Question

how are rigid transformations used to justify the sas congruence theorem?
to justify the sas congruence theorem
sample response: rigid transformations preserve segment lengths and angle measures. if you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. to prove sas, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the sas congruence theorem.
what did you include in your response? check all that apply
☐ rigid transformations preserve segment lengths and angle measures
☐ a rigid transformation, or a combination of rigid transformations, will produce congruent figures

Explanation:

1. For the first option: The sample response starts by stating that rigid transformations preserve segment lengths and angle measures, so this should be included.
2. For the second option: The sample response says that if you can find a rigid transformation or combination to map one triangle onto the other, they are congruent (meaning rigid transformations produce congruent figures), so this should be included.

Answer:

• $\boldsymbol{\checkmark}$ Rigid transformations preserve segment lengths and angle measures
• $\boldsymbol{\checkmark}$ A rigid transformation, or a combination of rigid transformations, will produce congruent figures