Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Figures A B C D and E F G H, with different orientations. Segments A B and E F each have 1 tick mark, B C and F G each have 2 tick marks, C D and G H each have three tick marks. Angles A B C and E F G each have 1 tick mark, Angles B C D and F G H each have two tick marks.
If two figures are congruent, then there is a sequence of rigid motions that takes one figure onto the other. We can use this fact to prove that any point is congruent to another point. We can also prove segments of the same length are congruent. Finally, we can put together arguments to prove entire figures are congruent.
These statements prove is congruent to .
Segments and are the same length, so they are congruent. Therefore, there is a rigid motion that takes to . Apply that rigid motion to figure .
If necessary, reflect the image of figure across to be sure the image of , which we will call , is on the same side of as .
must be on ray since both and are on the same side of and make the same angle with it at .
Since points and are the same distance along the same ray from , they have to be in the same place.
Therefore, figure is congruent to figure .