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Tenth Grade (Grade 10) Symmetry and Transformations Questions

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Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2
How is the transformation between the two graphs best described?
Graph - Linear Function y=1/2x Graph - Linear Function y=2x
  1. translation
  2. rotation
  3. reflection
  4. reflection and rotation
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2
How is the transformation between the two graphs best described?
Graph - Linear Function y=-xGraph - Linear Function y=x
  1. Translation
  2. Rotation
  3. Reflection
  4. Reflection or rotation
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    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 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if ΔABC≅ΔADC?
Diamond ABCD
  1. Translate triangle ABC down by vertical distance between ¯AC and point B.
  2. Reflect triangle ABC over the line containing ¯AC.
  3. Rotate triangle ABC 180° around midpoint of ¯AC.
  4. Translate triangle ABC down by half the vertical length between ¯AC and point B, and then rotate it 180° about its centroid.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2
A translation is best described as
  1. sliding.
  2. flipping.
  3. spinning.
  4. warping.
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   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.7
Which of the following transformations would show if ΔABD≅ΔCDB?
Parallelogram ABCD v3
  1. Translate triangle ABD right by the length of ¯AD.
  2. Reflect triangle ABD over the line containing ¯BD.
  3. Rotate triangle ABD 180° about the midpoint of ¯BD.
  4. Reflect triangle ABD over the line containing ¯BD then translate 14→BD.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8
You are given two triangles, ABC and DEF. If you know that ¯AB≅¯DE,¯BC≅¯EF and ∠B≅∠E. Which of the following could be true? Select all that apply.
  1. There is not enough information to make any conclusions.
  2. A dilation and translation map triangle ABC onto triangle DEF.
  3. A translation and rotation map triangle ABC onto triangle DEF.
  4. A rotation and reflection map triangle ABC onto triangle DEF.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.6
Obtuse Triangle ABC v2       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 10 Symmetry and Transformations CCSS: HSG-CO.B.7
In the diagram below, Shannon knows that ∠BAC≅∠BCA≅∠DFE≅∠DEF and that ¯BE || ¯AD. To prove that the two triangles, ABC and FDE, are congruent, she proposes the following sequence of transformations to map ΔABC onto ΔFDE: translate triangle ABC up by the length of the vertical distance between line segments ¯BE and ¯AD, then translate triangle ABC right by the length of ¯BF plus half the length of ¯FE, then reflect it over the line containing points B and E. Is this correct and why?
Parallelogram ABCDEF v1
  1. No, the sequence of transformations is incorrect.
  2. No, you have to use a triangle congruence theorem.
  3. Yes, if the triangles map exactly onto each other (corresponding sides and angles are congruent), this proves ΔABC≅ΔFDE.
  4. It is unnecessary, since we can determine that ∠ABC≅∠FDE, and so already know the triangles are congruent.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if ΔABF≅ΔECD?
Trapezoid ABCDEF
  1. Translate triangle ABF right by the length of ¯FD.
  2. Reflect triangle ABF about the line joining the midpoints of ¯BC and ¯FD.
  3. Rotate triangle ABF 180° about the midpoint of the line joining the midpoints of ¯BC and ¯FD.
  4. Translate triangle ABF right by the length of ¯FE.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
In the regular hexagon pictured, the center is M (not pictured). Which of the following transformations show that ΔBMC≅ΔDME? Choose all correct answers.
Hexagon ABCDEF
  1. Reflect triangle BMC over the line joining the midpoints of ¯CD and ¯AF.
  2. Rotate triangle BMC 120° counterclockwise about point M.
  3. Translate triangle BMC right the length of ¯CD, then rotate it 120° clockwise about its centroid.
  4. Rotate triangle BMC 60° clockwise about point M, then reflect it over the line passing through C and F.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

This question is a part of a group with common instructions. View group »

From parts A and B, which of the following triangle congruence theorems could be used to show ΔABC≅ΔLMN?
  1. SAS
  2. ASA
  3. SSS
  4. AAS
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2
Señor Domínguez made the following conjecture: "Any transformation of triangle LMN on a coordinate grid results in a congruent image."

Which transformation represents a counterexample to this statement?
  1. Triangle LMN is relfected over the line y = -5.
  2. Triangle LMN is translated 4 units left and 2 units down.
  3. Triangle LMN is rotated 90° counterclockwise about the origin.
  4. Triangle LMN is dilated with a scale factor of 2 about the origin.
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