

B:

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 $$\frac{2}{5}$$.

C:

Dilate using center $$E$$ by scale factor $$\frac25$$.

D:

Dilate using center $$E$$ by scale factor $$\frac52$$.

### Solution

(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

(From Unit 3, Lesson 5.)

### Problem 7

Select the quadrilateral for which the diagonal is a line of symmetry.

A:

parallelogram

B:

square

C:

trapezoid

D:

isosceles trapezoid

### Solution

(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 $$ACB$$.