Question
Triangle is reflected across the -axis to produce triangle . Which segment
on is congruent to the segment ?
on is congruent to the segment ?
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GPT-4o mini
When a triangle is reflected across the y-axis, the x-coordinates of each vertex of the triangle change sign, while the y-coordinates remain the same.
Let's denote the original triangle as triangle \( ABC \) and the reflection of triangle \( ABC \) across the y-axis as triangle \( A'B'C' \).
If segment \( AB \) from triangle \( ABC \) is reflected, the corresponding segment in triangle \( A'B'C' \) will be segment \( A'B' \). Since reflection across the y-axis preserves lengths and angles, segment \( A'B' \) will be congruent to segment \( AB \).
Thus, the segment on triangle \( A'B'C' \) that is congruent to the segment \( AB \) from triangle \( ABC \) is segment \( A'B' \).
Let's denote the original triangle as triangle \( ABC \) and the reflection of triangle \( ABC \) across the y-axis as triangle \( A'B'C' \).
If segment \( AB \) from triangle \( ABC \) is reflected, the corresponding segment in triangle \( A'B'C' \) will be segment \( A'B' \). Since reflection across the y-axis preserves lengths and angles, segment \( A'B' \) will be congruent to segment \( AB \).
Thus, the segment on triangle \( A'B'C' \) that is congruent to the segment \( AB \) from triangle \( ABC \) is segment \( A'B' \).
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