# Connecting Similarity and Transformations

ID: hilik-masot
Illustrative Mathematics
Subject: Geometry

11 questions

# Connecting Similarity and Transformations

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##### 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. 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.