Reasoning about Similarity with Transformations

ID: lovak-sahil
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Reasoning about Similarity with Transformations

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

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

A template for answering this question. Ask your instructor for an alternative.
Problem 2

2) Write 2 different sequences of transformations that would show that triangles ABCABC and AEDAED are similar. The length of ACAC is 6 units.

A template for answering this question. Ask your instructor for an alternative.
Problem 3

3) What is the definition of similarity?

Problem 4

4) Select all figures which are similar to Parallelogram PP. 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

A template for answering this question. Ask your instructor for an alternative.
Problem 5

5) Find a sequence of rigid transformations and dilations that takes square ABCDABCD to square EFGHEFGH.

A template for answering this question. Ask your instructor for an alternative.
a) Translate by the directed line segment AE, which will take B to a point B. Then rotate with center E  by angle BEF. Finally, dilate with center E by scale factor 52.\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) Translate by the directed line segment AE, which will take B to a point B. Then rotate with center E  by angle BEF. Finally, dilate with center E by scale factor 25.\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) Dilate using center E by scale factor 25.\text{Dilate using center } E \text{ by scale factor } \frac{2}{5} \text{.}d) Dilate using center E by scale factor 52.\text{Dilate using center } E \text{ by scale factor } \frac{5}{2} \text{.}
Problem 6

6) Triangle DEFDEF is formed by connecting the midpoints of the sides of triangle ABCABC. What is the perimeter of triangle ABCABC?

A template for answering this question. Ask your instructor for an alternative.
Problem 7

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

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

8) Triangles FADFAD and DCEDCE are each translations of triangle ABCABC. Explain why angle CADCAD has the same same measure as angle ACBACB.

A template for answering this question. Ask your instructor for an alternative.