# Connecting Similarity and Transformations

11 questions

# Connecting Similarity and Transformations

##### Problem 1

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

##### Problem 2

Quadrilaterals $Q$ and $P$ are similar.

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

3) What is the scale factor of the dilation that takes $Q$ to $P$?

##### Problem 3

4) What is our definition of similarity?

##### Problem 4

5) 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 $BC$?

##### Problem 5

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

##### Problem 6

7) Right angle $ABC$ is taken by a dilation with center $P$ and scale factor $\frac{1}{2}$ to angle $A'B'C'$. What is the measure of angle $A'B'C'$?

##### Problem 7

8) Dilate point $C$ using center $D$ and scale factor $\frac{3}{4}$.

9) Dilate segment $AB$ using center $D$ and scale factor $\frac{1}{2}$.

##### Problem 8

10) 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?

##### Problem 9

11) Select **all** the statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

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.