Working with Rigid Transformations

ID: lutoh-nalot
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Working with Rigid Transformations

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Problem 1

1) Quadrilateral ABCDABCD is congruent to quadrilateral ABCDA'B'C'D'. Describe a sequence of rigid motions that takes AA to AA', BB to BB', CC to CC', and DD to DD'.

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Problem 2

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

a) Rotation of 180180^{\circ} around AA\quadb) Rotation of 180180^{\circ} around BB \quadc) Rotation of 180180^{\circ} around the midpoint of segment ABAB

d) Reflection across the line ABAB \quade) Reflection across the perpendicular bisector of segment ABAB

f) Translation by the directed line segment ABAB \quad g) Translation by the directed line segment BABA

Problem 3

3) Triangle ABCABC is congruent to triangle ABCA'B'C'. Describe a sequence of rigid motions that takes AA to AA', BB to BB', and CC to CC'.

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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

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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 BADCBADC, AB=ADAB = AD and BC=DCBC = DC. The line ACAC is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why angles ACBACB and ACDACD have the same measure.

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Problem 8

8) Which of these constructions would construct a line of reflection that takes the point AA to point BB?

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

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

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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.