Given Response area, you can show that a sequence of Response area will map one triangle onto the other triangle such that they overlap perfectly. This means that Response area. Therefore, Response area Theorem is true.

Answer 1

It seems like your statement is about a specific topic related to geometry and the concept of mapping one triangle onto another, possibly in the context of transformations or congruence. However, it appears that there are some phrases like "Response area" that might be terminology not commonly used or may be incorrect.

Based on your inquiry, it seems you want to discuss how triangles can be mapped onto each other through transformations such as translations, rotations, or reflections. Here’s a clearer outline of how we might approach this idea:

Triangle Congruence and Transformation

1. Definitions:

   • Two triangles are said to be congruent if one can be transformed into the other using rigid motions: translations, rotations, and reflections.
   • The Response area might refer to the area of a triangle, but it's not clear from your context. We usually discuss congruence in terms of side lengths and angles rather than areas.

2. Mapping Triangles:

   • If we have two triangles, say △ABC and △DEF, we can show that there exists a sequence of transformations (like those mentioned) that can map triangle ABC onto triangle DEF.
   • The transformations can be accomplished in a specific order: first, translate the triangle to an appropriate position, then rotate it to align correctly, and finally reflect if necessary.

3. Overlap:

   • Once the transformations have been applied correctly, the triangles will overlap perfectly, indicating that they are indeed congruent.

4. Area Consideration:

   • If the triangles are congruent, they have the same area. This could be where the mention of "Response area" comes into play. In essence, if triangle ABC maps perfectly onto triangle DEF, then the area calculation will yield the same value for both triangles.

5. Theorem Conclusion:

   • Therefore, we conclude that if two triangles can be shown to overlap perfectly through a series of transformations, they are congruent, confirming that the properties defining congruence (including area) hold true.

Conclusion

If "Response area" pertains to another concept that needs to be clarified, or if you meant to reference a specific theorem such as the Triangle Congruence Theorems (SSS, SAS, ASA, AAS), please provide additional context. Otherwise, the essence of your claim aligns with the principles of triangle congruence and transformation in geometry!