# Connecting Similarity and Transformations

ID: hilik-masot Illustrative Math
Subject: Geometry

# Connecting Similarity and Transformations

Classroom:
Due:
Student Name:
Date Submitted:
##### 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?

a) $\text{If 2 figures have the same angles, then they are similar.}$b) $\text{If 2 figures have proportional side lengths, then they are similar.}$c) $\text{If there is a sequence of rigid transformations taking one figure to another, then they are similar.}$d) $\text{If there is a sequence of rigid transformations and dilations that take one figure to the other, then they are similar.}$
##### 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 ﻿$BC$﻿? a) $\text{3 units}$b) $\text{4 units}$c) $\text{6 units}$d) $\text{8 units}$
##### 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?

a) $\frac{1}{2}$b) $\frac{2}{3}$c) $\frac{3}{4}$d) $\frac{4}{3}$
##### 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. ﻿$\quad\quad$﻿ b) Both sets of opposite sides of a parallelogram are parallel and congruent. c) A trapezoid is a parallelogram. ﻿$\quad\quad$﻿ d) Diagonals of a parallelogram bisect each other. ﻿$\quad\quad$﻿ e) Diagonals of a parallelogram are congruent.