To show that △ABC and △EFD are congruent using rigid transformations, we need to find a sequence of transformations such that the corresponding vertices of the two triangles overlap perfectly.
1. First, we can perform a translation. We can move triangle △EFD so that point E coincides with point C. This translation ensures that the corresponding sides are parallel and have the same length.
2. Next, we can perform a rotation. We rotate triangle △EFD around point E so that side ED aligns with side BC. This rotation ensures that the corresponding angles at E and C are congruent.
3. Finally, we can perform another translation. We move triangle △EFD so that point F coincides with point B. This translation ensures that the corresponding sides are parallel and have the same length.
By carefully performing these transformations, we can ensure that all three pairs of corresponding vertices, A and D, B and E, and C and F, overlap perfectly.
This sequence illustrates the SAS Congruence Theorem. SAS stands for Side-Angle-Side, which states that if two triangles have two pairs of corresponding sides that are congruent, and the included angle between these sides is also congruent, then the triangles are congruent.
In our case, the sequence of transformations ensures that side AB is congruent to side DE, side BC is congruent to side EF, and angle ABC is congruent to angle DEF. Therefore, by the SAS Congruence Theorem, we can conclude that △ABC is congruent to △EFD.
Describe a sequence of rigid transformations that could be used to show that △ABC≅△EFD . Be sure to explain how you know that each pair of corresponding vertices will overlap perfectly. Then, explain why this sequence illustrates the SAS Congruence Theorem.
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