G.6.1.3 Congruent by Coordinates

Calculate the length of each side and the measure of each angle in triangles ABC and DEF.

The triangles are congruent. How do you know this is true?

Because the triangles are congruent, there is a sequence of rigid motions that takes one to the other. Use the applet below to perform the sequence of rigid motions that takes triangle ABC to trianlge DEF and then list them below. Use the sentence frames below: (as needed)

  • Translate (object) by the directed line segment from point ( , ) to point ( , )
  • Reflect the image of (object) over the line ____
  • Rotate the image of (object) ___ degrees clockwise/counterclockwise about center ( , )

Do you need to show that every pair of sides and every pair of angles is congruent to prove the triangles are congruent?