Sequence of Rigid Transformations:
1. Translation: Move triangle EFD (the second triangle) so that point E coincides with point A in triangle ABC (the first triangle).
Explanation: We can slide triangle EFD horizontally or vertically without changing its shape in order to align point E with point A. This move ensures that the corresponding vertices E and A of both triangles will overlap perfectly.
2. Rotation: Rotate triangle EFD around point E until side EF aligns with side AB.
Explanation: By rotating triangle EFD around point E, we can bring side EF into the same position as side AB. This rotation ensures that the corresponding sides EF and AB of both triangles will overlap perfectly.
3. Translation: Move triangle EFD (the rotated triangle) so that point D coincides with point C in triangle ABC (the first triangle).
Explanation: We can slide triangle EFD horizontally or vertically without changing its shape in order to align point D with point C. This move ensures that the corresponding vertices D and C of both triangles will overlap perfectly.
This sequence of rigid transformations illustrates the SAS Congruence Theorem. According to this theorem, if two triangles have two pairs of corresponding sides that are congruent and the angles between these sides are also congruent, then the triangles are congruent.
In our case, we have shown that side AB is congruent to side EF, side BC is congruent to side FD, and angle BAC is congruent to angle EFD. These are the pairs of corresponding sides and angles that satisfy the SAS Congruence Theorem. Therefore, by performing these rigid transformations, we have proven that triangle ABC is congruent to triangle 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.
explain in tenth grader vocabulary words and use tenth grader heading and punctuation
1 answer