Latex: \triangle ABC △
A
B
C
was transformed using two rigid transformations.

a. Compare all of the corresponding parts (angles and sides) of the image and preimage. Describe the results.

b. Explain why the results are true.

When two triangles are congruent to each other, each triangle has six parts (three angles and three sides) that are congruent to those six parts of the other triangle. This can be proven using rigid transformations. But suppose you don't know the rigid transformations that map one triangle to another.

a. How can you prove the two triangles are congruent without using rigid transformations?

b. Will you need to show that all of the parts of one triangle are congruent to all of the parts of the other triangle to prove they are congruent? Explain.