# Lesson 6

Connecting Similarity and Transformations

• Let’s identify similar figures.

### Problem 1

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

### Problem 2

Quadrilaterals $$Q$$ and $$P$$ are similar.

1. What is the scale factor of the dilation that takes $$P$$ to $$Q$$?
2. What is the scale factor of the dilation that takes $$Q$$ to $$P$$?

### Problem 3

What is our definition of similarity?

A:

If 2 figures have the same angles, then they are similar.

B:

If 2 figures have proportional side lengths, then they are similar.

C:

If there is a sequence of rigid transformations taking one figure to another, then they are similar.

D:

If there is a sequence of rigid transformations and dilations that take one figure to the other, then they are similar.

### Problem 4

Triangle $$DEF$$ is formed by connecting the midpoints of the sides of triangle $$ABC$$. The lengths of the sides of $$DEF$$ are shown. What is the length of $$BC$$?

A:

3 units

B:

4 units

C:

6 units

D:

8 units

(From Unit 3, Lesson 5.)

### Problem 5

If $$AB$$ is 12, what is the length of $$A'B'$$

(From Unit 3, Lesson 5.)

### Problem 6

Right angle $$ABC$$ is taken by a dilation with center $$P$$ and scale factor $$\frac12$$ to angle $$A’B’C’$$. What is the measure of angle $$A'B'C'$$?

(From Unit 3, Lesson 4.)

### Problem 7

1. Dilate point $$C$$ using center $$D$$ and scale factor $$\frac{3}{4}$$.
2. Dilate segment $$AB$$ using center $$D$$ and scale factor $$\frac12$$.
(From Unit 3, Lesson 4.)

### Problem 8

A polygon has perimeter 12. It is dilated with a scale factor of $$k$$ and the resulting image has a perimeter of 8. What is the scale factor?

A:

$$\frac12$$

B:

$$\frac23$$

C:

$$\frac34$$

D:

$$\frac43$$

(From Unit 3, Lesson 3.)

### Problem 9

Select all the statements that must be true.

A:

Parallelograms have four congruent sides.

B:

Both sets of opposite sides of a parallelogram are parallel and congruent.

C:

A trapezoid is a parallelogram.

D:

Diagonals of a parallelogram bisect each other.

E:

Diagonals of a parallelogram are congruent.

(From Unit 2, Lesson 13.)