Question
△ABC is congruent to △GHE . Describe a sequence of transformations from △ABC to △GHE that proves their congruence. (2 points)
Bro just go to the lesson 8 (Congruent Figures) and go to page 9 out of 13, it gives you the answer right off the bat (Just use it in your own words, K) :)
Bro just go to the lesson 8 (Congruent Figures) and go to page 9 out of 13, it gives you the answer right off the bat (Just use it in your own words, K) :)
Answers
Answered by
GPT-4o mini
To show that triangle \( \triangle ABC \) is congruent to triangle \( \triangle GHE \), we can use a sequence of transformations:
1. **Translation**: First, we can translate triangle \( \triangle ABC \) so that point \( A \) aligns with point \( G \). This shifts the entire triangle to a new position without altering its shape or size.
2. **Rotation**: Next, we can rotate the translated triangle \( \triangle ABC \) around point \( G \) (or its new position) so that side \( AB \) matches up with side \( GH \). This rotation aligns one corresponding side of the two triangles.
3. **Reflection (if needed)**: If necessary, we can reflect the triangle across a line (like the line through points \( G \) and \( H \)) to ensure the remaining corresponding points \( B \) and \( C \) align with \( H \) and \( E \).
Through this sequence of transformations—translation, rotation, and possibly reflection—we can demonstrate that \( \triangle ABC \) is congruent to \( \triangle GHE \) because all corresponding sides and angles will match up perfectly.
1. **Translation**: First, we can translate triangle \( \triangle ABC \) so that point \( A \) aligns with point \( G \). This shifts the entire triangle to a new position without altering its shape or size.
2. **Rotation**: Next, we can rotate the translated triangle \( \triangle ABC \) around point \( G \) (or its new position) so that side \( AB \) matches up with side \( GH \). This rotation aligns one corresponding side of the two triangles.
3. **Reflection (if needed)**: If necessary, we can reflect the triangle across a line (like the line through points \( G \) and \( H \)) to ensure the remaining corresponding points \( B \) and \( C \) align with \( H \) and \( E \).
Through this sequence of transformations—translation, rotation, and possibly reflection—we can demonstrate that \( \triangle ABC \) is congruent to \( \triangle GHE \) because all corresponding sides and angles will match up perfectly.