# Reasoning about Similarity with Transformations

ID: lovak-sahil
Illustrative Math
Subject: Geometry

# Reasoning about Similarity with Transformations

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##### Problem 1

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

##### Problem 2

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

3) What is the definition of similarity?

##### Problem 4

4) Select all figures which are similar to Parallelogram ﻿$P$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) Figure a ﻿$\quad\quad$﻿ b) Figure b ﻿$\quad\quad$﻿ c) Figure c ﻿$\quad\quad$﻿ d) Figure d ﻿$\quad\quad$﻿ e) Figure e

##### Problem 5

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

a) $\text{Translate by the directed line segment } AE \text{, which will take } B \text{ to a point } B' \text{. Then rotate with center } E \text{ } \newline \text{ by angle } B'EF \text{. Finally, dilate with center } E \text{ by scale factor } \frac{5}{2} \text{.}$b) $\text{Translate by the directed line segment } AE \text{, which will take } B \text{ to a point } B' \text{. Then rotate with center } E \text{ } \newline \text{ by angle } B'EF \text{. Finally, dilate with center } E \text{ by scale factor } \frac{2}{5} \text{.}$c) $\text{Dilate using center } E \text{ by scale factor } \frac{2}{5} \text{.}$d) $\text{Dilate using center } E \text{ by scale factor } \frac{5}{2} \text{.}$
##### Problem 6

6) Triangle ﻿$DEF$﻿ is formed by connecting the midpoints of the sides of triangle ﻿$ABC$﻿. What is the perimeter of triangle ﻿$ABC$﻿?

##### Problem 7

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

a) $\text{Parallelogram}$b) $\text{Square}$c) $\text{Trapezoid}$d) $\text{Isosceles trapezoid}$
##### Problem 8

8) Triangles ﻿$FAD$﻿ and ﻿$DCE$﻿ are each translations of triangle ﻿$ABC$﻿. Explain why angle ﻿$CAD$﻿ has the same same measure as angle ﻿$ACB$﻿.