When a triangle is reflected across a line, several properties are preserved between the original triangle and its image. The following properties remain unchanged:
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Congruence: The original triangle and its reflected image are congruent; this means all corresponding sides and angles are equal.
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Angle Measures: The measures of the angles in the original triangle are preserved. Therefore, the corresponding angles in the image triangle are equal to those in the original triangle.
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Side Lengths: The lengths of the sides in the original triangle are preserved. The corresponding sides in the reflected image are equal in length to those in the original triangle.
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Collinearity of Points: If three points are collinear in the original triangle, their reflected points will also be collinear.
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Betweenness: The relative positions of points on the triangle are preserved. If point B is between points A and C in the original triangle, the reflection will keep this order.
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Area: The area of the triangle remains the same in both the original and the reflected image, since the shape does not change.
In summary, reflection preserves congruence, angle measures, side lengths, collinearity, betweenness, and area. However, the orientation of the triangle is not preserved—this means that if the original triangle is oriented in a certain way, the reflected triangle will be a mirror image with opposite orientation.
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