1. Check it out! 1.4.2: Defining Congruence in Terms of Rigid Motions
1.4.2: Defining Congruence in Terms of Rigid Motions

2. August’s grandparents bought her family a new flat-screen TV as a housewarming present. However, the new TV is too wide to fit into the piece of furniture that was holding the old TV. August proposed that they rotate the TV 30º counterclockwise about point R to slide the TV into the cabinet. She drew a scaled diagram that shows the top view of the TV and TV cabinet. Use the diagram on the next slide to solve the problems that follow.
Common Core Georgia Performance Standard: MCC9–12.G.CO.6
1.4.2: Defining Congruence in Terms of Rigid Motions

3. Rotate the TV counterclockwise 30º about point R.
Will the rotated TV fit into the cabinet? Justify your answer.
1.4.2: Defining Congruence in Terms of Rigid Motions

4. Rotate the TV counterclockwise 30º about point R.
1.4.2: Defining Congruence in Terms of Rigid Motions

5. Will the rotated TV fit into the cabinet? Justify your answer.
Since the drawing is
a scaled representation
of the actual figures,
use the units provided
on the grid and draw
the diagonal of the
TV cabinet. Use the
Pythagorean Theorem
to calculate the length
of the diagonal.
1.4.2: Defining Congruence in Terms of Rigid Motions

6. 42 + 72 = d 2, for which d is the diagonal 16 + 49 = d 2 65 = d 2
Since distance can only be positive,
Count the length of the TV.
The TV is 8 units. Therefore, the TV should fit into the cabinet on the diagonal. However, the fit will be tight.
Connection to the Lesson
• Students will be introduced to the terms and concepts of transformations as rigid and non-rigid motions.
• Students will use the Pythagorean Theorem to determine if rigid motions have occurred.
1.4.2: Defining Congruence in Terms of Rigid Motions