Question

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.

Answer 1

thanks

Answer 2

In order to show that △ABC is congruent to △DEF, we can use a sequence of rigid transformations.

1. Translation: We can translate △ABC to a new position where one of its vertices coincides with the corresponding vertex of △DEF. This ensures that the triangles have the same size and shape.

2. Rotation: By rotating △ABC around its coinciding vertex, we can align another pair of corresponding vertices of the triangles. This rotation preserves the shape and size of the triangles.

3. Reflection: Finally, we can reflect △ABC across a line passing through the coinciding vertex. This step aligns the remaining vertices of the triangles.

Each transformation in this sequence preserves both shape and size, which means that △ABC remains congruent to △DEF throughout the entire process.

This sequence of rigid transformations illustrates the ASA (Angle-Side-Angle) Congruence Theorem. By using a translation, rotation, and reflection in that order, we show that the two triangles have corresponding side lengths in the same order and corresponding angles with the same measures. This confirms that △ABC and △DEF are indeed congruent.

Answer 3

You're welcome! If you have any more questions, feel free to ask.