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Common Core Standard HSG-CO.A.4 Questions

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

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Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4
Quadrilateral ABCD is reflected over line l. Its image is A'B'C'D'. What can be said about the relationship between line segment ¯AA′ and line l? Choose all correct answers.
  1. l and ¯AA′ are perpendicular.
  2. l and ¯AA′ are parallel.
  3. l and ¯AA′ do not intersect.
  4. l bisects ¯AA′.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4
Given quadrilateral ABCD, you rotate it x degrees counterclockwise about the point O, resulting in the transformed image, A'B'C'D'. Which of the following are true? Choose all correct answers.
  1. ¯AO⊥¯A′O
  2. m∠AOA′=180°-x°
  3. ¯AO≅¯A′O
  4. m∠AOA′=x°
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4
Triangle ABC is translated 7 units right and 3 units up. The translated image is A'B'C' (not shown). Ellen believes that quadrilateral B'BCC' is a parallelogram and gives the following reasoning why. She knows that because rigid transformations do not change the size of a line segment, that ¯BC≅¯C′B′. Also, ¯BB′≅¯CC′ since line segments formed by corresponding points of translated images are congruent. James disagrees with her and says that she has not shown quadrilateral B'BCC' is a parallelogram. Who is correct and why?
Obtuse Triangle ABC v2
  1. Ellen is correct. Her statements are correct and sufficient to conclude that B'BCC' is a parallelogram.
  2. James is correct. Although Ellen's statements are correct, they are not sufficient to conclude that B'BCC' is a parallelogram.
  3. James is correct. Ellen's reasoning as to why ¯BB′≅¯CC′ is not incorrect.
  4. James is correct. There are other ways to prove B'BCC' is a parallelogram.

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