Section B Section B Checkpoint

Problem 1

Here is a line segment CDCD with midpoint MM.

  1. Rotate segment CDCD 90∘90^\circ clockwise around point MM, and label the image as FGFG.
  2. Rotate segment CDCD 180∘180^\circ around point EE and label the new segment HJHJ. 
  3. Which segment is parallel to segment CDCD?
Show Solution
Solution

  1. See image
  2. See image
  3. HJHJ is parallel to CDCD
Show Sample Response
Sample Response

  1. See image
  2. See image
  3. HJHJ is parallel to CDCD

Problem 2

Triangle EDCEDC is the image of triangle ABCABC after a rigid transformation.

  1. Describe a rigid transformation that takes ABCABC to EDCEDC.
  2. Name 2 angles that have the same measure and explain how you know.
  3. Name 2 side lengths that must be the same and explain how you know.
Show Solution
Solution

Sample responses:

  1. Rotate triangle ABCABC 180∘180^\circ around point CC.
  2. Angle AA is the same as angle EE, or angle BB is the same as angle DD, or angle ACBACB is the same as angle ECDECD; since triangle EDCEDC is the image of triangle ABCABC after a rigid transformation, the corresponding angles are the same measure.
  3. ABAB is the same length as EDED, or BCBC is the same length as DCDC, or ACAC is the same length as ECEC; since triangle EDCEDC is the image of triangle ABCABC after a rigid transformation, the corresponding side lengths are the same.
Show Sample Response
Sample Response

Sample responses:

  1. Rotate triangle ABCABC 180∘180^\circ around point CC.
  2. Angle AA is the same as angle EE, or angle BB is the same as angle DD, or angle ACBACB is the same as angle ECDECD; since triangle EDCEDC is the image of triangle ABCABC after a rigid transformation, the corresponding angles are the same measure.
  3. ABAB is the same length as EDED, or BCBC is the same length as DCDC, or ACAC is the same length as ECEC; since triangle EDCEDC is the image of triangle ABCABC after a rigid transformation, the corresponding side lengths are the same.