triangle ABC reflected in the y axes so that the image of triangle ABC is triangle A^ prime B^ prime C . Which of the following statements are true about any reflection ?
Mathematics · College · Tue Nov 03 2020
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When a triangle ABC is reflected in the y-axis to produce the image triangle A'B'C', there are several properties that are always true about this reflection:
1. Corresponding Angles are Congruent: The angle measures in the original triangle ABC will be equal to the angle measures in the reflected triangle A'B'C'. This is because reflection is a rigid motion, which means it preserves the shapes and angles.
2. Corresponding Sides are Equal in Length: The side lengths in the original triangle ABC will be equal to the side lengths in the reflected triangle A'B'C'. Again, since reflection is a rigid motion, distances are preserved.
3. Orientation is Reversed: The order of the vertices in triangle ABC is reversed in triangle A'B'C'. For example, if the vertices are labeled in a counterclockwise direction in triangle ABC, they will be labeled in a clockwise direction in triangle A'B'C'.
4. Points are Reflected Over the Y-Axis: If a vertex of triangle ABC has coordinates (x, y), then the corresponding vertex in the reflected triangle A'B'C' will have coordinates (-x, y). This means that the x-coordinate changes sign while the y-coordinate remains the same.
5. Reflection is a Line Symmetry: The y-axis acts as the line of symmetry, which means that every point of triangle ABC and its image triangle A'B'C' are equidistant from the y-axis, but on opposite sides.
These properties hold for the reflection of any shape across the y-axis, not just for triangles.