Question

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

answerSample 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.

Answer 1

The lengths and angles of a shape's sides and angles are unaltered when it undergoes rigid transformation.

The SAS congruence theorem is justified by rigid transformation by maintaining the side lengths and angle after transformation.

Assume two sides of a triangle are:

$\begin{aligned}A B &=5 \mathrm{~cm} \\B C &=4 \mathrm{~cm}\end{aligned}$

And the angle between the two sides is:

$\theta=90^{\circ}$

The appropriate side lengths and angle for a rigid transformation of the triangle (such as translation, rotation, or reflection) would be:

$\begin{aligned}&A^{\prime} B^{\prime}=5 \mathrm{~cm} \\&B^{\prime} C^{\prime}=4 \mathrm{~cm} \\&\theta=90^{\circ}\end{aligned}$

Keep in mind that the sides and angles remain constant.

The SAS congruence theorem is therefore justified by stiff transformation by maintaining the side lengths and angle after translation.

The stiff transformation is illustrated in the attachment.

A stiff transformation in mathematics is a geometric transformation of a Euclidean space that keeps the Euclidean distance between each pair of points. Rotations, translations, reflections, or any combination of these are examples of stiff transformations.

Read more about rigid transformations at:

brainly.com/question/1761538

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