Working with Rigid Transformations

ID: lutoh-nalot
Illustrative Math
Subject: Geometry

Working with Rigid Transformations

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Problem 1

1) Quadrilateral ﻿$ABCD$﻿ is congruent to quadrilateral ﻿$A'B'C'D'$﻿. Describe a sequence of rigid motions that takes ﻿$A$﻿ to ﻿$A'$﻿, ﻿$B$﻿ to ﻿$B'$﻿, ﻿$C$﻿ to ﻿$C'$﻿, and ﻿$D$﻿ to ﻿$D'$﻿.

Problem 2

2) Select all transformations that must take any point ﻿$A$﻿ to any point ﻿$B$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) Rotation of ﻿$180^{\circ}$﻿ around ﻿$A$﻿﻿$\quad$﻿b) Rotation of ﻿$180^{\circ}$﻿ around ﻿$B$﻿ ﻿$\quad$﻿c) Rotation of ﻿$180^{\circ}$﻿ around the midpoint of segment ﻿$AB$﻿

d) Reflection across the line ﻿$AB$﻿ ﻿$\quad$﻿e) Reflection across the perpendicular bisector of segment ﻿$AB$﻿

f) Translation by the directed line segment ﻿$AB$﻿ ﻿$\quad$﻿ g) Translation by the directed line segment ﻿$BA$﻿

Problem 3

3) Triangle ﻿$ABC$﻿ is congruent to triangle ﻿$A'B'C'$﻿. Describe a sequence of rigid motions that takes ﻿$A$﻿ to ﻿$A'$﻿, ﻿$B$﻿ to ﻿$B'$﻿, and ﻿$C$﻿ to ﻿$C'$﻿.

Problem 4

4) A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the triangle have the same length. ﻿$\quad\quad$﻿ b) All angles of the triangle have the same measure.

c) All rotations take one half of the triangle to the other half of the triangle. ﻿$\quad\quad$﻿ d) It is a right triangle.

e) None of the sides of the triangle have the same length. ﻿$\quad\quad$﻿ f) None of the angles of the triangle have the same measure.

Problem 5

5) Select all the angles of rotation that produce symmetry for this flower. Write each corresponding letter in the answer box and separate letters with commas.

a) 30 ﻿$\quad\quad$﻿ b) 45 ﻿$\quad\quad$﻿ c) 60 ﻿$\quad\quad$﻿ d) 90 ﻿$\quad\quad$﻿ e) 120 ﻿$\quad\quad$﻿ f) 135 ﻿$\quad\quad$﻿ g) 180

Problem 6

6) A right triangle has a line of symmetry. Select all conclusions that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the triangle have the same length. ﻿$\quad\quad$﻿ b) All angles of the triangle have the same measure.

c) Two sides of the triangle have the same length.﻿$\quad\quad$﻿ d) Two angles of the triangle have the same measure.

e) No sides of the triangle have the same length. ﻿$\quad\quad$﻿ f) No angles of the triangle have the same measure.

Problem 7

7) In quadrilateral ﻿$BADC$﻿, ﻿$AB = AD$﻿ and ﻿$BC = DC$﻿. The line ﻿$AC$﻿ is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why angles ﻿$ACB$﻿ and ﻿$ACD$﻿ have the same measure.

Problem 8

8) Which of these constructions would construct a line of reflection that takes the point ﻿$A$﻿ to point ﻿$B$﻿?

a) $\text{Construct the midpoint of segment } AB \text{. }$b) $\text{Construct the perpendicular bisector of segment } AB \text{. }$c) $\text{Construct a line tangent to circle } A \text{ with radius } AB \text{. }$d) $\text{Construct a vertical line passing through point } A \text{ and a horizontal line passing through point } B \text{.}$
Problem 9

Here is triangle ﻿$POG$﻿ followed by images of four rotations of ﻿$POG$﻿. Match each description below with one of the images. Write the number of the corresponding image in the answer box.

9) Rotate 300 degrees clockwise around O.

10) Rotate 60 degrees clockwise around O.

11) Rotate 60 degrees clockwise around P.

12) Rotate 240 degrees counterclockwise around O.