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Common Core Standard HSG-CO.B.6 Questions

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

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Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.6
What transformations to the first image would show that these two figures are congruent? Choose all that apply.

T Q2 Vertical Inverted [math] \ \ [/math] T Q4 Vertical
  1. They are not congruent.
  2. 270° counter-clockwise rotation about the origin.
  3. Horizontal translation by +5 units, reflection over the x-axis.
  4. Dilate by 1.5, reflect over the line y = x.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.6
Are the shapes congruent? If so, what transformations take the first image and transform it to the second image?

2x6 Q2 Horizontal [math] \ \ \ [/math] 2x6 Q4 Horizontal
  1. No, they are not congruent.
  2. Yes, a 180° rotation about the origin.
  3. Yes, a reflection about the y-axis and then a translation of 2 units to the right.
  4. Yes, a vertical translation of -4 units and then a horizontal translation of -2 units.
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
Choose all the correct ways that the first image can be transformed to show that it is congruent to the second image.

T Q2 Vertical [math] \ \ \ [/math] T Q4 Horizontal Inverted
  1. 90° counter-clockwise rotation about the origin, reflection over the y-axis.
  2. 90° clockwise rotation about the origin, reflection over the x-axis.
  3. Reflection about the line y = x.
  4. 180° rotation about the origin, 90° rotation counter-clockwise about the point (2.5, -2.5).
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.6
Obtuse Triangle ABC v2 [math] \ \ \ \ \ \ [/math] Scalene Triangle v3

In trying to determine if the two triangle are congruent, which transformations would allow you to superimpose triangle ABC on the other triangle? Choose all correct answers.
  1. Through a series of rotations and reflections.
  2. Through a series of translations and dilations.
  3. Through a series of translations.
  4. Through a series of rotations (about different points).
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
Which of these transformations is not rigid?
  1. Translate 4 to the left and rotate [math]180 deg[/math]
  2. Reflect across the [math]x[/math]-axis and translate down by 6
  3. Rotate [math]90 deg[/math] clockwise and dilate by a factor of 2
  4. Translate down 2, reflect across the [math]y[/math]-axis, and rotate [math]180 deg[/math]
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
Which of these transformations will create a shape which is not congruent with the original?
  1. Rotate [math]90 deg[/math] clockwise and dilate by a factor of 2
  2. Translate 4 to the left and rotate [math]180 deg[/math]
  3. Translate down 2, reflect across the [math]y[/math] axis, and rotate [math]180 deg[/math]
  4. Reflect across the [math]x[/math] axis and translate down by 6
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
A pentagon is translated down 10, dilated 0.8, and reflected across the [math]x[/math]-axis.
  1. The transformation is non-rigid, the shape changes size.
  2. The transformation is rigid, the shape is congruent.
  3. The transformation is non-rigid, the shape does not change size.
  4. The transformation is rigid, it only translates.
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
Which of the following illustrates a non-rigid transformation?
  1. Shooting a hockey puck.
  2. Growing a plant.
  3. Bouncing a ball.
  4. Jumping on a trampoline.
Grade 11 Symmetry and Transformations CCSS: HSG-CO.B.6
Which of the following illustrates a rigid transformation?
  1. Inflating a balloon
  2. Building a house
  3. Driving a car
  4. Filling a water tank

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