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Common Core Standard HSG-CO.B.8 Questions

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

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Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Would the sequence of transformations that mapped ¯AB onto ¯LM be the same for mapping ¯AC onto ¯LN and ¯BC onto ¯MN?
  1. No.
  2. Only for mapping ¯AC onto ¯LN.
  3. Only for mapping ¯BC onto ¯NM.
  4. Yes.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Because the three sides of ABC can be mapped by the same sequence of rigid transformations to the three sides of triangle LMN, what does this imply and why?
  1. ΔABC≅ΔLMN, since no rotations were used.
  2. ΔABC≅ΔLMN, since rigid transformations preserve size and shape.
  3. The triangles are not necessarily congruent, since we know nothing about the angles.
  4. The triangles are not necessarily congruent, since each side was considered separately.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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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.B.8

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What is the measure of ∠PQR?
  1. 0°
  2. 30°
  3. 90°
  4. 180°
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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What are the coordinates of the transformed points, P', Q', R', if they are rotated 90° clockwise about the origin and then translated 4 units to the left?
  1. (-3, -2), (0, -1), (1, -4)
  2. (-5, 2), (-8, 1), (-9, 4)
  3. (1, 2), (4, 3), (5, 0)
  4. (-6, -1), (-5, -4), (-8, -5)
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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What is the measure of ∠P′Q′R′?
  1. 90°
  2. 180°
  3. 60°
  4. 0°
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Aside from calculating the length of each line segment, what reasoning can be used to conclude that ¯PQ≅¯P′Q′ and ¯QR≅¯Q′R′?
  1. They have similar names.
  2. The points which define them were transformed by the same rigid transformations.
  3. Reflections were not involved in the transformations.
  4. They are specified by Cartesian coordinates.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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We know that ΔPQR≅ΔP′Q′R′, due to the points defining the triangles being transformed by the same sequence of rigid transformations. However, if we did not know the coordinates of these points, and only knew the information of parts A, C, and D, could we still conclude that ΔPQR≅ΔP′Q′R′, and why?
  1. No, there would not be enough information to make this conclusion.
  2. No, because then the two triangles could have been transformed by other transformations.
  3. Yes, because of the SSS theorem.
  4. Yes, because of the SAS theorem.
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.8
You are given two triangles, ABC and GHF, plotted on a set of axes. You know that you can map ¯AB onto ¯GH by a reflection over the x-axis and a rotation of 160° clockwise about the origin. You also know that ∠A≅∠G and ∠B≅∠H. Which of the following statements are true? There may be more than one correct answer.
  1. ΔABC≅ΔGHF
  2. ¯BC can be mapped onto ¯HF by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
  3. ¯AC can be mapped onto ¯GF by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
  4. m∠C=m∠F+160°
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Which of the following sequences of transformations would map ¯AB onto ¯LM, such that point A corresponds with point L and point B with point M?
  1. Reflection over the y-axis, translation of one unit right, reflection over the x-axis.
  2. Reflection over the x-axis, translation 7 units right.
  3. Rotation of 90° about the origin, translation 3 units down.
  4. Reflection over the line y = x, translation 7 units right, translation 4 units down.
Grade 11 Similar and Congruent Figures CCSS: HSG-CO.B.8
If triangle TRS is congruent to triangle TUV, which of the following is true?
  1. STR≅TUV
  2. TRS≅UVT
  3. ¯TR≅¯UV
  4. ∠U≅∠R

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