Describe a sequence of rigid transformations that could be used to show that △ABC≅△DEF . Explain how you know each transformation will result in a congruent figure. Then, explain how this sequence of rigid transformations illustrates the ASA Congruence Theorem. (4 points)
To show that △ABC is congruent to △DEF, we can use a sequence of rigid transformations.
1. Translation: We can translate △ABC to move any of its vertices to the corresponding vertex of △DEF. This will result in a congruent figure because a translation preserves the shape and size of the original triangle.
2. Rotation: After the translation, we can rotate the translated triangle △ABC to align its sides and angles with the corresponding sides and angles of △DEF. This rotation will also result in a congruent figure because a rotation preserves the shape and size of the original triangle.
3. Reflection: Finally, we can reflect the rotated triangle over a line to further align it with △DEF. This reflection will also result in a congruent figure because a reflection preserves the shape and size of the original triangle.
This sequence of rigid transformations illustrates the ASA Congruence Theorem because we are showing that two triangles are congruent by identifying a pair of equal angles, a pair of equal sides, and the included side. In this case, the translation aligns the corresponding vertices, the rotation aligns the corresponding sides and angles, and the reflection further aligns the triangles to make them congruent. Therefore, the ASA Congruence Theorem is illustrated by this sequence of transformations.