Question

Make a conjecture. How are rigid transformations and congruent figures related? Check all that apply.

Rigid transformations preserve segment lengths and angle measures.
Rigid transformations produce congruent figures.
If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will map one onto the other.

Answer 1

All of the answers are correct, meaning that A,B, and all true.

Answer 2

Rigid transformations preserve segment lengths and angle measures.

Rigid transformations produce congruent figures.

If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will map one onto the other.

Explanation:

• A rigid transformation or an isometry is a transformation that does not change the sides and angle of plane figures.

• Reflection in the plane, translations and rotation or a combination of them produce images that are congruent to the preimage.

• This implies that, two figures are congruent if and only if a rigid transformation or a combination of one or more rigid transformations will map one plane figure onto another.

• Therefore all the given options are true.