Question

How are rigid transformations used to justify the SAS congruence theorem?

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Answer 1

When a shape is transformed by rigid transformation, the sides lengths and angles remain unchanged.

Rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Assume two sides of a triangle are:

And the angle between the two sides is:

When the triangle is transformed by a rigid transformation (such as translation, rotation or reflection), the corresponding side lengths and angle would be:

Notice that the sides and angles do not change.

Hence, rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Explanation: